Archimedes computation of pi

What was discovered

Using inscribed and circumscribed 96-sided polygons, he proved that 3+10/71 < pi < 3+1/7. The first rigorous bounding of a mathematical constant and a model of algorithmic approximation.

Archimedes also showed that the area of a circle equals that of a triangle whose base is the circumference and whose height is the radius.

What it led to

• the calculations of pi by Liu Hui, Zu Chongzhi and al-Kashi
• infinite series for pi
• numerical analysis

Built on

• Method of exhaustion and theory of proportionsc. 370 BCE
• Eudoxus's method of exhaustion

Made possible

• engineering calculation of wheels, domes and circumferences

Links