# πr², but Books are Rectangular

Humans have long known that a special relationship exists between the diameter and circumference of a circle. As early as 2000 BCE, some had even found numbers to represent this relationship. By this date, the Babylonians knew that the circumference of a circle was always approximately 3 1/8 times larger than its diameter, while the Egyptians put the value at 4(8/9)2 (Beckmann 10). Hindu astronomy books known as the Siddhantas tell us that by 380 CE the Hindus had arrived at 3 177/1250, or 3.1416, as a constant value for the circumference/diameter ratio, and in the fifth century CE Chinese mathematicians determined that the constant must be greater than 3.1415926 and less than 3.1415927 (Beckmann 24-27). The Maya likely also knew of this ratio, and, given their sophisticated methods of calculation, had probably determined its value with a high degree of accuracy. However, it may be impossible to know for certain, as Diego de Landa, Bishop of Yucatan, burned most of the Mayas’ written records in the 1560s, believing that they were filled with “‘superstition and lies of the devil’” (Beckmann 33).

Although knowledge of the constant ratio between a circle’s circumference and its diameter—the ratio we now call “pi”—is ancient, the use of the Greek letter “π” to represent it is not. Use of the π symbol is usually dated to William Jones’ work Synopsis Palmariorum Matheseos: or, a New Introduction to the Mathematics, published in 1706 and shown above. After spending some time in the Royal Navy as the mathematics master on a man-of-war, Jones worked as an itinerant teacher and then private tutor in London, and later edited and published editions of several of Isaac Newton’s works. His Synopsis Palmariorum Matheseos consists of two major sections, the first dealing with “Numeral and Literal Arithmetick” and the second with the “Principles of Geometry.” Jones uses the π symbol several times throughout the second part, in both diagrams and equations. Although Jones is generally credited as the first to clearly set the letter π equal to the value 3.14 . . ., he may actually have borrowed this use of the π symbol from the writings of the astronomer John Machin, who had calculated π out to one hundred decimal places, and whose work Jones cites elsewhere in his Synopsis (Arndt and Haenel 166). Regardless of which man used the π symbol first, mathematicians adopted the symbol as standard only after the noted mathematician Euler used it in his writings, approximately thirty years after the publication of Jones’ work (Beckmann 141). BS

William Jones, Synopsis Palmariorum Matheseos: or, a New Introduction to the Mathematics. London: Printed by J. Matthews for J. Wale, 1706.

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Selected Bibliography

Arndt, Jörg, and Christoph Haenel. Pi –Unleashed. Trans. Catriona Lischka and David Lischka. Berlin: Springer, 2000. Print.

Beckmann, Petr. A History of Pi. 2nd ed. Boulder: Golem, 1971. Print.

McConnell, Anita. “Machin, John (bap. 1686?, d. 1751).” Oxford Dictionary of National Biography. Oxford: Oxford UP, 2008. Web. 13 March 2015.

Wallis, Ruth. “Jones, William (c.1675–1749).” Oxford Dictionary of National Biography. Oxford: Oxford UP, 2012. Web. 11 March 2015.