<P> 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 . 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 r 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 , but did not identify the constant of proportionality . </P>
<P> 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 . 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 r 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 , but did not identify the constant of proportionality . </P>
where did the formula for area of a circle come from
where did the formula for area of a circle come from
Archimedes
Archimedes