Algebra, Analysis, Geometry

Pi

A number that needs no introduction, π is an MVP when it comes to Maths. Many people have one on their shirts, even I’m thinking about getting a tattoo with it. Why? Cause people like π, it’s their connection to mathematics, beyond the mundane arithmetic of everyday life and let’s face it, it sounds sweet! For many, it’s their first introduction to infinity.

Pi, or π, is defined as the ration of the circumference of a circle to its diameter:

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This often leads to confusion among people because as I told you in an previous post, π is ‘irrational’, which means that it cannot be expressed as a fraction. The thing we need to remember is that a fraction has integer elements. But with π either the circumference or the diameter will be irrational. This is interesting and strange: it means that if you can write the value of the diameter, you will never be able to write the exact value of the circumference as a decimal, and vice versa.  It’s kinda hard to measure a circle, right? We don’t really have a circular ruler, do we?

The idea of π as a constant has been around for millennia. The Egyptians estimated it at 25/8 (or 3.125), while the Mesopotamians gave it a value of 3.162.

tabel pi

Archimedes was the first to examine π in depth. By drawing polygons both inside and outside the circle, and calculating their perimeters, he was able to estimate for π between 223/71 and 22/7, which is where the common aproximation of π as 22/7 comes from. Since Archimedes’ time the accuracy of π has been increasing, especially with the IT development for which we are thankful for billions of digits.

archimedes

The symbol of π was introduced by William Jones in 1706 in his book Synopsis Palmariorum Mathesios. However, π can also be represented as an infinite series of numbers. The Indian mathematician and astronomer, Madhava, produced the following series:

serie1

This can be used to estimate π, but it’s slow. The very famous Swiss mathematician Leonhard Euler used the series:

serie2

While another intersting series was given by John Wallis which he published in 1656. It starts off with:

serie3

Without drowning too deep into the mathematics, these series show some of the many properties of π; and perhaps this is the reason for its enduring appeal.

How’s π affecting your everyday life? Well think about the speedometer or how to calculate the volume of every tin can. 😉

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