| Pi Day 2025 - The Mystery Of Infinity |
| Written by Mike James | |||
| Friday, 14 March 2025 | |||
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Pi isn't infinite but it exemplifies the problem with allowing infinity into your life. Every year March 14 (3.14) is celebrated as Pi Day by π aficionados across the globe who can use it as a excuse to muse on all things transcendental - or just to eat pies. You may know that, or you may never have thought about it, that there are the infinities of the small and the infinities of the big. The big infinity is generally the one we tend to think of - here take this infinite stick. Arguably the more interesting infinity, however, is that of the small because to quote William Blake you really can hold an infinity in the palm of your hand - it's easy. Consider two points on a line, no matter how close they are together there is always another point between them. If there wasn't they would be the same point. What this means is that between any two points there are as many points as you care to think about. We say in short hand that between any two points there are an infinity of other points. This is the small infinity and yes you can hold it in the palm of your hand and as I said it is easy. So what has this got to do with Pi? The answer is that we, mathematicians in particular, associate each point on a line with a number that gives its distance from an arbitrary starting point - the origin. So if this is so between every pair of numbers no matter how close there is no only another number but an infinity of other numbers. This is the model of the "real" numbers and it leads directly to the question of how to write down such a number? The usual solution is to use an infinite sequence of digits to represent a real number and here we have the big infinity playing a part in the life of the little infinity. Pi is a number and it is defined as the ratio of the circumference of a circle to its diameter. Now consider a perfect circle, 1 unit in diameter D, and place it on a perfect plane. Now roll the circle along the plane without slipping - the distance travelled is exactly Pi and the point at the end of the travel is Pi units from the start. If you try to write this number down you will discover that it needs an infinite number of digits that never fall into a repeating pattern. The formula Pi times D picks out just one single point, but you can never finish writing down the number that picks that point out on the number line - it's a big infinity needed to pin down a point in a small infinity of points. Such numbers are known as irrational numbers and Pi is irrational. It is also a transendental number which roughly means that it isn't the solution to any finite equation. This in turn means that there is no finite equation that defines the point in question. Again the big infinity is needed to pin down the small infinity. Pi isn't infinite - but it does contain an infinite number of digits. On a lighter note, here's is a song composed to help you memorise the digits at the start of Pi - something that many π aficionados across the globe like to do to celebrate Pi Day.
Thre are many more things to say about Pi - see you next Pi day, or you can just look back over our coverage of this topic since 2012, plus some other related articles.
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| Last Updated ( Friday, 14 March 2025 ) |
