The earliest records of mankind’s awareness of π are to be found among the Babylonians and Egyptians. Some four thousand years ago, they knew about π as the ratio of the circumference of a circle to its diameter.
The Babylonians gave the value of π as 25⁄8, while the Egyptians used (4⁄3)⁴, which works out to be 256⁄81. It is amazing that the Babylonian value is only 0.5% off the correct value of π, while the Egyptian estimate is 0.6% off.
Today, students in elementary schools routinely use the estimate of 22⁄7 for π, which despite its simplicity is only 0.04% off its correct value. This estimate is attributed to the great Greek mathematician and physicist Archimedes (287–212 BC). Yes, he is the one who ran naked in the streets and shouted “Eureka” after discovering the principle of displacement of water.
A more accurate approximation of π, but still a simple ratio, is 355⁄113. This gives π accurate to six decimal places.
π is also essential for calculating many properties of curved figures and objects:
Area of a circle = πR² (R is the radius)
Surface area of a sphere = 4πR²
Volume of a sphere = (4⁄3)πR³
Surface area of a hollow cylinder = 2πRH (H is the height of the cylinder)
Volume of a cylinder = πR²H
This simple number, π, has proven to be an extremely important universal constant that finds applications in many branches of mathematics, science, and technology, beginning with the simple circle and sphere.
At the other extreme of complexity, π also appears in one of Albert Einstein’s field equations for his theory of general relativity (1916), which describes mathematically how gravity arises from the curvature of space-time:
Rₐᵦ − ½Rgₐᵦ = (8πG⁄c⁴)Tₐᵦ
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