Somerset Times

Approximately Pi Day Today

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Somerset Times Edition

Week 2,
Term Three, 2016

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The 22nd of July every year is known by mathematicians in the know as π Approximation Day since π has a value of roughly 22/7. Writing it as a fraction implies that it is a rational number, which is not the case.

The exact value of π has never been determined as it is irrational and therefore goes on for ever without repeating. Currently, π is known to around 1013 decimal places and evaluating its digits remains the oldest of all mathematics problems, having been worked on since antiquity.

π is the ratio of the circumference (C) of a circle to its diameter (D) so to calculate the circumference of any circle we can use the equation,C = π D π is mentioned in the Bible 1 Kings 7:23 with a value of 3 although it was known by the Babylonians in 1900 BCE as 25/8 = 3.125 which is within 1% of the true value. The earliest method of calculating π was devised by Archimedes. He drew regular polygons both outside and inside a circle to compute an upper and a lower limit of the elusive number. He obtained an upper bound value of 22/7 and a lower bound value of 223/71 using 96-sided polygons. This value of 22/7 was subsequently referred to as the Archimedes constant.

In the Netherlands, in 1609, Ludolph Van Ceulen calculated π using the same method of polygons with 262 sides to obtain 35 digits. Van Ceulen was originally from Germany and until the 18th Century pi was still known in Germany as the Ludolphine number. On his grave, he had the 35 digits of pi engraved and this was the first scientific publication written on a tombstone. Unfortunately his tombstone was ‘lost’ and to right that wrong, the people of Leiden resurrected a replica as part of the Millennium celebrations in 2000. Elly Van Vliet, a Somerset parent, grandparent and staff member who hails from the Netherlands, recently tracked the tomb stone down at St Peters Church in Leiden.

Pi crops up in many areas of mathematics but unexpectedly, it even crops up in on the badge of an air force squadron. The 22nd RAF squadron has a pi symbol right in its centre and this is an acknowledgement of the squadron’s efforts in World War I, when they flew missions in France as part of the 7th Wing. As the pilots flew over the 7th Wing headquarters they would be literally 22 over 7. I am sure there would have been jokes about ‘pie in the sky’. The squadron was last active in 2015 in Anglesey in Wales as part of the air sea rescue operation and this was where Prince William worked as a pilot until recently.

Anglesey is coincidentally the home of William Jones, a mathematician who in 1706 recorded the first published use of pi in scientific literature. It is thought that he chose the Greek letter π to represent p for periphery. The symbol was popularised by Euler in the 18th Century but was not adopted universally until 1934.

The Somerset Mathematical Society celebrated Pi on March 14th (3/14) which is the official day of recognition, as legislated by the US congress. The next SMS celebration will be Phi (commonly referred to as the Golden Ratio) and will be held on Phiday August 5th at 5:05 in the SLC. Phi (Ф), like Pi is also irrational and the evening will be full of talks, tricks and more - including phi reciting. It is suitable for all ages and there are refreshments in the aftermath. I look forward to seeing you there.

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