## Monday, April 20, 2015

### Pi -- Part Four

In 1706, William Jones — a self-taught mathematician — published his seminal work, Synopsis palmariorum matheseos, roughly translated as “A summary of achievements in mathematics.”

It is a work of great historical interest because it is where the symbol “π” appears for the first time in scientific literature to denote the ratio of a circle’s Circumference to its Diameter. This is where the association of the Greek letter and the important ratio of circle measurements began.

Jones realized that the decimal 3.141592 … never ends and that it cannot be expressed precisely. “The exact proportion between the diameter and the circumference can never be expressed in numbers,” he wrote. That was why he recognized that it needed its own symbol to represent it.

It is thought that he chose π either because it is first letter of the word for periphery (περιφέρεια) or because it is the first letter of the word for perimeter (περίμετρος). (Or because of both).

The symbol π was popularized in 1737 by the Swiss mathematician Leonhard Euler (1707–83), but it wasn’t until as late as 1934 that the symbol was adopted universally. By now, π is instantly recognized by school pupils worldwide, but few know that its history can be traced back to a small village in the heart of Anglesey, an island off the north west coast of Wales.

William Jones was born in 1674 on a small holding close to the village of Capel Coch in the parish of Llanfihangel Tre’r Beirdd, north of the county town of Llangefni in the middle of the island.

When he was still a small child the family moved a few miles further north to the village of Llanbabo. He attended the charity school at nearby Llanfechell, where his early mathematical skills were drawn to the attention of the local squire and landowner, who arranged for Jones to go to London, where he was given a position as a merchant’s accountant. He later sailed to the West Indies, an experience that began his interest in navigation.

When he reached the age of 20, Jones was appointed to a post on a warship to give lessons in mathematics to the crew. Based on that experience, he published his first book in 1702 on the mathematics of navigation as a practical guide for sailing. On his return to Britain he began to teach mathematics in London, possibly starting by holding classes in coffee shops for a small fee. Shortly afterwards he published Synopsis palmariorum matheseos, a book written in English, despite the Latin title.

William Jones became friendly with Sir Thomas Parker, later the Earl of Macclesfield, and tutored the young George Parker, who was to become the second Earl. He later lived at the family home, Shirburn Castle, near Oxford, where he developed close links with the family. Through his numerous connections William Jones amassed at Shirburn an incomparable library of books on science and mathematics. He also maintained links with Wales, particularly through the Morrises of Anglesey, a family of literary brothers renowned for their cultural influences and activities who, although a generation younger than William, came from the same part of Anglesey and had strong London-based connections.

In the wake of publishing his Synopsis, William Jones was noticed by two of Britain’s foremost mathematicians: Edmund Halley (who had a comet named after him) and Sir Isaac Newton. He was elected a Fellow of the Royal Society (FRS) in 1711 and was vice-president of the society during part of Sir Isaac Newton’s presidency. William Jones became an important and influential member of the scientific establishment. He also copied, edited and published many of Newton’s manuscripts. In 1712 he was appointed a member of a committee established by the Royal Society to determine whether the Englishman, Isaac Newton, or the German, Gottfried Wilhelm Leibniz, should be accorded the accolade of having invented the calculus — one of the jewels in the crown of contemporary mathematics. Not surprisingly, considering the circumstances, the committee adjudged in favor of Newton.

In his will William Jones bequeathed his library of roughly 15,000 books together with some 50,000 manuscript pages, many in Newton’s hand, to the third Earl of Macclesfield. Some 350 of these books and manuscripts were written in Welsh, and this portion of the original library was safeguarded in about 1900 to form the Shirburn Collection at the National Library of Wales in Aberystwyth.

And so concludes my short expedition seeking the story of π. Whether these mathematical relationships are invented or discovered, we do owe the simple Greek letter all school children learn early in their mathematical careers to the Welshman of some fame.

The Welch term for “beauty,” is “harddwch.” And there’s beauty in that too, although I have no idea how to pronounce it. And so ends our journey through mathematics. May you find enlightenment and beauty in the story I’ve told.