It is also worth mentioning that many of the concepts of calculus were invented as a result of their collaboration during their letter correspondents; important discoveries such as the power series. One of the most compelling pieces of evidence to support the theory that both men invented calculus independently, comes from further reviewing their letters and papers. Newton who was more interested in the Physics aspect, tackled calculus from the derivatives as applied to motion an velocity. While on the other hand Leibniz had a more geometrical
One of the most renowned philosophers of the time, Archimedes of Susa, became one of the forefathers of calculus with his method of finding the area of shapes that were previously impossible to figure (Harding, 1976). Harding and Scott focused mainly on this method of Archimedes, which was known as the “method of exhaustion,” (Harding, 1976). By his method, Archimedes could calculate the areas of formerly impossible figures by using infinitely smaller, possible shapes within the impossible one. An example that the authors claim to be extremely well-known was his approximation of the area of a circle using tangent lines and po... ... middle of paper ... ...nd their words came across in a manner and language that someone who did not understand the subject would understand. They answered the questions that they asked the audience in the introduction in great detail, but without becoming overbearing.
Newtons dicoveries was made up of several different things. It consisted of combined infinite sums which are known as infinite series. It also consisted of the binomial theorem for frational exponents and the algebraic expression of the inverse relation between tangents and areas into methods that we refer to today as calculus. However, the story is not that simple. Being that both men were so-called universal geniuses, they realized that in different ways they were entitled to have the credit for “inventing calculus”.
Math had made it possible to understand this aspect of the cosmos, yet there were some differences on how they really worked. The Greeks were the first to “propose explanations for the motions of astronomical objects that relied on logic and geometry” Bennett, Donahue, Schneider, and Voit (2004). Math, helped explain, and defy the beliefs held for many years. The Greeks created a geocentric model, which places the earth in the center of the universe. This was attributed, to Thales (c. 624-546 B.C.
The other is “the history of mathematical analysis” which goes back to the times of Archimedes, who was in the same era as Aristotle and Euclid. These to groups or streams were separate for a long time until Newton invented Calculus, which brought Math and logic together. Somebody who studies mathematical logic and gives his or her own concepts about it is called a logician. Some well known logicians include Boole and Frege. They were trying to give a definite form to what formal deduction really was.
In addition, the Pascaline, invented and built by a French philosopher and mathematician Blaise Pascal, was the first mathematical adding machine (Long 54). The Pascaline was a gear-driven machine that allowed the user to calculate answers without doing arithmetic (Hoyle). In addition to the abacus and the Pascaline, Babbage's Folly, also known as the difference machine, "hastened the development of computers. [and] advanced the state of computational hardware" (Long 55). This engine, designed by the Cambridge professor Charles Babbage, could do any of the basic functions of mathematics: adding, subtracting, multiplying, and division in series at a "rate of 60 additions per minute" (55) could all be accomplished with minimal effort.
The use of circle to represent zero is usually attributed to Hindu mathematics. Early Indians are also known to be the first to establish the basic mathematical rules for dealing with zero. They had also established the laws that could be used to manipulate and perform calculation on negative numbers, something that was not manifested in unearthed mathematical works of other ancient mathematics. Brahmagupta, a Hindu mathematician, showed that quadratic equations could have two possible solutions and one of which could be negative. In India, there was an era called “the Golden Age of Indian Mathematics.
Isaac Newton not only changed the world with the invention of calculus, but also with his theory of light and color, and his invention of physical science and the law of universal gravitation (Margaret, 11). To begin with, Isaac Newton laid down the foundations for differential and integral calculus. It all began when Newton was enrolled at Cambridge College, the University that helped him along in his studies. Here, he began reading what ever he could find, especially if it had something to do with mathematics. He read books on geometry by Descartes, algebra books by John Wallis, and eventually developed the binomial theorem which was a shortcut in multiplying binomials (Margaret, 46).
Benoit B. Mandelbrot is a key figure behind the rise of this new science. A Professor of mathematical Sciences at Yale and an IBM Fellow, Mandelbrot is the man who coined the term "fractal" in 1975. Mathematicians, such as Gaston Julia, only defined them as sets before this and could only give properties of these sets. Also, there was no way for these early fractal researchers to see what they were hypothesizing about. As Mandelbrot states in The Fractal Geometry of Nature, "I coined fractal from the Latin adjective fractus.
The Fluxional Method, Newton's first achievement was in mathematics. He generalized the methods that were being used to draw tangents to curves and to calculate the area swept by curves. He recognized that the two procedures were inverse operations. By joining them in what he called the fluxional method, Newton developed in 1666 a kind of mathematics that is known as calculus. Calculus was a new and powerful method that carried modern mathematics above the level of Greek geometry.