Archimedes

= ﻿ ﻿Archimedes of Syracuse = =Born: c. 287 BC in Syracuse, Sicily = =Died: c. 212 BC during the Siege of Syracuse by a Roman soldier even though there were orders that Archimedes was not to be harmed. = == Archimedes was not only a naked man that ran through the streets yelling "Eureka!" but was also an extraordinary mathematician. He was known as "the father of integral calculus" and "the father of mathematical physics". ==

machines and pulley systems, and also possibly a water screw and organ . He discovered
== the relationship between the volume and surface of a sphere and Archimedes Principle. == == His principle on the circle is that the surface area of any sphere of radius //r// is four times that of its greater circle and the volume is two-thirds that of the cylinder in which it is inscribed. He also studied the value of pi as the ratio between the diameter and the circumference of a sphere. ==



==== Archimedes proved that the area enclosed by a parabola and a straight line is 4⁄3 times the area of a corresponding inscribed triangle. He came up with the solution to the problem as an infinite geometric sequence with the common ratio as 1/4:    ====

If the first term in this formula is the area of the triangle, then the second term is the sum of the areas of two triangles whose bases are the two smaller secant lines, and so on. This proof uses a variation of the series 1/4 + 1/16 + 1/64 + 1/256 +. . . which sums to 1⁄3.