Archimedes is considered to be one of the greatest mathematicians in history. Although, he was a well known and a great inventor with complex lever systems and mirrors designed to burn ships. He is mainly known for his contribution in the field of mathematics. His work had to do with volume of a sphere, Pi, and "The Method". All of his work leading to have small contributions in the creation of Calculus.
In his development of integration and calculus, he was attempting to find the value of Pi. "The area of any circle is equal to a right-angled triangle in which one of the sides about the right angle is equal to the radius, and the other to the circumference, of the circle"(Measurement of a Circle). So he decided to use a 96 sided polygon. He used the inside and outside of a circle to come up with 31/7. Which if simplified down equals 3.1429, in other words Pi. This was considered to be extremely accurate and precise. Today, we us Pi in all types of math problems and equations like finding Sine, Cosine, Tangent, but mostly finding areas and volumes of shapes.
The finding of the sphere and the cylinder was from a technique called Exhaustion. He also used that method to, "Calculate the area of an arc of a parabola". Archimedes later found out, "That the surface of any sphere is four times the greatest circle in the sphere"(On the Sphere and Cylinder, Book II) giving more contributions to
mathematics and geometry too. On certain shapes, he calculated the areas using his methods with formulas and Pi. For example, in his work called, " The Measurement Circle, Archimedes discovers the value of the square root of 3 as being more then 265/153 and less then 1351/780". Which approximately is 1.732 and 1.7320512. This becoming another one of his principles without an explanation as to how he did it.
Although, Archimedes didn't fully create calculus. He had contributions to some of its principles that it follows today. This principle was said to be called...