Special numbers can be found all over in the entire spectrum of mathematics. Constants have been derived from time to time to theorize a hypothesis. Each of them has been used to explain some natural phenomenon. Whenever I think about them it amazes me. Though nature is most appealingly described by poetry, it’s perhaps most accurately described by numbers. Among the various numbers that has mystified mathematicians and philosophers for ages, Pi surely has its own distinguished position.
The first time I heard about this number during my junior school geometry class, I was stuck by its unique property. The fact that one single constant can be used to define the ratio of the circle’s circumference to its diameter wasn’t something that I could accept. As a child, I began to wonder if it was really true. It was hard for me to believe that I can’t draw a circle that would not follow the Pi rule. However, as time passed, I made peace with myself. I began to acknowledge these amusing facts about nature. I started to believe that God do communicate with us through nature using these fascinating constants. Pi is ubiquitous in nature and you can find it in many and almost all of the natural phenomena.
We can see Pi in the disks of the moon and the sun. The double helix of DNA revolves around Pi. Pi is there in all the naturally occurring circles or semi circles like the arc of the rainbow, the pupil of the eye and even in the most appealing body parts. Pi is not only present in geometry, it is equally important for trigonometry and thereby the waves. We can’t communicate everyday without using Pi. Some of the most interesting transpirations of nature like the colors and music have Pi in its core. One of the greatest mysteries is how nature seems to know so much about numbers. It has used Pi even for defining tables of naturally occurring deaths, the Gaussian distribution of deaths in a population; that is, when a person dies, the event links to Pi. Here is link to one interesting result based on that.
There are many more interesting occurrences in nature that hold this unique constant. Albert Einstein, who was born on the Pi day, suggested that rivers have a tendency towards an even loopier path because the slightest curve will lead to faster currents on the outer side, which in turn will result in more erosion and a sharper bend. The sharper the bend, the faster the currents on the outer edge, the more the erosion, and the more the river will twist and so on. However, increasing the loopiness will result in rivers doubling back on themselves and effectively short-circuiting, creating an ox-bow lake. The balance between these two opposing factors leads to an average ratio of Pibetween the actual length and the direct distance between source and mouth. Therefore, under ideal conditions (uniform gentle slope on a homogeneously erodible substrate), the ratio between the actual length of a river and its straight-line from source to mouth length tends to approach Pi.
The greatest contribution that Pi perhaps made to history was the pyramids of Egypt. It is unknown how the builders of pyramids knew about this magical number. Even then they used it in their designs. The vertical height of the pyramid has the same relationship to the perimeter of its base as the radius of a circle has to its circumference.
Though Pi is present in nature defining many of its uniformity, it itself isn’t uniform at all. It is digits are as random as any number could be. No definite sequence has yet been discovered. Mathematicians have tried in vain to find some relation between its digits. The only few sequences that have been found are not that appropriate. Though it has not been proved, but Pi is considered as normal number i.e. all numbers of the same number of digits inside pi occur with the same frequency: 234 appears as often as 876, and 23,568 as often as 98,427. At position 763 there are six nines in a row. This is known as the Feynman Point.
In 1882, Lindemann proved that pi is more than just an irrational number. It is also transcendental, i.e. it is not the solution of any polynomial equation with integral coefficients. This means it is not possible to square a circle. In other words, it is not possible to draw (with straight edge, compass and pencil only) a square exactly equal to the area of a given circle. This problem was set by the Greeks two thousand years ago and was only put to rest with Lindemann’s discovery. It is also not possible to represent pi as an exact expression in surds, like root2, root3 or root7+root6/root7, etc.
It’s amazing to see how such randomness is being used to define things which are apparently pretty symmetrical (like music or colors). Does it mean that ultimately symmetries are formed out of randomness and chaos? Is chaos the ultimate order?? These questions are still mysteries to scientist and philosophers. I believe as time will pass, nature will slowly reveal all its numbers and help us understand it better. Till then we can continue to be amazed by the ones we got. Let’s salute the quest of mathematics and all the heroes who have dedicated their lives to cultivate it on this occasion of Pi Day!
Happy Pi Day to everyone. May your lives be ordered amidst all the chaos. Before I end I would like to provide the readers with a technique, which I learnt in some book, to remember the first few digits of this most wonderful number. Count the number of characters in each word of the following line.
How I want a drink, alcoholic of course, after the heavy lectures involving quantum mechanics!!
On a lighter note : Don’t forget to have some Pi(e) today!