Let’s pay our homage to π on Pi day which is celebrated around the world today on March 14 (3/14). To the uninitiated, that is π with two significant digits! It also happens to be the greatest scientist Einstein’s birthday! It was started by physicist Larry Shaw in 1988. Π is one of the select few numbers which has its own symbol and continuously tantalizes us by appearing in the most unexpected places! In 1737, the great mathematician Leonhard Euler popularized the symbol π . Many schools across the country hold fun events on this day. Let’s explore some of the reasons about what makes it so special but first some basics!
Understanding the nature of π
Π is an irrational number which means it cannot be expressed as a simple fraction and goes on forever (non-terminating), without repeating (non-periodic). In school, we sometimes use 22/7 for π but that is only for ease of calculation. It is a rational approximation and not really π! It is defined as the ratio of the circumference of the circle to its diameter.
The first 50 decimal digits of π are 3.14159265358979323846264338327950288419716939937510…. Even a cursory glance shows the randomness of the digits! On Pi day, many contests are held in which one has to recite the maximum number of digits of π from memory! The current Guinness World Record is held by Lu Chao of China, who, in 2005, recited a whopping 67,890 digits of pi!
Origins of the value of π
It is believed that the Babylonians between 1900-1680 BC were the first to approximate the value of π at around 3. In 1650 BC, mathematicians in ancient Egypt calculated the value using a formula to be 3.1605. In 287-212 BC, the first calculation by Archimedes was completed by using the Pythagorean theorem to be 3.142857. Around the 5th century AD, Indian mathematics made a five-digit approximation and Chinese mathematics approximated π to seven digits, both using geometrical techniques. The historically first exact formula for π, based on infinite series, was found in the 14th century- the Madhava–Leibniz series was discovered in Indian mathematics. In the 20th and 21st centuries, mathematicians and computer scientists combined new approaches with powerful computers, extended the decimal representation of π to many trillions of digits after the decimal point.
But why this obsession with π? It is just another irrational number!
As it turns out, it is observed in countless important and significant places in natural sciences and mathematics and rather unexpectedly at times! Here are a few samplings!
π in Mathematics
π in Physics
π in Nature
If we take the length of a natural river from start to finish and divide it by the straight path from start to finish, we get what is known as the Sinuocity. It measures how “bendy” a river is. In the 1990’s, Hans-Henrik Stolum published in a paper in science that the average sinuosity of all the natural rivers in the world should be π! Although, it is a daunting task to measure the Sinuocity of all-natural rivers in the planet, a study of rivers in Norway has shown this to be true!
There you have it! The exposition of why we celebrate π and why it continues to dazzle and amaze us! Perhaps by the next years event, you would have discovered many more instances where it appears magically. Till then – Happy Pi day!
(Pankaj Jha is the founder of makeageek.com. Having been educated in three continents- US, UK and India, he works closely with schools, teachers and students to help them achieve their very best. Views expressed here are personal)
Mar 14, 2019 16:09 IST
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