Funding for this project generously provided by Overdeck Family Foundation

1706

### Jones's Use of the Symbol π

π gets its symbol

The Greek letter π (pi) was originally used as an abbreviation for the Greek word for "periphery" and combined with the Greek letter δ (delta; for diameter) or ρ (rho; for radius) to indicate relevant dimensions of a circle. William Oughtred made the first known use of such a notation (π/δ) to indicate the ratio of circumference to diameter in 1647, and Barrow and Gregory used similar notations (π/δ for 3.14… and π/ρ for 6.28, respectively). The first known use of the symbol π on its own to mean 3.14… was published by William Jones in 1706. This notation was universally adopted following advocacy by Euler, though disagreement on the convention of π = 3.14… vs. 6.28… persisted at least until 1761.

Self-taught Welsh mathematician William Jones published Synopsis Palmariorum Matheseos (A New Introduction to the Mathematics) in 1706. Page 263 of that work contains the earliest standalone use of the symbol π to denote the ratio of a circle's circumference to its diameter 3.14…. Interestingly, page 243 uses the same symbol to refer to twice that value, or 6.28…, so it appears Jones suffered from the same difficulty in deciding between those two conventions that persisted for more than 50 years subsequently.

Artifact dimensions

Artifact origin

Wales, United Kingdom

### Additional Reading

• Arndt, J. and Haenel, C. The Symbol Pi. In Pi Unleashed. Berlin: Springer-Verlag, pp. 165–166, 2001.
• Beckmann, P. A History of Pi. New York: Barnes and Noble, p. 145, 1993.
• Berggren, J.; Borwein, J.; and Borwein, P. "William Jones: The First Use of π for the Circle Ratio." In Pi: A Source Book. New York: Springer-Verlag, pp. 108–109, 1997.
• Cajori, F. § 395–398 in A History of Mathematical Notations: Two Volumes Bound as One, Vol. 2. New York: Dover, pp. 9–13, 1993.
• Jones, W. Synopsis Palmariorum Matheseos: Or, a New Introduction to the Mathematics: Containing the Principles of Arithmetic & Geometry, etc. London: Printed by J. Matthews for Jeff Wale, 1706.