Zhao Youqin's π algorithm

Zhao Youqin's π algorithm is an algorithm devised by Yuan dynasty Chinese astronomer and mathematician Zhao Youqin (赵友钦, ?

– 1330) to calculate the value of π in his book Ge Xiang Xin Shu (革象新书).

Zhao Youqin started with an inscribed square in a circle with radius r.[1] If

denotes the length of a side of the square, draw a perpendicular line d from the center of the circle to side l. Let e denotes r − d. Then from the diagram: Extend the perpendicular line d to dissect the circle into an octagon;

denotes the length of a side of hexadecagon similarly Proceeding in this way, he at last calculated the side of a 16384-gon, multiplying it by 16384 to obtain 3141.592 for a circle with diameter = 1000 units, or He multiplied this number by 113 and obtained 355.