This Demonstration gives Newton's approximation of
based on calculating the area of a semicircle using an integral.
under the arc
(light blue) is equal to the area of the sector
minus the area of triangle
(light green), that is,
On the other hand, the semicircle has equation
to 16 decimal places using 20 terms of the binomial series [1, p. 177].
 W. Dunham, Journey through Genius
, New York: Penguin Books, 1990 pp. 174–177.