This weekend will be full of Pi all over. For those of you that don’t know I have organized another event on Facebook: Pi Love, where I invite people to share their love of this day in any way they like.
Today I will talking about some historically interesting facts about Pi and then tomorrow will be a more funny chill day. So let us get to the facts:
- From a Babylonian tablet of sunbaked clay found in 1936 at Susa it appears that, besides the approximation 3, the Babylonians also used the value 3.125;
- In the Rhind Papyrus of old Egypt, we find a solved problem that states that the area of a circle of nine length units in diameter is the same as the are of a square whose side is eight units of length, which gives π=3.16049…;
- The early Greeks also began with a π = 3 for everyday use, but for matters more serious they evolved other values such as π = √10 = 3.1622…;
- The most important contribution of the early Greeks to our knowledge of π is the “method of exhaustion” attributed variously to Antiphon, Euclid and, more likely, to Eudoxus;
- In the 2nd century BC, Hipparchus computed an extensive table of chords and proposed the value π = 3.14166, which is correct to 3 decimals, a remarkably good approximation for that time;
- The following quote from an extant part of Archimedes’ book On the Measurement of the Circle:
The ration of the circumference of any circle to its diameter is less than 3 1 ⁄ 7 but greater than 3 10 ⁄ 71.
- In India, we have the following values for Pi: π = 3.1416… (Aryabatha, 499), π = √10 = 3.1622… (Brahmagupta, born in 598) and π = 3.14156… (Bhaskara, born in 1114), all of them without any extra explanations;
- In China, Liu Hui in 263 AD published the limit 3.141024… < π < 3.142704…;
- An interesting value was suggested by the astronomer Tsu Chung-chih ( 430 – 501 ): π = 3.1415929…, which is correct to six decimal places and was not to be bettered in Europe until the 16th century, more than a thousand years later;
- Fibonacci, calculated the value π = 3.1416818… , correct to three decimal places;
- In Persia, Jamshid Masud al-Kashi in 1424 found the value π = 3.141 592 653 589 793 25…, which is correct to sixteen decimal places;
- Ludolph van Ceulen – a fencing master teaching arithmetic, surveying and fortification at the engineering school at Leyden in Holland – in 1596 gave 20 decimals of π, followed by 32 decimals publish posthumously in 1615, and 35 decimals published in 1621 by his pupil Willebrord Snel. Van Ceulen’s accomplishment so impressed his contemporaries that π was often called the Ludolphine constant;
- The 1st to devise an infinite product for π was the French mathematician Francois Viete;
- In 1655, John Wallis found the first expression for π as a product of rational numbers;
- Everything escalated after finding the series expansion of the arctan function in 1670 by the Scottish mathematician – astronomer James Gregorie and, independently, by Gottfried Wilhelm von Leibniz in 1673;
Hope you enjoyed this small journey (interesting facts) about the journey of finding as many decimals as possible, though that is a little impossible. Don’t forget about the event and also let me know what is the most interesting thing you know about Pi? Comment down bellow.
Don’t forget that maths is everywhere! Enjoy! ~LThMath