# Eudoxus' Contribution To Calculus Essay

641 words - 3 pages

Eudoxus was a notable mathematician and astronomer of ancient times, particularly 408 – 355 BC. He lived in Greece and studied under Plato, one of the most notable philosophers ever. In Calculus, Eudoxus is known for advancing Antiphon’s ideas on the method of exhaustion. The method of exhaustion is very important to calculus because one of the fundamental themes of calculus is sending variables (or whatever it happens to be) to infinity, which is a branch of the method of exhaustion. This is known as taking the limit.
Eudoxus used the method of exhaustion to calculate volume and area. One example of this is his work with the area of a circle. At the time they hadn’t established this yet. If you didn’t know the formula for finding the area of a circle, you would need to approximate it, just like how we have learned to approximate the area under a curve with Rieman Sums. First, you could inscribe a circle in a triangle, and use the area of the triangle to approximate the area of the circle. But that would not give you a very accurate answer, so next you would draw a square around your circle. Still, this is not very accurate, so you would keep adding to the number of sides of your polygon until you approached infinity, giving you the most accurate answer possible without the formula. This is how Eudoxus would have figured out the area of a circle – with limits.
It seems thus that Eudoxus was the first person to develop the definition of a limit. This definition has evolved through the centuries, and today we know a limit as “f(x) gets close to L as x gets close to a” (taken from mathisfun.com). In simpler language, as x approaches a, y approaches L. L and a are the constants that you would already know. After Eudoxus came Archimedes, another Greek philosopher. He used Eudoxus’ ideas but furthered them by drawing regular polygons in and tangent...

## Find Another Essay On Eudoxus' Contribution to Calculus

### MATHEMATICS -ARA Essay

4768 words - 19 pages Mathematics, study of relationships among quantities, magnitudes, and properties and of logical operations by which unknown quantities, magnitudes, and properties may be deduced. In the past, mathematics was regarded as the science of quantity, whether of magnitudes, as in geometry, or of numbers, as in arithmetic, or of the generalization of these two fields, as in algebra. Toward the middle of the 19th century, however, mathematics came to be...

### The Bernoulli's: A Family of Reckoners

2308 words - 9 pages Having more than one mathematician in a family is not unheard of. There have been many father-son and father-daughter duos in the history of mathematics, e.g. Theon and Hypatia, Farcas Bolyai(1775-1856) and Janos Bolyai(1802-1860), George David Birkhoff(1884-1944) and Garrent Birkhoff, Emil and Michael Artin, Elie and Henri Cartan, etc. The Riccati family in Italy managed to produce three mathematicians, but the their contributions to mathematics...

### Aristotle's Fundamentals

1526 words - 6 pages Since the beginning of human civilization, people have tried to describe the way the world works, some fundamental truths that can explain why things are as they are. Many ancient worldviews have been suggested, such as Parmenides' which says that change is illusory or the Pythagoreans' numerical perfection. However, one view that persisted well into the middle ages was Aristotle's, whose empirical descriptions provided the conceptual framework...

### History of Islamic philosophy

3194 words - 13 pages At the beginning of the seventh century Byzantium, the Eastern Empire now completely separate from the disintegrated west, was the most powerful force in the world rivaled by Persia under the Sassanian dynasty. But in a small settlement in south Arabia a man was born who was to change the history of the east forever. In the last chapter I touched briefly on the differences between "inner-directed' and "outer-directed cultures." In an inner...

### Philosophy in Mathematics

3219 words - 13 pages Philosophy in Mathematics Mathematics has contributed to the alteration of technology over many years. The most noticeable mathematical technology is the evolution of the abacus to the many variations of the calculator. Some people argue that the changes in technology have been for the better while others argue they have been for the worse. While this paper does not address specifically technology, this paper rather addresses influential...

### Marie-Sophie Germain

571 words - 3 pages Marie-Sophie Germain, born April 1, 1776 to a French merchant, Ambroise-Francois Germain, "was probably the most profoundly intellectual woman that France has ever produced" (H.J. Mozans qtd. by Singh). Her interest in mathematics was inspired by her readings of the tragic death of Archimedes, who was murdered at the hands of a Roman soldier because he was too engrossed in a geometric problem to take notice of his situation. Germain immediately...

### Albert E

643 words - 3 pages Albert EMarch 14 1879 - April 18 1955Born Ulm, Germany. Died Princeton, USA.Albert Einstein was a very famous Scientist, he was mostly famous for his theory of Relativity.In 1894 Einstein's family moved to Milan and Einstein decided officially to relinquish his German citizenship in favor of Swiss. In 1895 Einstein failed an examination that would have allowed him to study for a diploma as an electrical engineer at Zurich. After attending...

### A Biography on Albert Einstein

1137 words - 5 pages "Imagination is more important than knowledge." (Albert Einstein). That was said by arguably the greatest thinker of the twentieth century, Albert Einstein. He was a renown physicist who brought us E=mc2, and who won the Nobel Prize. As you will find out, he has also succeeded in many different aspects of his life.Albert Einstein was born on March 14, 1879, in Ulm, Germany. He was the first child of Herman and Pauline Einstein. Herman was the...

### Behind the Scenes: The Effects of Acting on Personal Identity

1506 words - 6 pages Scientists have found it most valuable to study the cases of twins in order to determine the relative contribution of genetics or environmental factors to intelligence. First off, it is important to have an understanding of the genetic distribution between the different groups. Identical twins share the exact same genetic material, giving them 100% genetic overlap. Secondly, all other first degree family members such as fraternal twins,...

### Genius Paper Pathagoras

1420 words - 6 pages As we have studied and presented on famous philosophers in our Interdisciplinary Capstone class, I think it is important to reflect back on our educational journey with the University of Phoenix and appreciate the paths our journey took. I have definitely taken the time to reflect on my travels throughout my three-year journey. With this journey in mind, one of the most important studies in my journey was researching Pythagoras. For me,...

### HUM 100 - Genius - Pythagoras

1253 words - 6 pages Pythagoras was considered to be the world's first pure mathematician. Many European philosophers call him the father of philosophy. Various scientists will call him the father of science. To musicians, nonetheless, Pythagoras is the father of music. Pythagoras was also the founder of the Pythagorean School. According to researchers, very little information is known about him and his life. All that is known of him comes from what was recorded by...

## Similar Essays

### Calculus Essay

536 words - 2 pages Calculus "One of the greatest contributions to modern mathematics, science, and engineering was the invention of calculus near the end of the 17th century," says The New Book of Popular Science. Without the invention of calculus, many technological accomplishments, such as the landing on the moon, would have been difficult. The word "calculus" originated from the Latin word meaning pebble. This is probably because people many years ago...