where did the formula for area of a circle come from
Area of a circle Modern mathematics can obtain the area using the methods of integral calculus or its more sophisticated offspring, real analysis. However the area of a disk was studied by the Ancient Greeks. Eudoxus of Cnidus in the fifth century B.C. had found that the area of a disk is proportional to its radius squared.[1] Archimedes used the tools of Euclidean geometry to show that the area inside a circle is equal to that of a right triangle whose base has the length of the circle's circumference and whose height equals the circle's radius in his book Measurement of a Circle. The circumference is 2πr, and the area of a triangle is half the base times the height, yielding the area π r2 for the disk. Prior to Archimedes, Hippocrates of Chios was the first to show that the area of a disk is proportional to the square of its diameter, as part of his quadrature of the lune of Hippocrates,[2] but did not identify the constant of proportionality.
Fundamental theorem of calculus The first published statement and proof of a rudimentary form of the fundamental theorem, strongly geometric in character,[2] was by James Gregory (1638–1675).[3][4] Isaac Barrow (1630–1677) proved a more generalized version of the theorem,[5] while his student Isaac Newton (1642–1727) completed the development of the surrounding mathematical theory. Gottfried Leibniz (1646–1716) systematized the knowledge into a calculus for infinitesimal quantities and introduced the notation used today.