Paragraph – Pi

 

Pi

The number π is a mathematical constant, the ratio of a circle’s circumference to its diameter, approximately equal to 3.14159. Being an irrational number, π cannot be expressed exactly as a common fraction, although fractions such as 22/7 and other rational numbers are commonly used to approximate π.  Approximate fractions include (in order of increasing accuracy) 22/7, 333/106, 355/113, 52163/16604, 103993/33102, and  245850922/78256779. The earliest known use of the Greek letter π to represent the ratio of a circle’s circumference to its diameter was by mathematician William Jones in his 1706 work Synopsis Palmariorum Matheseos; or, a New Introduction to the Mathematics. For most numerical calculations involving π, a handful of digits provide sufficient precision. According to Jörg Arndt and Christoph Haenel, thirty-nine digits are sufficient to perform most cosmological calculations, because that is the accuracy necessary to calculate the volume of the known universe with a precision of one atom. Many persons have memorized large numbers of digits of π, a practice called piphilology .In 1958 Albert Eagle proposed replacing π by τ = π/2 to simplify formulas. However, no other authors are known to use tau in this way. Some people use a different value for tau, τ = 6.283185… = 2π, arguing that τ, as the ratio of a circle’s circumference to its radius rather than its diameter, is more natural than π and simplifies many formulas. However this use of τ has not made its way into mainstream mathematics.

– Utsav Munendra