Circumference pi, is represented by the Greek letter . The first few decimal digits of the numerical value of are 3.141592653589793 ... Pi is defined as the ratio of a circle's circumference to its diameter : Or, equivalently, as the ratio of the circumference to twice the radius. The above formula can be rearranged to solve for the circumference: The use of the mathematical constant is ubiquitous in mathematics, engineering, and science. In "Measurement of a Circle" written circa 250 BCE, Archimedes showed that this ratio (, since he did not use the name ) was greater than 3 but less
Earth's circumference shadow on the ground. Using the length of the rod, and the length of the shadow, as the legs of a triangle, he calculated the angle of the sun's rays. This angle was about 7°, or 1/50th the circumference of a circle; taking the Earth as perfectly spherical, he concluded that the Earth's circumference was 50 times the known distance from Alexandra to Syene (5,000 stadia, a figure that was checked yearly), i.e. 250,000 stadia. Depending on whether he used the "Olympic stade" (176.4m) or the Italian stade (184.8m), this would imply a circumference of 44,100 km (an error of