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Discovery of calculus
Sir Isaac Newton contributions to math
Sir Isaac Newton contributions to math
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Recommended: Discovery of calculus
Abstract—During a one hundred year period, seven great mathematicians made contributions to our mathematical knowledge and notation that enabled the emergence of calculus. All were men of either the Catholic or opposing Protestant faith. Religious politics served as both an impetus and a hindrance to the men’s mathematical advances. The men were Francois Viéte, Simon Stevin, John Napier, Adriaan van Roomen, Galileo Galilei, René Descartes, and Pierre de Fermat.
Index Terms—analytical geometry, decimal notation, differential calculus, logarithms, number theory
I. INTRODUCTION
During the Renaissance Period, prior to Isaac Newton’s discovery of calculus, mathematicians from across Europe began laying the foundation for modern mathematics and
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He developed a system of converting fractions to decimal notation, yet without a decimal point [1]. This decimal representation would make “mathematics a serviceable tool” [1]. In keeping with making mathematics serviceable, he advocated “application of the decimal system to all weights and measures and to coinage” [5]. Like other mathematicians of the Renaissance, he challenged Aristotle’s beliefs and predictions. Before Newton and Galileo, he proved that heavier objects do not fall faster than lighter objects as Aristotle predicted [5].
IV. JOHN NAPIER (1550-1617)
John Napier, born in Marchison Castle, Edinburg, Scotland, worked to make calculation simpler, especially for astronomers, by inventing the logarithm [10]. During his time, religious tension between Protestants, of which Napier was one, and Catholics brought peril and bloodshed in the politics of Spain, England, Scotland, and France. Napier invented war machines and wrote in defense of Protestant theology. He considered his personal interest in the development of mathematics secondary to his greatest work on Christian Apologetics, Plaine Discovery of the Whole Revelations of Saint John [13].
In 1594, Napier’s initial logarithms were in effect base 1/e [1]. Working with Brigg, a professor at Oxford, Napier developed logs
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2 Pierre de Fermat [11]
Pierre de Fermat, see fig. 2, a Catholic Frenchman, mathematician, and contemporary of Descartes, liked to pose difficult problems. His last theorem, where x, y, z, and n are positive integers has no solution if n is greater than 2, was finally proven by Andrew Wile in 1995 [1].
Number theory fascinated him [11]. Other mathematicians did not share in his interest in number theory. Descartes thought he was an amateur and disagreed with him on the principles of refraction of life, rectification of algebraic curves, and methods for investigating tangents to curves [2]. Apparently, the only other mathematician that he could influence and enjoy an amicable relationship with was Bernard Frenicle de Bessy. Through their correspondence, Fermat began to develop number theory.
Because of his work with tangents to curves and their minimum and maximum points, mathematicians consider him to be the inventor of the differential calculus [2].
IX.
When most people hear the name Isaac Newton, they think of various laws of physics and the story of the apple falling from the tree; in addition, some may even think of him as the inventor of calculus. However, there was much more to Newton’s life which was in part molded by the happenings around the world. The seventeenth century was a time of great upheaval and change around the world. The tumultuousness of this era was due mostly to political and religious unrest which in effect had a great impact on the mathematics and science discoveries from the time Newton was born in 1646 until the early 1700’s.
Ball, Rouse. “Sir Isaac Newton.” A Short Account of the History of Mathematics. 4th ed. Print.
The first generation of Bernoulli mathematicians include brothers Jacob I(James, Jacques) (1654-1705), Nicolaus (1662-1716), and Johann I(John, Jean) (1667-1748), second generation are brothers Daniel I (1700-1782), Johann II(1710-1790), and their cousin Nicolaus II (1687-1759), and the third generation are brothers Johann III(1746-1807) and Jacob II(1759-1789). It would be exhausting to discuss the accomplishments of all the Bernoulli mathematicians, so our focus will be on the brothers Jacob I and Johann I, who contributed a substantial amount to the fields of mathematics we know today as elementary calculus and the theory of probability.
Newton was educated at the King’s School, Grantham from the age of twelve to seventeen where he learned only Latin and no mathematics. His mother re...
...logarithm. Napier actually calculated these entries in the opposite manner, however. He generated a list of logarithms first and then selected those values that corresponded to a sine of an arcminute. Figure 4 demonstrates how Napier may have computed values for his table and Figure 5 shows the first page of Napier’s table of logarithms (Clark, 2001).
Pierre de Fermat Pierre de Fermat was born in the year 1601 in Beaumont-de-Lomages, France. Mr. Fermat's education began in 1631. He was home schooled. Mr. Fermat was a single man through his life. Pierre de Fermat, like many mathematicians of the early 17th century, found solutions to the four major problems that created a form of math called calculus. Before Sir Isaac Newton was even born, Fermat found a method for finding the tangent to a curve. He tried different ways in math to improve the system. This was his occupation. Mr. Fermat was a good scholar, and amused himself by restoring the work of Apollonius on plane loci. Mr. Fermat published only a few papers in his lifetime and gave no systematic exposition of his methods. He had a habit of scribbling notes in the margins of books or in letters rather than publishing them. He was modest because he thought if he published his theorems the people would not believe them. He did not seem to have the intention to publish his papers. It is probable that he revised his notes as the occasion required. His published works represent the final form of his research, and therefore cannot be dated earlier than 1660. Mr. Pierre de Fermat discovered many things in his lifetime. Some things that he did include: -If p is a prime and a is a prime to p then ap-1-1 is divisible by p, that is, ap-1-1=0 (mod p). The proof of this, first given by Euler, was known quite well. A more general theorem is that a0-(n)-1=0 (mod n), where a is prime...
The argument in this paper that even though the onus of the discovery of calculus lies with Isaac Newton, the credit goes to Leibniz for the simple fact that he was the one who published his works first. Appending to this is the fact that the calculus wars that ensue was merely and egotistic battle between humans succumbing to their bare primal instincts. To commence, a brief historical explanation must be given about both individuals prior to stating their cases.
» Part 1 Logarithms initially originated in an early form along with logarithm tables published by the Augustinian Monk Michael Stifel when he published ’Arithmetica integra’ in 1544. In the same publication, Stifel also became the first person to use the word ‘exponent’ and the first to indicate multiplication without the use of a symbol. In addition to mathematical findings, he also later anonymously published his prediction that at 8:00am on the 19th of October 1533, the world would end and it would be judgement day. However the Scottish astronomer, physicist, mathematician and astrologer John Napier is more famously known as the person who discovered them due to his work in 1614 called ‘Mirifici Logarithmorum Canonis Descriptio’.
No other scholar has affected more fields of learning than Blaise Pascal. Born in 1623 in Clermont, France, he was born into a family of respected mathematicians. Being the childhood prodigy that he was, he came up with a theory at the age of three that was Euclid’s book on the sum of the interior of triangles. At the age of sixteen, he was brought by his father Etienne to discuss about math with the greatest minds at the time. He spent his life working with math but also came up with a plethora of new discoveries in the physical sciences, religion, computers, and in math. He died at the ripe age of thirty nine in 1662(). Blaise Pascal has contributed to the fields of mathematics, physical science and computers in countless ways.
Abstract—The transition to calculus was a remarkable period in the history of mathematics and witnessed great advancements in this field. The great minds of the 17th through the 19 Centuries worked rigorously on the theory and the application of calculus. One theory started another one, and details needed justifications. In turn, this started a new mathematical era developing the incredible field of calculus on the hands of the most intelligent people of ancient times. In this paper, we focus on an amazing mathematician who excelled in pure mathematics despite his physical inability of total blindness. This mathematician is Leonard Euler.
John Napier: mathematician, philosopher, writer, and inventor. He was a very important man in the sixteenth century and his contributions are still standing today! John is best known as the great scottish mathematician who invented logarithms. Not only did he invented logarithms but also napier bones, at least one war weapon, as well as other incredible works. This paper about the famous mathematician, John Napier is going to inform you all about John’s early life, his area of expertise, and what kind of impact john made on the world.
The Bernoulli family had eight significant and important mathematicians, starting with Jacob Bernoulli, born in 1654. Though there was a great deal of hatred and jealousy between the Bernuollis, they made many remarkable contributions in mathematics and science and helped progress mathematics to become what it is today. For example, Daniel discovered a way to measure blood pressure that was used for 170 years, which advanced the medical field. Daniel’s way of measuring pressure is still used today to measure the air speed of a plane. Without the Bernoulli family’s contributions and advancements to calculus, probability, and other areas of mathematics and science, mathematics would not be where it is now.
Calculus, the mathematical study of change, can be separated into two departments: differential calculus, and integral calculus. Both are concerned with infinite sequences and series to define a limit. In order to produce this study, inventors and innovators throughout history have been present and necessary. The ancient Greeks, Indians, and Enlightenment thinkers developed the basic elements of calculus by forming ideas and theories, but it was not until the late 17th century that the theories and concepts were being specified. Originally called infinitesimal calculus, meaning to create a solution for calculating objects smaller than any feasible measurement previously known through the use of symbolic manipulation of expressions. Generally accepted, Isaac Newton and Gottfried Leibniz were recognized as the two major inventors and innovators of calculus, but the controversy appeared when both wanted sole credit of the invention of calculus. This paper will display the typical reason of why Newton was the inventor of calculus and Leibniz was the innovator, while both contributed an immense amount of knowledge to the system.
Zeno of Elea was the next person who attempted to prove irrational numbers by challenging the Pythagorean mathematics as well. He lived from 490BC to 430BC. Zeno had influence from Socrate...
The 17th Century saw Napier, Briggs and others greatly extend the power of mathematics as a calculator science with his discovery of logarithms. Cavalieri made progress towards the calculus with his infinitesimal methods and Descartes added the power of algebraic methods to geometry. Euclid, who lived around 300 BC in Alexandria, first stated his five postulates in his book The Elements that forms the base for all of his later Abu Abd-Allah ibn Musa al’Khwarizmi, was born abo...