section_path: History/Adoption of the symbol π
section_name: Adoption of the symbol π
paragraph_text: Adoption of the symbol π
  
  In the earliest usages, the Greek letter π was used to denote the semiperimeter (semiperipheria in Latin) of a circle and was combined in ratios with δ (for diameter or semidiameter) or ρ (for radius) to form circle constants. (Before then, mathematicians sometimes used letters such as c or p instead.) The first recorded use is Oughtred's " δ. π {\displaystyle \delta.\pi } ", to express the ratio of periphery and diameter in the 1647 and later editions of Clavis Mathematicae. Barrow likewise used " π δ {\textstyle {\frac {\pi }{\delta }}} " to represent the constant 3.14..., while Gregory instead used " π ρ {\textstyle {\frac {\pi }{\rho }}} " to represent 6.28....
  
  The earliest known use of the Greek letter π alone to represent the ratio of a circle's circumference to its diameter was by Welsh mathematician William Jones in his 1706 work Synopsis Palmariorum Matheseos; or, a New Introduction to the Mathematics. The Greek letter appears on p. 243 in the phrase " 1 2 {\textstyle {\tfrac {1}{2}}} Periphery (π)", calculated for a circle with radius one. However, Jones writes that his equations for π are from the "ready pen of the truly ingenious Mr. John Machin ", leading to speculation that Machin may have employed the Greek letter before Jones. Jones' notation was not immediately adopted by other mathematicians, with the fraction notation still being used as late as 1767.
  
  Euler started using the single-letter form beginning with his 1727 Essay Explaining the Properties of Air, though he used π = 6.28..., the ratio of periphery to radius, in this and some later writing. Euler first used π = 3.14... in his 1736 work Mechanica, and continued in his widely read 1748 work Introductio in analysin infinitorum (he wrote: "for the sake of brevity we will write this number as π; thus π is equal to half the circumference of a circle of radius 1 "). Because Euler corresponded heavily with other mathematicians in Europe, the use of the Greek letter spread rapidly, and the practice was universally adopted thereafter in the Western world, though the definition still varied between 3.14... and 6.28... as late as 1761.