<P> Swiss scientist Johann Heinrich Lambert in 1761 proved that π is irrational, meaning it is not equal to the quotient of any two whole numbers . Lambert's proof exploited a continued - fraction representation of the tangent function . French mathematician Adrien - Marie Legendre proved in 1794 that π is also irrational . In 1882, German mathematician Ferdinand von Lindemann proved that π is transcendental, confirming a conjecture made by both Legendre and Euler . Hardy and Wright states that "the proofs were afterwards modified and simplified by Hilbert, Hurwitz, and other writers". </P> <P> In the earliest usages, the Greek letter π was an abbreviation of the Greek word for periphery (περιφέρεια), and was combined in ratios with δ (for diameter) 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.... </P> <P> 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 first appears there in the phrase "1 / 2 Periphery (π)" in the discussion of a circle with radius one . However, he 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 . </P> <P> 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 radius to periphery, 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 . </P>

Who is credited with first using the symbol for pi in what year
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