22 July
PI APPROXIMATION DAY
Thanks to Pi Day, our readers are surely familiar with the number Pi. But have you heard about its approximation? If not, then read the article by Prof. Maciej Sablik from the Institute of Mathematics.
„Save the date” is a series of articles that have been written to celebrate various unusual holidays. The authors of the presented materials are students, doctoral students and employees of the Faculty of Science and Technology of the University of Silesia.
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The number π has been known since ever, or at least since a wheel has been invented. The symbol represents the ratio of circumference of a circle to its diameter and even the ancients knew that it is a constant value and equals to… 3? 3 and 1/8? 4^4/3^(4)? 355/113? 3.14? 22/7? Exactly: these are only a few rational expressions, all estimated, of course. Archimedes, when studying polygons inscribed in a circle, estimated the number π as a number between 3 and 10/71 or between 3 and 1/7. In recognition of his achievements, the number π is also called Archimedes’ constant. Ludolph van der Ceulen, a Dutch mathematician of German origin, used Archimedes’ technique and calculated 20-decimal value of π. He devoted the rest of his life to these calculations and later expanded the number to 35 decimals (in his calculations, he used a polygon of as many as 2^62 sides!). The value has been engraved on his tombstone in Leiden (the original tombstone has been lost, but its copy can be seen in one of Leiden churches transformed into a museum). Van der Ceulen lived between 1540 – 1610 and in his honour, π is still sometimes referred to as the “Ludolphine number”.
Nowadays, calculations of π are conducted with the use of computers. For example, in January 2020, Timothy Mullican calculated the number to 50 trillion decimals with the use of y-cruncher software. The calculations took 303 days, and the number alone took up approx. 281 TB of space.
All the estimates I have provided are rational numbers; in fact, π is an irrational number (it was proven by Johann Heinrich Lambert in 1761) and even a transcendental number, i.e. it is not the root of a non-zero polynomial of rational coefficients (a result of research by Ferdinand Lindemann from 1882).
In 1706, a Welsh mathematician William Jones introduced the symbol of π as an abbreviation of the Greek word περίμετρον, i.e. circumference. That symbol was later used by many mathematicians, but the use by Leonhard Euler in 1737 caused the Greek letter to become one of the most known in culture, science, and – and it should be emphasised – in the subculture. It is Euler to whom we owe the most beautiful Maths formula, i.e. 𝐞^𝐢π+𝟏=𝟎, combining the most important equations and constants in Maths.
In 1988, Larry Shaw introduced Pi Day which ever since that day has been celebrated in the USA, and later all around the world. The date 14 March is not coincidental as it is written as 3/14 according to the date format in the United States. As 𝘱𝘪𝘦 and π are homophones, a lot of pie contests happen there on that day. Since in Europe a different date format (DDMM) has been adopted, on 22 July (22/7) we celebrate Pi Approximation Day. It is one of the oldest approximations of the ratio of circumference of a circle to its diameter. To the elderly, 22 July might be also associated with the E. Wedel company (?!?), thus, we have a very pleasant reason for celebration. Since 2007, we have been celebrating Pi Day on 14 March at the Faculty of Science and Technology.
It is a shame that another important number, i.e. 𝙚, also known as Euler’s number, does not have its own day. But 𝐞≈𝟐,𝟕𝟏𝟖𝟐𝟖𝟏𝟖𝟐𝟖, and as one of my friends has noticed, in 1828, Lev Nikolayevich Tolstoy was born (9 September). Maybe we should establish E Day on 9 September, shouldn’t we?