# William Jones: pi-man extraordinary

Collections / Exhibitions - Posted 13-03-2015

Tomorrow, the 14th of March will be Pi Day, celebrated on the same day every year since 1988. It has a particular resonance this year March 14, ’15, at 9:26:53 (corresponding to the first 10 digits of pi: 3.141592653).

The Greek mathematician Archimedes (*c*.287–212 BC) discovered formulae to calculate some of the properties of curved shapes like cones and spheres (in three dimensions) and circles (in two dimensions). All of these formulae make use of a very special number, whose value is slightly greater than 3. Archimedes knew its approximate value but, by today, we know that its value is the never-ending 3.141592…

About two thousand years later, William Jones (1674–1749), a self-taught mathematician from Anglesey, suggested using a special symbol to represent Archimedes’ number. This symbol, the Greek letter ? (pi), appears for the first time in 1706 in the book, *Synopsis palmariorum matheseos: or, a new introduction to the mathematics *by William Jones. A book written in English, despite the Latin title, which may be roughly translated as ‘A summary of achievements in mathematics’. The symbol ? appears in this book for the first time to denote the ratio of a circle’s circumference to its diameter. In Greek, ? is the first letter of the word for periphery (??????????) and ? is also the first letter of the word for perimeter (??????????). It is thought that one or the other influenced his choice of this particular symbol. William Jones was the first to realise that the decimal 3.141592 … never ends and that it cannot be expressed precisely. That was why he recognised that it needed its own symbol to represent it. In *Synopsis palmariorum matheseos*, Jones wrote that ‘the exact proportion between the diameter and the circumference can never be expressed in numbers.’

A local history society, based in Llanfechell, maintains a website http://www.cymdeithashanesmechell.co.uk/ that includes a short section on William Jones: http://www.cymdeithashanesmechell.co.uk/william_joness.html (the images, accessed 13.03.15, are clearer on the Welsh-language version of this page).

*Synopsis palmariorum matheseos*, together with other scientific books from the Library’s collection will appear in the exhibition, *The Secret Working of Nature, *which will be held at the Library from next July to the beginning of January to commemorate 350 years since the publication of *Micrographia *by Robert Hooke, a book published by the *Royal Society,* which was a trailblazer for the popularisation of science and the early scientific method.

*We are grateful to Dr. Gareth Ffowc Roberts, Professor Emeritus at Bangor University for providing text and photographs to create this blog, some of which comes from his Welsh language book, Mae Pawb yn Cyfrif pp. 65-75. Dr. Roberts, along with Dr. Rowland Wynne will be delivering a lecture at the National Library of Wales in October to coincide with the exhibition.*