Masculinity in Shakespeares Macbeth :: GCSE English Literature Coursework

Masculinity in Macbeth Shakespeare   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚     The great masterpiece Macbeth, which is written by William Shakespeare, deals with many different hidden themes. One of the best-hidden themes in Macbeth is manhood. Shakespeare's descriptions of his characters give real descripitions of living beings, not actors upon a stage. His manuscript is able to show the masculinity of men as well of women.   Masculinity is not just for men; some women are just like men in their quest for ambition.   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   In the play Macbeth, it seems that Lady Macbeth is a man trapped in a woman's body. She is filled with greed, envy, and hate, and she will use any person or any thing until she gets what she wants or accomplishes her evil goals. In the play she hides her true feelings and pretends to be a normal lady. However, her evil nature shines through her false face. This just proves that Lady Macbeth is like a rose. A rose is pretty and smells great but if one is not careful the thorns will prick the fingers.   Lady Macbeth appears to lose her sanity the night of Duncun's murder and cannot relate to her feelings or guilty conscience. She admits that "she could kill her only child just as easy (I vii 72-74)". This really means that Lady Macbeth is colder than ice and seems that she lost all preception of right and wrong.   Then she tell her husband " a little water clears of the deed" (II ii 66)". Lady Macbeth thought the killing would, be easy to accomplish, but in fact it was not as easy as she said or thought.   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚      In the play, to die without any fear seems to be the highest accomplishment of one's life. It seems that not fearing death is more important than inventing a great invention that could change the world. When young Siward dies, his father is more worried about how he was killed. Siward wants to know where the wounds on his son were. When Ross tells Siward that his son had marks on the front of his body, his father is proud and brags about his death, "Why then, God's solider be he ( V viii l 46)". Siward father seems to have no grief over his son's death by what he was saying.  Ã‚     Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   Ambition seems to be in all men, and all men strive to fill their need for it.

The Life and Work of Galileo Essay -- Essays Papers

The Life and Work of Galileo Galileo Galilei is considered to be one of the greatest mathematicians of all time. He made life changing discoveries and mystified many with his knowledge. However, not all of his work was accepted well. Galileo challenged the church creating a controversy that will never be forgotten. Galileo Galilei was born in Pisa, Italy February 18, 1564. He was the son of Vincenzo Galilei, a member of a Nobel family, a musician and a mathematician. Galileo, at an early age, developed a great love for mathematics and mechanics. However, his parents urged him to seek medical professions which promised more fortune. Galileo’s love for mathematics turned him away from his parents wishes only to follow his natural talents. Before reaching the age of twenty, Galileo made a great observation of mechanics. He observed a swinging lamp in the cathedral of Pisa which led to his theory of the pendulum and fifty years later led to the construction of an astronomical clock. In 1588, he was given the title of the Archimedes of his time. He also received a position of lecture-ship at the University of Pisa. With this position, he began his research on free-fall and eventually proved that all objects in a vacuum would fall at the same rate of speed. This observation was contradictory to the previous beliefs that the rate of fall of an object was proportional to the object’s mass. The Aristoteleans refuted his findings, however, and remained faithful to their master’s discoveries. By the influence of his friends, he received a position as the chair of mathematics at the University of Pisa. He remained there for eighteen years before returning to the original home of his family in Florence. There he was appointed math... ...mple, in the Bible it says that God created the earth. Science merely attempts to decipher how it was done. Today, the truth about Galileo’s studies has received proper recognition, and it is understood that science is a reflection of reason, and reason a reflection of science. Footnotes 1. The Catholic Encyclopedia. Online. Internet. 25 Sept 1999. 2. see Catholic Encyclopedia 3. Modern History Sourcebook: The Crime of Galileo: Indictment and Abjuration of 1633. Online. Internet. 25 Sept. 1999. 4. see Catholic Encyclopedia Bibliography - Spangenburg, Ray and Diane K. Moser. The History of Science from the Ancient Greeks to the Scientific Revolution. New York, New York: Facts on File, Inc., 1993 - Spangburg, Ray and Diane K. Moser. The History of Science in the Eighteenth Century. New York, New York: Facts on File, Inc., 1993 The Life and Work of Galileo Essay -- Essays Papers The Life and Work of Galileo Galileo Galilei is considered to be one of the greatest mathematicians of all time. He made life changing discoveries and mystified many with his knowledge. However, not all of his work was accepted well. Galileo challenged the church creating a controversy that will never be forgotten. Galileo Galilei was born in Pisa, Italy February 18, 1564. He was the son of Vincenzo Galilei, a member of a Nobel family, a musician and a mathematician. Galileo, at an early age, developed a great love for mathematics and mechanics. However, his parents urged him to seek medical professions which promised more fortune. Galileo’s love for mathematics turned him away from his parents wishes only to follow his natural talents. Before reaching the age of twenty, Galileo made a great observation of mechanics. He observed a swinging lamp in the cathedral of Pisa which led to his theory of the pendulum and fifty years later led to the construction of an astronomical clock. In 1588, he was given the title of the Archimedes of his time. He also received a position of lecture-ship at the University of Pisa. With this position, he began his research on free-fall and eventually proved that all objects in a vacuum would fall at the same rate of speed. This observation was contradictory to the previous beliefs that the rate of fall of an object was proportional to the object’s mass. The Aristoteleans refuted his findings, however, and remained faithful to their master’s discoveries. By the influence of his friends, he received a position as the chair of mathematics at the University of Pisa. He remained there for eighteen years before returning to the original home of his family in Florence. There he was appointed math... ...mple, in the Bible it says that God created the earth. Science merely attempts to decipher how it was done. Today, the truth about Galileo’s studies has received proper recognition, and it is understood that science is a reflection of reason, and reason a reflection of science. Footnotes 1. The Catholic Encyclopedia. Online. Internet. 25 Sept 1999. 2. see Catholic Encyclopedia 3. Modern History Sourcebook: The Crime of Galileo: Indictment and Abjuration of 1633. Online. Internet. 25 Sept. 1999. 4. see Catholic Encyclopedia Bibliography - Spangenburg, Ray and Diane K. Moser. The History of Science from the Ancient Greeks to the Scientific Revolution. New York, New York: Facts on File, Inc., 1993 - Spangburg, Ray and Diane K. Moser. The History of Science in the Eighteenth Century. New York, New York: Facts on File, Inc., 1993

Operation management †London eye case study Essay

â€Å"Quality means consistence conformance to costumer expectations† (Slack, Chambers & Johnston 2010 pg 40) Quality for the London eye could mean designing a structure that provides a bird’s eye view of London. Quality could also mean a high design of their processes, including ensuring that all 32 capsules are cleaned, staff are well trained in health and safety and are always professional at all times. Quality also means the London eye is safe and reliable. Quality also means that the timed admissions booking systems (TABS) is on time. Quality could also mean error free processing for their timed admissions system. Quality means that all parts for the London eye is made to specification and the assembly is made to specifications. Speed objectives: Speed within the operation could mean minimising the time it takes costumers from boarding to disembarking. Speed could also mean minimising the time it takes from designing and planning the London eye to the completion of construction to the London eye. Speed could also mean providing a high throughput rate during the year to cope with passengers demand. Example – The London eye take approximately six million people each year the London eye would have to provide a high throughput rate for the year to manage the demand. â€Å"Speed could mean the immediate stoppage of the London eye if an error is found with the wheel, a good example in March 2008 engineers found a problem, the London eye was immediately stopped and emergency repairs take place†. (Ronca 2002 pg 3) Dependability objectives: â€Å"Dependability means doing things in time for costumers to receive their goods or services†. (Slack, Chambers & Johnston 2010 pg 44) Dependability for the London eye include on time opening hours and closing hours, on time boarding and disembarking , keeping to reasonable queuing times to prevent long queues and increasing the flow of passengers boarding and disembarking and Keeping to TABS time. Flexibility objectives: â€Å"Changing the operation in some way either by changing what the operation does, how the operation is done or when it is being done†. (Slack, Chambers & Johnston 2010 pg 46) Mix flexibility – The London eye main objective is to provide a bird’s eye view of London in the early years, now with mix flexibility the London provides a range of other services including private capsules, wedding partnerships and corporate events. The London eye also provides volume flexibility by providing by changing the opening hours and closing hours during the winter months and summer months. Ensuring more people can avail of their services during the summer months compared to the winter months. Cost objectives: The London eye costs include staff costs construction costs, transportation costs and maintenance costs. The staff costs include staff wages and training, Construction costs include the making of the parts of the London eye, this includes the A-frame legs, hub and spindle, back –stay cables, spoke cables, rim, and insulated capsules. Transportation costs contain transferring each parts of the London eye using barges up the River Thames. Maintenance costs include a safety check on all parts of the eye especially the hydraulic motors, drive systems, safety systems and the backup safety system. Day to day operating costs includes heating, lighting and cleaning of the capsules. (See excel document for breakdown). Overall maintenance costs and construction costs take up most of the London eye. Operating costs especially heating can be reduced by providing a system were the heat in empty capsules can be switched off over a long period of time especially during the winter months because they may expect low passenger demand. E.g – On a cold and wet winter day, the passengers numbers for the London eye will be reduced compared to a summer day. Heating could be turned off at this time. This reduces costs and at the same time increase productivity. Question 2 32 capsules X 25 people = 800 passengers for half can hour. 800 people X 2 = 1600 passengers per hour. Summertime schedule 10am – 9.30pm = 12 hours 1600 passengers X 12 hours = 19,200 passengers for 12 hours/day. 19,200 passengers X 7 days = 134,440 passengers per week. Summer weeks = 24 weeks. Therefore total capacity for the summer is: 134,440 passengers per week X 24 weeks = 3,225,600 passengers Winter Schedule 1600 X 8 hours = 12, 800 passengers for an 8 hours/day 10am – 6pm = 8 hours 12,800 passengers X 7 days = 89,600 passengers per week. Winter weeks = 28 weeks. Therefore total capacity for the winter is: 89,600 passengers per week X 28 weeks = 2,508,800 passengers Total capacity based on the operating schedule of the London eye is: schedule Passengers Winter schedule 2,508,800 Summer schedule 3,225,600 Total operating Capacity 5,734,400 Question 3 There could be a loss of utilisation on the London eye due to variety of issues. Weather conditions The weather conditions can affect the London eye in a number of ways examples – utilisation can be affected in a number of ways. Heavy winds can affect the utilisation of the eye forcing it to stop also heavy snowfall can delay and reduce the amount of rotations the eye can perform or worse snowfall could mean that the London eye will not be operational. Blackouts Blackouts will have a major impact on the London eye. The London eye is powered electrically it needs electricity to rotate and in the event of a blackout, the London eye will be defective meaning it won’t be available to the public. Maintenance Maintenance in the case of the London eye mean checking for problems with the machines and servicing and replacing parts of the machines, maintenance could also mean cleaning the thirty two capsules. This can affect the utilisation of the service. Maintenance would not affect the utilisation if it is carried out after the opening hours of the London eye. Industrial actions Industrial actions in the form of strike can result to a loss in utilisation because without employees operating the London eye it means tourist cannot make use of the service it offers leading to a loss in utilisation. Security threats Although this is very unlikely, security threats especially terrorism threats or bomb blasts can also lead to a loss in utilisation. A bomb blast around the London eye could totally destroy it or cause massive damage making the London eye unrepairable while a terror threats would force the staff to evacuate tourists on the London eye. Health issues Health issues could pose a threat to the utilisation of the eye, If a tourist is being sick or injured or a pregnant woman is in one of the capsules during the rotation and goes into labour. The passengers would need to be rushed to the hospital, passengers won’t be allowed in any capsules until the passengers have been taken of the capsules. Future development. Future development could lead to a loss of utilisation in the future for the London eye if larger buildings are built around the area of the London eye and thus hindering the view of famous buildings around the eye, People won’t find the London eye, causing passengers numbers to fall leading to loss in utilisation. Competition based tourist destinations. This could also lead to a loss in utilisation indirectly. If people find other tourist destinations in London more attractive than the London eye, like the Big Ben or Chessington world of adventures or the globe. This could lead to a loss in passenger’s numbers to a low level for the London eye which creates loss in utilisation. The London eye process. This is relates more on the employees if employees are handling the operations of getting passengers on and off the capsules badly this could lead to sometimes not all capsules being filled, longer queues and a major loss in the utilisation of the London eye. Bibliography 1. Debra Ronca,(2008) ‘How the London eye work’ Available from http://adventure.howstuffworks.com/london-eye2.htm. [Accessed 28 November 2012] 2. Slack, Chambers & Johnston,(2010), Operations Management London Prentice Pearson

Key aspects of legislation Essay

For example: Having a training session in a room only accessible by stairs would discriminate against a person with difficulty walking due to disability or age. Unnecessarily strict dress codes could discriminate against a person who wears a turban, hijab or sari. In most cases, such inadvertent discrimination could be avoided by ensuring that full details of any requirements are obtained at registration. It is vital that the reasonable adjustments required by the student are available right from the start, if possible without the student having to ask for them. This will enable that student to participate at the same level as their peers, without drawing specific attention to their additional requirements. A teacher would also need to be on guard to ensure that no deliberate or accidental discrimination took place between students, such as sexism or racism, even in jest. One way of addressing this is to have the students themselves develop and agree to a code of conduct from the start. Health and Safety at Work Act 1974 This Act is concerned with securing the â€Å"health, safety and welfare of persons at work† (Health and Safety Act 1974) as well as protecting other people in connection with the activities of the person at work (for example, students). Some examples of this might include: Ensuring that electrical equipment is tested and safe before use Ensuring that there are no trailing wires which may cause a trip hazard Ensuring the teaching space is safe and suitable before the students arrive Checking any materials for possible hazards, such as risk of allergic reaction Carrying out and maintaining a risk assessment. Other legislation and codes of conduct to be mindful of include: Child Protection Guidelines – although my area of interest is with teaching adults, it is feasible that I would come into contact with children under 16 professionally Data Protection Act 1998 – I would need to ensure that all personal data held on my students was stored accordingly Freedom of Information Act 2000 – this legislation may apply should I be employed by a public body Copyright, Designs and Patents Act 1988 – for example, the use of photographs downloaded from the internet and used in training materials Specific codes of conduct issued by employers. References www.legislation.gov.uk Last accessed:12th May 2014

History of Trigonometry

Running Head: History of Trigonometry History of Trigonometry Rome Fiedler History of Mathematics 501 University of Akron April 29, 2012 History of Trigonometry: An Introduction Trigonometry is useful in our world. By exploring where these concepts come from provides an understanding in putting this mathematics to use. The term Trigonometry comes from the Greek word trigon, meaning triangle and the Greek word meatria meaning measurement. However it is not native to Greek in origin. The mathematics comes from multiple people over a span of thousands of years and has touched over every major civilization.It is a combination of geometry, and astronomy and has many practical applications over history. Trigonometry is a branch of math first created by 2nd century BC by the Greek mathematician Hipparchus. The history of trigonometry and of trigonometric functions sticks to the general lines of the history of math. Early research of triangles could be found in the 2nd millennium BC, in Egyp tian and Babylonian math. Methodical research of trigonometric functions started in Greek math, and it reached India as part of Greek astronomy.In Indian astronomy, the research of trigonometric functions flourished in the Gupta dynasty, particularly as a result of Aryabhata. Throughout the Middle Ages, the research of trigonometry continued in Islamic math, while it was implemented as a discrete subject in the Latin West beginning in the Renaissance with Regiomontanus. The growth of contemporary trigonometry shifted in the western Age of Enlightenment, starting with 17th-century math and reaching its contemporary type with Leonhard Euler (1748) Etymology The word â€Å"trigonometry† originates from the Greek â€Å"trigonometria†, implying â€Å"triangle measuring†, from triangle + to measure.The name developed from the study of right triangles by applying the relation ships between the measures of its sides and angles to the study of similar triangles (Gullberg , 1996). The word was introduced by Barthoolomus ptiticus in the title of his work Trigonometria sice de solutione triangularumtractus brevis et perspicius†¦ in 1595. The contemporary word â€Å"sine†, is originated from the Latin word sinus, which implied â€Å"bay†, â€Å"bosom† or â€Å"fold†, translation from Arabic word jayb. The Arabic word is in origin of version of Sanskrit jiva â€Å"chord†.Sanskrit jiva in learned used was a synonym of jya â€Å"chord†, primarily the word for â€Å"bow-string†. Sanskrit jiva was taken into Arabic as jiba (Boyer, 1991). This word was then changed into the real Arabic word jayb, implying â€Å"bosom, fold, bay†, either by the Arabs or erroneously of the European translators such as Robert of Chester, who translated jayb into Latin as sinus. In particular Fibonacci's sinus rectus arcus was significant in creating the word sinus. Early Beginnings The origin of the subject has rich di versity. Trigonometry is not the work of one particular person or place but rather a development over time.The primitive Egyptians and Babylonians had known of theorems on the ratios of the sides of analogous triangles for many centuries. However pre-Greek societies were deficient of the concept of an angle measure and as a result, the sides of triangles were analyzed rather, a field that would be better known as â€Å"trilaterometry†(Boyer, 1991). The Babylonian astronomers kept comprehensive records on the rising and setting of stars, the movement of the planets, and the solar and lunar eclipses, all of which needed knowledge with angular distances measured on the celestial sphere.Founded on one explanation of the Plimpton 322 cuneiform tablet, some have even claimed that the primitive Babylonians had a table of secants. There was, on the other hand, much discussion as to whether it is a table of Pythagorean triples, a solution of quadratic equations, or a trigonometric tab le. The Egyptians, in contrast, applied an ancient kind of trigonometry for construction of pyramids and surveying the land in the 2nd millennium BC. The early beginnings of trigonometry ar thought to be the first numerical sequences correlating shadow lengths to time of day.Shadow tables were simple sequences of numbers which applied the shadow of a vertical stick, called a gnomon, is long in the morning and shortens to a minimum at noon. Then becomes longer and longer as the afternoon progresses (Kennedy, 1969). The shadow tables would correlate a particular hour to a particular length and were used as early as 1500 BC by the Egyptians. Similar tables were developed by other civilizations such as the Indians and Greeks. Greek mathematics Shadow tables were the primary development in creation of trigonometry however the Greeks really developed Trigonometry into an ordered science.The Greeks continued as the Babylonians astronomers did and studied the relation between angles and cir cles in lengths of chords to develop their theories on planetary position and motion (Mankiewicz, 2001). [pic] The chord of an angle subtends the arc of the angle. Ancient Greek mathematicians used the chord. Given a circle and an arc on the circle, the chord is the line that subtends the arc. A chord's perpendicular bisector traverses the center of the circle and bisects the angle. One half of the bisected chord is the sine of the bisected angle, that is, [pic] nd consequently the sine function is also known as the â€Å"half-chord†. As a result of this relationship, several trigonometric identities and theorems that are known at present were also known to Greek mathematicians, however in their equivalent chord form. Though there is no trigonometry in the works of Euclid and Archimedes, there are theorems presented in a geometric method that are similar to particular trigonometric laws or rules. Theorems on the lengths of chords are applications of the law of sines. In addit ion Archimedes' theorem on broken chords is similar to rules for sines of sums and differences of angles.From the primitive landmarks of shadow tables and the Greeks’ gain and expansion of astronomical knowledge from the Babylonians, there was a gap in the improvement of trigonometry until the time of Hipparchus. Hipparchus The first trigonometric table was in fact compiled by Hipparchus of, who is known as an as â€Å"the father of trigonometry†(Boyer, 1991). Hipparchus was the first to put into a table the corresponding values of arc and chord for a series of angles. He did this by considering every triangle was inscribed in a circle of fixed radius. Each side of the triangle became a chord, a straight line drawn between two points on a circle.To find the parts of the triangle he needed to find the length of the chord as a function of the central angle. [pic] For Example, in the diagram triangle ACB is? inscribed in circle O. So the sides of the triangle become chord ? AC, chord CB and chord AB. Hipparchus would have sought to? find the length of the chord, AC, as a function of the central? angle. He deduced a trigonometric formula for the? length of a chord sketched from one point on the circumference of? a circle to another (Motz, 1993). This could therefore be used to help understand the positioning of the planets on the sphere.Though it is not known when the methodical use of the 360 ° circle came into math, it is known that the methodical introduction of the 360 ° circle introduced a little after Aristarchus of Samos comprised of On the Sizes and Distances of the Sun and Moon, since he measured an angle a part of a quadrant. It seemed that the systematic used of the 360 ° circle was mainly as a result of Hipparchus and his table of chords. Hipparchus might have taken the idea of that division from Hypsicles who had previously divided the day into 360 parts, a division of the day that might have been recommended by Babylonian astronomy .In primeval astronomy, the zodiac had been divided into twelve â€Å"signs† or thirty-six â€Å"decans†. A recurring cycle of approximately 360 days could have corresponded to the signs and decans of the zodiac by dividing each sign into 30 parts and each decan into 10 parts. It was as a result of the Babylonian sexagesimal numeral system that each degree was divided into 60 minutes and each minute was divided into 60 seconds. Though Hipparchus is attributed as the father of trigonometry all of his work is lost except one but we gain knowledge of his work through Ptolemy. [pic] http://www. ies. co. p/math/java/vector/menela/menela. html Menelaus Menelaus of Alexandria wrote in three books his Sphaerica. In Book I, he created a basis for spherical triangles analogous to the Euclidean basis for plane triangles. He established a theorem that is without Euclidean analogue, that two spherical triangles were similar if corresponding angles are equal, however he did not diff erentiate between congruent and symmetric spherical triangles. Another theorem that he established was that the sum of the angles of a spherical triangle is more than 180 °. Book II of Sphaerica applied spherical geometry to astronomy.In addition Book III contained the â€Å"theorem of Menelaus†(Boyer, 1991). He further gave his well-known â€Å"rule of six quantities†(Needham, 1986). This theorem came to paly a major role in spherical trigonometry and astronomy. It was also believed that Melaus mya have developed a second table of chords based on Hipparchus works, however these were lost (Smith, 1958). Ptolemy Afterwards, Claudius Ptolemy developed upon Hipparchus' Chords in a Circle in his Almagest, or the Mathematical Syntaxis. The Almagest was mainly a work on astronomy, and astronomy relied on trigonometry.The 13 books of the Almagest were the most prominent and important trigonometric work of ancient times. This book was a composition of both astronomy and trig onometry and was derived from the work of Hipparchus and Menelaus. Almagest contains a table of lengths of chords in a circle and a detailed set of instructions on how to construct the table. These instructions contain some of the earliest derivtions of trigonometry. Ptolemy distinguished that Menelaus started by dividing a circle into 360o, and the diameter into 120 parts. He did this because 3 x 120 = 360, using the previous application of 3 for pi.Then each part is divided into sixty parts, each of these again into sixty parts, and so on. This system of parts was based on the Babylonian sexagesimal or base 60-numeration system, which was the only system available at the time for handling fractions (Maor, 1998). This system was based on 60 so that the number of degrees corresponding to the circumference of a circle would be the same as the number of days in a year, which the Babylonians believed to be 360 days (Ball 1960). From Menlaus Ptolemy developed the concept that the sine i s half of a chord.Ptolemy took Menelaus’ construction _ crd  · 2_ and said that the complement angle could be written as _ crd  · (180 o -2_), since 180o was half the circumference of the circle. Since today, cos_ = sin(90 o -_), it can be shown that cos_ = _ crd  · (180 o -2_), using a similar argument as the one shown above (van Brummelen, 2009). From these two expressions, one of the greatest identities known today was created. That is, (_ crd  · 2_) 2 + {_ crd  · (180 o -2_)} 2 = 1 which is exactly sin2_ + cos2_ = 1 (van Brummelen, 2009). [pic]http://nrich. maths. org/6853 [pic] http://en. ikipedia. org/wiki/Ptolemy's_table_of_chords Using his table, Ptolemy believed that one could solve any planar triangle, if given at least one side of the triangle (Maor, 1998). A theorem that was fundamental to Ptolemy's calculation of chords was what was still known at present as Ptolemy's theorem, that the sum of the products of the opposite sides of a recurring quadrilater al was equivalent to the product of the diagonals. Ptolemy used these results to develop his trigonometric tables; however whether these tables were originated from Hipparchus' work could not be proved.Neither the tables of Hipparchus nor those of Ptolemy had survived to the present day, though descriptions by other ancient authors exhibits they existed. In his work, Ptolemy founded formulas for the chord of? difference and an equivalent for our modern day half-angle? formulas. Because of Ptolemy’s discoveries, given a chord of? an arc in a circle, the chord of half an arc can be determined as? well. Ptolemy also discovered chords of sum and difference, chords of half an arc, and chords of half degree, from which he then built up his tables to the nearest second of chords of arcs from half degree.In the Almagest, a true distinction was made between plane and spherical trigonometry. Plane trigonometry is the branch of trigonometry which applies its principles to plane triangle s; Spherical trigonometry, on the other hand, is the branch of trigonometry in which its principles are applied to spherical triangles, which are triangles on the surface of the sphere. Ptolemy began with spherical trigonometry, for he worked with spherical triangles in many of his theorems and proofs. However, when calculating the chords of arcs, he unintentionally developed a theory for plane trigonometry. Trigonometry was created for use in astronomy; and because spherical trigonometry was for this purpose the more useful tool, it was the first to be developed. The use of plane trigonometry†¦ is foreign to Greek mathematicians† (Kline, 1972). Spherical trigonometry was developed out of necessity for the interest and application of astronomers. In fact, spherical trigonometry was the most prevalent branch of trigonometry until the 1450s, even though Ptolemy did introduce a basis for plane trigonometry in the Almagest in 150 A. D. IndiaThe next major contribution to trig onometry came from India. The trigonometry of Ptolemy was based on the functional relationship between chords of a circle and central angles they subtend. The Siddhantas, a book thought to be written by Hindu scholars in late fourth century, early fifth century A. D. , changed Ptolemy’s trigonometry to the study of the relationship between half of a chord of a circle and half of the angle subtended at he center by the whole chord (Kennedy, 1969). This came from the basis for the modern trigonometric function known as the sine.The Siddhantas introduction to the sine function is the chief contribution from India and marks a transformation in trigonometry. Indian mathematicians also contributed by creating their own sine table. Arya-Bhata, born in 476, was a great Indian mathematician and astronomer (Ball, 1960). He composed a book called Aryabhathiya, which contained most of the essential ideas we associate with sine and cosine. His most outstanding contribution to the topic, w hich distinguishes him from the other mathematicians of this time, was his work on sine differences (van Brummelen, 2009).His definition of sine was literally â€Å"half chord† and was abbreviated jya or jiva, which simply meant, â€Å"chord† (Smith 615). Sines were given in minutes, at intervals of 225 minutes. This measurement was not of the sines themselves, but instead, it was the measurement of the differences between the sines. His method of calculating them was as follows. The first sine was equal to 225. The second sine was defined as any particular sine being worked with in order to calculate the sine that directly follows (Clark 29).It was found using the following pattern: (225 – the previous sine) + (225 + the previous sine) 225 this total was then subtracted from 225 to obtain the sine table. Second sine: 225 – 225 = 0 225 / 225 = 1 0 + 1= 1 225 – 1 = 224 Third sine:? 225 – 224 = 1 (225 + 224) / 225 ? 2 225 – 2 = 222 (van Brummelen, 2009). Arya-Bhata concluded that dividing a quarter of the circumference of a circle (essentially one quadrant of the unit circle) into as many equal parts, with the resulting triangles and quadrilaterals would have, on the radius, the same amount of sines of equal arcs.Doing this, he was able to form a table of natural sines corresponding to the angles in the first quadrant (van Brummelen, 2009). Although much of his work had the right idea, many of Arya-Bhata’s calculations were inaccurate. Later, in 1150AD, an Indian mathematician known as Bhaskara gave a more accurate method of constructing a table of sines, which considered sines in every degree (van Brummelen, 2009). Although the Indian mathematicians made attempts at creating a table to help with astronomy, their table of sines was not as accurate as that of the Greeks. Islamic mathematicsThe ancient works were translated and developed in the medieval Islamic world by Muslim mathematicians of mostly Persian and Arab descent, who explained a large number of theorems which freed the subject of trigonometry from reliance upon the complete quadrilateral, as was the case in Greek mathematics as a result of the application of Menelaus' theorem. In accordance with E. S. Kennedy, it was following that development in Islamic math that â€Å"the first real trigonometry appeared, in the sense that only then did the object of study become the spherical or plane triangle, its sides and angles† (Kennedy, 1969).E. S. Kennedy pointed out that whilst it was possible in pre-Islamic math to calculate the magnitudes of a spherical figure, in theory, by use of the table of chords and Menelaus' theorem, the application of the theorem to spherical problems was very complex actually (Kennedy, 1969). With the aim of observing holy days on the Islamic calendar in which timings were established by phases of the moon, astronomers at first used Menalaus' method to compute the place of the moon and stars, a lthough that method proved to be ungainly and complex.It engaged creation of two intersecting right triangles; by applying Menelaus' theorem it was possible to solve one of the 6 sides, however only if the other 5 sides were known. To tell the time from the sun's elevation, for example, repeated applications of Menelaus' theorem were needed. For medieval Islamic astronomers, there was a clear challenge to find a simpler trigonometric rule (Gingerich, 1986). In the early 9th century, Muhammad ibn Musa al-Khwarizmi c a Persian Mathematician, was an early pioneer in spherical trigonometry and wrote a treatise on the subject creating accurate sine and cosine tables.By the 10th century, in the work of Abu al-Wafa' al-Buzjani, another Persian Mathematician established the angle addition formulas, e. g. , sin(a + b), and discovered the sine formula for spherical trigonometry. Abu’l-Wafa is believed to have helped introduced the concept of the tangent function. He also may have had s omething to do with the development of secant and cosecant. His trigonometry took on a more systematic form in which he proved theorems for double and half angle formulas. The law of sines, is also attributed to Abu’l-Wafa, even? hough it was first introduced by Ptolemy. This is in part? due to the fact that Abu’l-Wafa presented a? straightforward formulation of the law of sines for? spherical triangles, which states [pic] where A, B, and C are surface angles of the spherical? triangle and a, b, and c are the central angles of the? spherical triangle. In 830, Habash al-Hasib al-Marwazi created the first table of cotangents. Muhammad ibn Jabir al-Harrani al-Battani found the reciprocal functions of secant and cosecant, and created the first table of cosecants for each degree from 1 ° to 90 °.By 1151 AD, the ideas of the six trigonometric functions existed, they were just not named as we know them today. Europe It is from the Arabic influence that trigonometry reache d Europe. Western Europe favored Arabic mathematics over Greek geometry. Arabic arithmetic and algebra were on a more elementary level than Greek geometry had been during the time of the Roman Empire. Romans did not display much interest in Greek trigonometry or any facets of Greek math. Therefore, Arabic math appealed to them since it was easier for them to comprehend.Leonardo Fibonacci was one mathematician who became acquainted with trigonometry during his extensive travels in Arab countries. He then presented the knowledge he gained in Practica geometriae in 1220 AD (Gullberg, 1996). The first distinction of trigonometry as a science separate from astronomy is credited to the Persian, Nasir Eddin. He helped to differentiate plane trigonometry and spherical trigonometry. Other than that, little development occurred from the time of the 1200’s to the 1500’s, aside for the developments of the Germans in the late 15th and early 16th century.Germany was becoming a prosp erous nation at the time and was engaged in much trade. Their interests also developed in navigation, calendar formation, and astronomy. This interest in astronomy precipitated a general interest and need for trigonometry (Kline, 1972). Included in this movement around the time of 1464, the German astronomer and mathematician, Regiomontanus (also known as Iohannes Molitoris) formulated a work known as De Triangulis Omnimodis, a compilation of the trigonometry of that time.When it was finally printed in 1533, it became an important medium of spreading the knowledge of trigonometry throughout Europe (Gullberg, 1996). The first book began with fifty propositions on the solutions of triangles using the properties of right triangles. Although the word â€Å"sine† was derived from the Arabs, Regiomontanus read the term in an Arabic manuscript in Vienna and was the first to use it in Europe. The second book began with a proof of the law of sines and then included problems involving how to determine sides, angles, and areas of plane triangles.The third book contained theorems found on Greek spherics before the use of trigonometry, and the fourth was based on spherical trigonometry. In the sixteenth century, Nicholas Copernicus was a revolutionary astronomer who could also be deemed as a trigonometer. He studied law, medicine and astronomy. He completed a treatise, known as De revolutionibus orbium coelestium, the year he died in 1543. This work-contained information on trigonometry and it was similar to that of Regiomontanus, although it is not clear if they were connected or not.While this was a great achievement, Copernicus’ student, Rheticus, an Indian mathematician, who lived during the years 1514-1576, went further and combined the work of both these men and published a two-volume work, Opus palatinum de triangulus. Trigonometry really began to expand and formalize at this point as the functions with respect to arcs of circles were disregarded. Fran cois Viete who practiced law and spent his leisure time devoted to mathematics also . contributed trigonometry around this time. He came to be known as â€Å"the father of the generalized analytic approach to trigonometry† (Boyer, 1991).He thought of trigonometry as? an independent branch of mathematics, and he worked? without direct reference to chords in a circle. He made? tables for all six trigonometric functions for angles to the? nearest minute. Viete was also one of the first to use the? formula for the law of tangents, which states the following: [pic] Viete was one of the first mathematicians to focus on analytical trigonometry, the branch of trigonometry which focuses on the relations and properties of the trigonometric functions.This form of trigonometry became more prevalent around the time of 1635 with the work of Roberval and Torricelli. They developed the first sketch of half an arch of a sine curve. This important development assisted in the progression of tri gonometry from a computational emphasis to a functional approach. This formed the basis of the European contribution of trigonometry. From the influence of oriental scientists, the Europeans focused on the computation of tables and the discovery of functional relations between parts of triangles.Europe developed appropriate symbols, which replaced the verbal rules and ordinary language in which the subject was usually presented. Previously, trigonometry was expressed in lengthy passages of confusing words, but the Europeans introduced such symbols as sin, cos, tan, etc. to simplify the subject and make it more concise. Prior to the analytic approach, the main usage of trigonometry was to measure geometric figures, but the transition of its influence from geometry to calculus began with the discovery of infinite series representations for the trigonometric functions.Trigonometric series became useful in the theory of astronomy, around the time of the eighteenth century. Since astrono mical phenomena are periodic, it was useful to have trigonometric series because they are periodic functions as well. The use of trigonometric series was introduced to determine the positions of the planets and interpolation, which is a mathematical procedure that estimates the values of a function at positions between given values (Kline, 1972). Many continued to make contributions to Trigonometry looking for more accurate tables to determine the six functions.These works continued up until the invention of the Scientific Calculator in 1968. In society today, trigonometry is used in physics to aide in the understanding of space, engineering and chemistry. Within mathematics it is typically seen in mainly in calculus, but also in linear algebra and statistics. Despite the minimal information available on the history of Trigonometry it is still a vital part of mathematics. The History shows progression from astronomy and geometry and the movement from spherical to plane geometry.Toda y, Trigonometry is used to understand space, engineering, chemistry as well as mathematics. By exploring the history of trigonometry we see the importance of it in our world. References Boyer, Carl B. (1991), A History of Mathematics (Second ed. ). John Wiley & Sons, Inc. 3 Bressoud, D. M. (2010). Historical Refelctions on Teaching Trigonometry. Mathematics Teacher, 104 (2), 106-112. Brummelen, G. V. (2009). The Mathematics of the Heavens and the Earth. Princeton, NJ: Princeton University Press. Gingerich, Owen (1986), â€Å"Islamic astronomy†. Scientific American 254 (10): 74.Gullberg, Jan. (1996)Mathematics from the Birth Of Numbers. New York:W. W. Norton and Company, Inc. Joyce, D. E. (n. d. ). History of Trigonometry Outline. Retrieved 3 21, 2012, from History of Trigonometry Outline: http://aleph0. clarku. edu/~djoyce/ma105/trighist. html Kennedy, E. S. (1969), â€Å"The History of Trigonometry†. 31st Yearbook (National Council of Teachers of Mathematics, Washingt on DC) (cf. Haq, Syed Nomanul. The Indian and Persian background. pp. 60–3, in Seyyed Hossein Nasr, Oliver Leaman (1996). History of Islamic Philosophy. Routledge. pp. 52–70.Kline, Morris. (1972) Mathematical Thought from Ancient to Modern Times. New York: Oxford University Press. Kluemper, A. (2010, 3 24). History of Trigonometry. Retrieved 3 5, 2012, from www. xtimeline. com: http://www. xtimeline. com/timeline/History-of-Trigonometry Mankiewicz, Richard. (2001)The Story of Mathematics. New Jersy:Princetion University Press. Maor, E. (1998). Trigonometric Delights. New Jersey: Princeton University Press. Miller, S. (2001). Understanding Transformations of Periodic Functions through Art. Mathematics Teacher , 94 (8), 632-635.Moussa, Ali (2011), â€Å"Mathematical Methods in Abu al-Wafa's Almagest and the Qibla Determinations†. Arabic Sciences and Philosophy. Cambridge University Press. 21 (1): 1–56. Needham, Joseph (1986), Science and Civilization in Chi na: Volume 3, Mathematics and the Sciences of the Heavens and the Earth. Taipei: Caves Books, Ltd. Rogers, L. (n. d. ). The History of Trigonometry- Part 1. Retrieved 3 1, 2012, from Enriching Mathematics: http://nrich. maths. org/6843/index Suzuki, J. (2009). Mathematics in Historical Context. Washington D. C. : The Mathematical Association of America.Smith, D. E. (1958)History of Mathematics. New York:Dover Publications, Inc. Toomer, G. J. (1998), Ptolemy's Almagest, Princeton University Press. Weber, K. (2005). Students Understanding of Trigonometric Functions. Mathematics Education Research Journal , 17 (3), 91-112. www. cartage. org. (n. d. ). Trigonometry History. Retrieved 3 5, 2012, from Trigonometry History: http://www. cartage. org. lb/en/themes/sciences/Mathematics/Trigonometry/history/History%20. html van Brummelen, G. (2009)The Mathematics of the Heavens and Earth. Princeton University Press. Princeton and Oxford.

Business models: a strategic management approach Essay

The 21st century presents new and exciting opportunities for doing business; the entrepreneurial realm is greatly expanding and becoming an excellent platform for personal and societal growth. Individuals and institutions are realizing the significance embedded in the development of vibrant business ideas. Doing business has become a lucrative venture in the world of today with the emergence of budding entrepreneurs in a quest to yield huge benefits in the corporate world. Indeed, the sale of goods and services to make profits is not a reserve of a chosen few as it was conventionally perceived, but it is a dynamic venture for virtually any innovative and growth-centered entrepreneur. Nevertheless, the fundamentals of doing business have not changed; success in business requires immense input and dedication. What is it that makes businesses grow exponentially? With the advent of technology, continuous globalization influence and the ever-increasing rate of competitors in the market, what are the appraisal factors for business expansion and development? These imperative questions should continually linger in the mind of an entrepreneur. Developing a feasible business concept is the most elemental factor for one to consider while venturing into the entrepreneurial real (Nagendra, 2010, p 146). The business concept, based on an entrepreneurial idea, should be in a position to integrate well into the market place. Of course, the integration process requires a substantial analysis of the pivotal factors influencing the growth of the business. This necessitates a deliberate evaluation of the internal and external environments of the business. Comprehending the strengths, weaknesses, opportunities and threats of the business concept is extremely important (Hannagan & Bennett, 2000 p 46).Outlining and executing the strategies for growth and development is equally vital in the process. Thus, this paper seeks to bring out the fundamentals of developing a business and ensuring its success. Moreover, a detailed analysis of the concepts involved will definitely unearth the drivers and constraints of business development. Business Concept             In the corporate world today, it has become increasingly important to develop strong corporate leadership capacity to drive the dynamic instruments in the business. The corporate leadership concept is significant in various fronts. It provides management solutions by streamlining the internal and external environments of a business enterprise (Davis, 2003, p 16). Of importance still, corporate leadership is the platform in which dynamism and innovation is accrued in a business through investing in the relevant resources. Accomplishing this calls for the management to put in best practices in accordance with a business’ goals and objectives. Human resource management is another imperative aspect in the business world. As the driving force in respect to capacity development, it is vital for businesses and corporate bodies to invest expansively in human resource development (Sims, 2007, p 361). Companies are realizing the need to enhance corporate leadership a nd develop vibrant human resource frameworks. In reference to the statements above, I believe that there is a gap in the corporate world that needs to be filled; an opportunity to provide solutions to the prevailing trends in many businesses today. In order to bridge this gap, I strongly believe that offering consultation services to corporate bodies in the areas of corporate leadership and human resource management will go a long way in addressing the inadequacies of the two elements in many businesses today. In other words, the need for strong corporate leadership structures and vibrant human resource management frameworks in corporate institutions offers me an entrepreneurial idea to develop a consultation firm in the significant areas. The business concept involves providing consultation services to companies in the realms of corporate leadership and human resource development. Given the need for corporate institutions to find lasting solutions in feasible management practices and investing in their employees, and the experi ence as well as the passion I have for consultancy in the areas, the business concept is certainly a viable entrepreneurial idea. Developing the Strategies for the Business Concept             Developing strategies for a business concept aims at improving its value in the market place. It is a process of ensuring that the structures of a business have a means of transition from one point to another. Successful strategies for growth are flexible and have the ability to foster growth; they encompass the instrumental elements of running a business (Nilsson & Rapp, 2005, p 361). Therefore, developing the most feasible business strategies for operating the corporate leadership and human resource development, consultancy firm will be an important starting point.Developing a business strategy with utmost proficiency will encompass the following areas: The purpose or aspirations for the business-This will simply portray the position of the business and what it aspires to achieve in respect to its aims and objectives. Clear goals and objectives will empower the employees of the firm as well as giving a clear-cut picture to its potential clients. A feasible purpose will also connect the business well with its expansive stakeholders. Instilling competitive advantage and creating a market niche. Ideally, this is coming up with excellent ways of convincing clients about the adeptness and quality of services in the firm (Effron, Gandossy & Goldsmith, 2003, p 61). Setting the boundaries for the strategy- This refers to the jurisdictions of the business; the products, services and markets that the firm will deal with. According to Kozami (2005), setting strategic boundaries will enhance its effectiveness and flexibility; hence, leading to growth. In this reference, too many boundaries create inflexible business patterns, while too few boundaries diminish the focus required by a company. Prioritizing- This involves emphasizing on the most significant goods and services in the market. In addition, it is important to identify the most significant clients and markets. This is a strategic move in fostering the much-needed growth and development in the business. This will also require the employees of the firm to have strategic responsibilities of unearthing the potential in the priorities. Management practices- Developing viable internal management practices are critical in integrating the functioning of the firm’s diverse structures. a) Purpose of the business             The consultancy firm is based on an entrepreneurial idea whereby it will offer consultation services and products to corporate bodies for a fee. The firm aims at providing consultation services in corporate leadership and human resource development to other companies. The firm’s objectives are: Providing in-depth training to managers on efficient management practices to foster growth in their companies Training employers on capacity building and how to empowering their employees for sustained growth Providing corporate leadership and human resource development services to companies Raising professional corporate leaders through mentorship programs Enhancing entrepreneurial skills to emerging entrepreneurs Creating effective manuals as viable products for reference to managers in corporate leadership and human resource development Goals of the firm include: To be the best consultancy firm in corporate leadership and human resource development To serve a wide clientele ranging from companies and businesses To offer dynamic and up to date services and products in the area of corporate leadership and human resource b) Creating a market niche             Creating a competitive advantage for a business in the market is a significant tool in advancing the purposes of the company (Barney & Hesterly, 2006, p 122). Competitive advantage improves the performance of a business enterprise in respect to other businesses. Ideally, creating a niche involves capitalizing on practices that attract customers more. In order to have a competitive advantage over other businesses in the industry, the consultancy firm will offer quality services to its clients. Offering quality services will certainly put the firm in a strategic position and attract more clients. Clients find it more satisfying to work with quality service providers (Rao, 2011, p 374). Moreover, offering quality consultation services to clients will undoubtedly enhance the firm’s corporate reputation. Corporate leadership and human resource development are extremely instrumental concepts that require services of utmost proficiency. Of significance still, is t he firm’s pricing index. Depending on the market trends in the industry, the firm’s products and services pricing policy seeks to accommodate all clients across the board. This is a competitive advantage platform of winning out the ever-increasing competition. c) The company’s boundaries             This refers to the strategic placements of the company in respect to its services provision. The firm will concentrate on offering consultation services to companies that wish to enhance their corporate leadership and human resource development functions. The company will work closely with companies that wish to outsource the above functions. Moreover, the firm’s jurisdiction also covers individuals who desire to grow their corporate leadership and human resource management portfolios. Apart from the consultancy market, the firm’s boundary accommodates training at part of its corporate jurisdiction. The training structures of the firm in corporate leadership encompass the mentoring of corporate leaders. In addition, offering manuals on effective human resource practices to companies is a significant product offering. The firm’s jurisdiction is also in the e-commerce realm where it offers its services and products through the internet. The abil ity of the company to stick to its corporate jurisdiction is an imperative growth impetus. Furthermore, the capacity of the consultancy firm to communicate clearly to its clients about the services offered is significantly vital in growing the client base. The business will foster a viable communication platform to allow clients to understand clearly its portfolio in the market. Setting and maintaining feasible boundaries in respect to the firm’s service and product offering is a pertinent aspect in the growth and development of the firm’s corporate identity and image. d) Areas of priority             In order for the business to grow, there is need for its structures to identify the areas of urgency and works towards improving them. Among the firm’s target market, there is more emphasis in the private sector. The firm sees more business prospects in the private sector, where by it reaches out to the management teams of private institutions for business propositions. Additionally, the firm’s target market is young entrepreneurs who do not have sufficient expertise in corporate leadership and the management of human resource. Through adequate market research, it is possible for the company to identify the areas of priority in the target market, and work towards its growth and development. Putting emphasis on the most significant clients is a viable way of enlarging the firm’s profit margins. In addition, the employees of the firm are an important resource in ensuring the realization of its priorities. Thus, strategies of empowering them go a long way in ensuring success both in the short-term and long-term. In reference to this, the employees have duties and responsibilities that seek to foster growth and development. Mathis & Jackson (2003) assert that an empowered human resource and a culture of high-involvement in any institution are strategic features in enhancing its chances of success. e) Management practices             The company’s initiative in creating a coherent working environment within its organs is an efficient way of realizing its objectives. The management’s commitment in streamlining the functions of each employee and fostering high-involvement in the internal structures of the firm is instrumental in the development of the best corporate practices. SWOT Analysis             Evaluating the strengths, weaknesses, opportunities and threats of the company will be extremely significant in understanding its objectives as well as the factors that influence them. This is a vital tool in unearthing the positive and negative factors, which affect the functioning processes of the consultancy firm. Given that the company is new in a highly competitive market, it is evident that a SWOT analysis will be beneficial in providing a realistic framework for growth. The analysis is indeed significant for growth as it provides a framework for development. Strengths Weaknesses Opportunities Threats I. Great expertise in corporate leadership and HRM consultancy II. Adequate and sufficient number of consultants III. Vibrant employees IV. Quality services Financial constraints Limited infrastructure The company is relatively new in the market Increase of emerging companies Expanding its target market portfolio An established market niche Competition from other consultancy firms Dominance by large companies Loss of employees to other companies Strengths             The company’s strengths place it at a favorable position of enhancing its growth index. Mainly, the strengths are attributed to the internal credentials that consequently contribute to a viable output. Expertise in corporate leadership and HRM concepts is an imperative platform of winning out competition. The availability of qualified consultants plays a pivotal role in creating a market niche and reaching out to clients effectively. Additionally, vibrant employees make it possible for the company to strengthen the internal structures of the company that complement the external success. Provision of quality services is an imperative impetus that attracts customers and enhances the much-needed growth. Building on the strengths calls on the concerted efforts from the internal organization of the firm Weaknesses             Given that the company in new in the market, chances of it taking relatively slow to catch up in the market are high. It places the company at a disadvantage in respect to other companies. Limited infrastructure limits the ability of the company to handle many job propositions. Additionally, lack of a stable financial status to finance the internal, and external functions of the company pose huge challenges to the growth of the company. In reference to this, the company needs to put in place viable measures of addressing the weaknesses in order to enhance its growth prospects. The firm’s management has a duty to ensure that its internal structures are in tandem with growth factors. Opportunities             The influx in emerging companies is an amazing opportunity for the growth of the company. The emerging companies provide an opportunity for offering consultancy services, given the importance attached to the function. Moreover, the firm has an opportunity to expand to other target markets because of the demand for its specialty. An established market niche because of a ready market provides the company with an immense opportunity to expand its corporate image and identity. Therefore, the opportunities presented by the external forces demonstrate positive prospects for the firm. Threats             Competition is a huge threat to the firm; its ability to penetrate the mainstream market is limited by the ever-increasing competition from other consultancy companies. The dominance by large established companies also threatens the ability of the company to grow. Losing highly qualified employees to other companies is a serious threat that incapacitates the ability of the company to expand its corporate jurisdiction. These constraints limit the goals and objectives of the company; hence, it is pertinent for the firm to articulate strategic platforms of addressing the threats. Value Innovation Analysis             Kaufman & Woodhead (2006) argue that value innovation analysis refers to the methodologies used in enhancing the value of a product, service or business. This is aimed at increasing the functionality of a service or product in order to enhance the satisfaction of a customer. According to Gregoriou (2010), value innovation analysis offers companies with competitive solutions for remaining relevant in the market by investing in the customer and finding practical answers to the needs of the customer. Based on the designed consultancy firm, it is evidently clear that value innovation analysis will play a significant role in its desire to offer value-centered services to its clients. The company, which is primarily a service provider, will enhance its ability to reach out to its clients by critically analyzing its functions in meeting the needs of an ever-increasing market. Innovation is significant in finding breakthrough in a high competitive market. Given that the consultancy firm is new in an industry that is value-centered, the value innovation analysis will enable it to realize its areas of functionality in order to improve the value of its services. I. Orientation stage             The orientation stage is the first process in analysis value innovation. This includes identifying the component for analysis. In respect to the consultancy firm, service offering is the most essential component of analysis. Based on its core objectives, the company offers consultation services with a specialty in corporate leadership and human resource management. The need to analyze this component arises from the value attached to it; it is an important aspect in the running of corporate organizations today. Corporate leadership and human resource management are elemental in the growth and development of businesses in the corporate world today (Jockenhofer, 2013, p 34). II. Information             The information stage involves understanding the areas of priority in relation to the target customers in the component discussion above. The firm’s most significant clients are emerging companies as well as established companies that need to outsource corporate leadership and HRM functions. The company’s function also encompasses small-scale businesses wishing to develop in the respective specialties. The customers’ opinions are extremely significant in realizing the fundamentals of functionality. Based on the preferences of the clients, it is the mandate of the service provider to enact innovative ways of producing the much-needed value (Murray, Markides & Galavan, 2008, p 63). Therefore, gaining sufficient knowledge and information on the target customer or client attached to the service offered is an important step in building value innovation. III. Analysis             This is important as it entails the transformation of a need into functionality that meets the needs of the client. Ideally, this step of analysis involves identifying the functions of precipitating from a service or product offering (Afuah, 2004, p 112). A detailed analysis of the products or services offered creates the values accrued to diverse functions of the component. Therefore, a deep evaluation and understanding of the service offerings in the consultancy firm indicates varied functions. The functions can be graded in order of importance; hence, giving the firm a platform to accord value to different functions depending on the needs of the clients. The need for efficient corporate leadership and human resource development has been more in high-involvement organizations with many structures and functions. The desire of managements to enhance the internal environments of their companies has precipitated the need for outsourcing the services offered by the c onsultancy firm. Hence, this implies that high functionality and value is placed on large institutions. Based on the needs of large organizations in enhancing their internal structures, the consultancy firm has a duty to place high functionality and values in them. Emerging companies also place dire need for effective corporate leadership and HRM management policies, thus it is also a valuable area of functionality according to the analysis. On the other hand, though small-scale businesses have a need for the services, there is little value depending on the frequency of services offered. It is worth noting that the price attached to the different functions depends on the values attached to the functions. The diverse clients to the company present different values and consequently, the cost of the services. IV. Innovation             This stage involves coming up with viable alternatives of complementing the existing structures or having a complete overhaul. Bilton & Cummings (2010) assert that designing creative strategies is an important innovative component in the growth and development of business functions. Therefore, the innovation stage implies that the consultancy firm needs to evaluate its functions and costs of service offering, and identify ways of either changing or improving the existing functions. It is utterly important for the firm to change its functions capacity and seek for ways of enhancing the value accrued in the small-scale businesses category of clients. This calls for creative measures of turning it from a low functioning ratio to a high functioning ratio. According to the analysis, the service offering needs to seek for ways of expanding its jurisdiction and having a comprehensive approach. V. Evaluation             This involves evaluating the alternatives brought forward in the enhancement of value in the functions of the company. The alternatives developed in the innovative stage are critical in defining the qualitative and quantitative analysis of the alternatives. The qualitative techniques involves a critical evaluation of the high value standards that should be advanced to transform the poor performing functions and improve the high performing functions (Rughase, 2006, p 67). Conducting market research and raising awareness among small-scale entrepreneurs is a viable qualitative approach in improving the value of the function. Additionally, the quantitative analysis techniques involve the application of innovative value-based measurements of increasing the value of functions. Budgeting for the effective value-based ways of improving the service offering to small-scale businesses is a viable option in the analysis. Website Specifications             The growth and development of a company requires excellent communication strategies in the internal and external environments (Das, 2009, p 140). Communication with the stakeholders especially with the customers is an imperative aspect in the growth of the business. Building a reputable website is an excellent platform in enhancing the communication between a company and its customers (Das, 2009, p 141). Therefore, it is important for the consultancy firm to have a functioning website as a marketing strategy. Since it is a new business in the market, the website is indeed a great tool in enhancing its corporate reputation. The following are the website specifications befitting the development of the budding consultancy firm. a) Home page details             Since the home page is the first point of contact between the firm and potential customers, it should have an appealing effect to the customers and communicate effectively about the business (McGovern & Norton, 2002 p 202). The firm’s logo is the first thing that visitors and customers should see when they visit the website. The professional logo of the company at the home page will play an instrumental role as a marketing tool. This will surely give the site’s visitors a perfect assurance that they are in the right place. Secondly, a tag line that describes the business is also available in the home page as a significant way of connecting with site visitors and creating an enthusiastic environment for potential customers to learn more about the consultancy services in the firm. The descriptive tag line is put strategically next to the company’s logo to connect the two and improve the communication aspect of the company. This is meant to creat e a strong appeal for clients about the products and service offerings in the company. Thirdly, a reception blurb is also a pertinent home page detail specified in the website. This is simply an advertising platform for customers to have a quick idea of the company’s specialty-consultancy in corporate leadership and human resource development. Finally, a critical aspect in the home page of the company’s website is the content teaser that connects visitors with the content they need. It is the methodology through which the customers will be connected with the information they will need about the company. b) Formatting details             Every page in the site contains the company’s logo and corporate theme colors. This is an important aspect in defining the identity of the company to the site visitors. A continuous reflection of the logo is critical in reassuring the customers on the firm’s specialty in corporate leadership and human resource development portfolios. Furthermore, the navigation bar is helpful in linking the site visitors with the primary and secondary content in the website. Tables, text effects, images and background colors are important formatting details in the website that make it easier for the customers to learn about the company. c) Menu structure and rationale             The website is organized in a straightforward way to allow site visitors to get the information they need. The web pages in the site are arranged in a focus-oriented design to allow maximum gain to the visitors (potential clients). The firm’s website is organized in a hierarchical; the web pages are structured well with an easy way of navigation through the different contents. In respect to the website’s menu structure and rationale, there are significant pages defining its content. The Home page, Services and products list page, Services and products details page, About us page and Contact us page are significant in defining the website’s content. The menu structure offers a strategic way of navigating through the content. d) Reports and management information             Reports and management information are clearly elaborated in the website. Potential clients and site visitors have the opportunity to learn and have a sufficient update on the financial and management information in the company. Quarterly, biannual and annual information is made available for the clients whenever they visit the website. In addition, significant information about the firm’s functions and employees is well articulated in the website content. e) E-commerce aspects of purchases             The platform for offering services and products on line is also an important aspect of the consultancy firm. This platform helps the company to sell services and products through an on line mechanism. This service is elaborated clearly in the services and products details page in the website. Clients favorable with e-commerce trends are able to connect with the company through the website. Critique on the design concept, strategy and website specifications             The design concept is indeed a vibrant platform in the industry, thus there is an influx of competitors in the field. Offering consultancy services to corporate institutions is an entrepreneurial approach that attracts many entrepreneurs in the trade. Based on the fact that the business concept is in great demand, the number of competitors is certainly on the increase. Based on the idea, a competitor would capitalize on the weaknesses in the business concept to maneuver ways of competing in the lucrative market. Based on a critical analysis, the concept is narrow in its conceptualization. Its specialties are only applicable to corporate institutions. A competitor would capitalize on the gap to increase the scope of the business venture and incorporate non-corporate bodies as clients. Balling (2006) argues that a limited scope of operations in business gives a competitor an added advantage in securing better returns. With adequate articulation of necessary business structures, a competitor would virtually have an upper hand in the expansion of the business; hence, competing effectively in the industry. Again, the business concept has a narrow boundary in relation to the target client. From a critical analysis, the business concept would accommodate nurturing corporate leadership and HRM fundamentals in learning institutions whereby professionals conduct public speaking forums for a fee, as well as organizing conferences and seminars on corporate leadership and HRM development. These are lucrative ideas lacking in the concept, which a competitor would find extremely beneficial. Thus, from a critical analysis perspective, it is true that the business concept has weaknesses that give advantages to a potential competitor. In view of the company’s business strategy, it is clear that it is not highly strategized because of the narrow scope of the business concept. A business concept has a huge impact on the goals and objectives that an entrepreneur enacts (Grant, 2008, p 18). This implies that it is important for a business concept to have a wide focus that will consequently affect its goals and objectives. In reference to the discussion above, the consultancy firm has a narrowed focus; hence, limiting its purpose. Based on the vibrancy of the industry, it is evident that a competitor would seek ways of enlarging the strategic jurisdiction of the industry. Through a wide scope business concept, a competitor has the capacity to increase goals and objectives of his business. This implies that the competitor will have a wider range of clientele compared to the existing consultancy firm. A competitor can look at the ways of enhancing competitive advantage to clients capitalized by the consultancy firm and unearth means of winning out the competition. Since there are many ways of creating competitive advantage, a competitor can offer price subsidies to a section of clients to attract more clients as well as to retain the existing ones. This is a strategy that the consultancy firm does not practice, thus giving the competitor a reasonable advantage in the market. Indeed, this is a strategic move in winning out competition from the firm. Offering quality products at a reduced cost is indeed a strategic move in advancing the competitive advantage of a company. It is certainly a creative way of increasing the value of the services offered by a company. The management practices of the company do not have a feasible platform of addressing the external environments of the company. A competitor can capitalize on increasing the opportunities in the market through this serious lapse. Williams (2000) asserts that it is through viable management practices that a company is able to grasp the needs of the external stakeholders effectively. By ensuring that the internal and external management practices of a company are working together to add value to the functions of the competitor, it is highly likely that the competitor will realize more opportunities than the consultancy firm will. Consequently, it is vital for companies to input the most strategic management functions in order to realize their full potential. In respect to the website specifications, there is an important aspect that the company gives advantage to competitors. This is about an outline of the companies that have benefitted from its consultation services. This imperative section sets the pace for other companies, and encourages them to seek their services. A website is an instrumental tool in communicating with customers and attracting potential customers as well. Therefore, it is significant for companies to include such details in their website specifications. This is a challenge to new companies that have not yet developed a wide client base. Thus, the lack of concrete historical background on the successes of the consultancy firm puts off some clients, and benefits a competitor with such web applications. The critique shows that there are various aspects, which would limit the company compared to other companies. The business concept, strategy outline and website specifications present lapses that could give an upper hand to competitors in the market. Despite the lapses, the consultancy firm has a high prospect of growing if more actions that are deliberate are put in place. Conclusion             In conclusion, it is apparent that entrepreneurship plays a huge role in the growth and development of markets and the corporate realm. This requires immense investment in the relevant structures of ensuring success. Individuals and companies need to put in place the most fundamental business platforms of ensuring success. Primarily, designing a viable business concept is significant in starting the entrepreneurship journey. One has to consider the market trends and growth factors surrounding the idea. This will ultimately play a huge role in defining the growth of the company. After coming up with an entrepreneurial idea, it is imperative to set strategic factors and steps of ensuring the success of the business concept. Ideally, the growth and development of a business concept depends on the capacity to integrate the internal and external environments of a business. Such initiatives, of course, by the careful articulation of management practices are integral in realizing the full potential of a business enterprise. Moreover, it is imperative to continually, conduct a value innovation analysis in order to enhance the functions of a business concept and explore new opportunities in the market. The dynamism in the market in today’s business world calls for companies to invest in value innovation to increase their chances of survival in the highly competitive environment. Additionally, effective communication with clients and customers is immensely essential, that is why the website is an instrumental tool in advancing the need. With efficient communication strategies, a company is able to connect and relate with its stakeholders in a practical manner. 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Determinants and Consequences of Early Marriage in Java Essay

This study analyzes the determinants and patterns of early marriage and explores its consequences on marital dissolution, work status and occupation, migration, and contraceptive use in Java, Indonesia. Data from the 1991 Demographic and Health Survey are obtained on 5816 ever married women, 15-49 years old, living on Java. Early marriage occurs among women before age 20. Subjects are grouped as residing in Jakarta, Bandung, Semarang, Jogyakarta, and Surabaya; residing in townships and other urban areas; and residing in rural areas. Findings indicate that 70% of ever married women in Java married early. Almost 80% of women who were reared in villages married early. 81.2% who still live in rural areas married early. 20% had no formal education. 74% of Muslim women married early. 79% without work before marriage married early. Dissolution was more common among women living in rural areas. 31% of women in rural areas, 20% living in big cities, and 23% living in towns were no longer in their first marriages. Women who married early were 3 times more likely to experience dissolution than women who married later. The percentage of women whose first marriages ended was highest among women who were married the longest. The effect of marriage age on current working status and the pattern of working status between early and late marriage were not significant. 80% had ever used contraception. Women who married late were more mobile and were more likely to have a higher occupational status. Logistic findings indicate that women’s education, work status before marriage, husband’s education, and current residence were significant predictors of early marriage. Education was the strongest predictor. The probability of dissolution was highest among uneducated, early married, Muslim women living in big cities. The lowest probability was among later married women, living in small cities, and with a tertiary level of education.