The never-ending pi

March 14 is globally celebrated as Pi Day. You might have already encountered π, or you are surely bound to in the near future. In any case, it is a good idea to have a closer look at it!

It is that day of the year when we celebrate irrationality!

Irrational behaviour is almost always frowned upon. So if I were to tell you that the irrationality of something is a reason why it is celebrated everywhere, you might think I am irrational myself. But when you realise that I am talking about an irrational number, and among the most famous at that, you might begin to see what this is all about…

Try this yourself! Here’s a small activity to get things rolling. Pick that jar lid or your plate or even that CD that is no longer used (you got the idea… we are looking for something circular). Measure its diameter (the width across the centre of circle) first. Then using a tape or a string, wrap around the outer edge so that you can find out its circumference. When you divide the circumference by the diameter, the answer is always pi.

Know it? Or know it! Can you name the theoretical physicist mentioned in this article, born on this day in 1879? Send your answer to ganesh.a.s@thehindu.co.in with your details. [subject: pi] Last week’s answer Kjeldahl flask is the round bottom flask with a long wide neck that is used in the determination of nitrogen. Roshan. A. G. of class 7, Alphonsa Matriculation Higher Secondary School, Nagercoil was among those who got it correct. Congratulations!

If it was the exactness in chemical research that drew Johan Kjeldahl, the romance with pi for many has largely been due to its irrationality, giving it a certain mystique. Known to humans for nearly 4,000 years, pi is now known to over millions of digits. There are those who memorise thousands of digits, those who have written poems and books in Pilish (words have number of letters according to digits of pi) and those who apply it in math and science.

The popularity of pi can be attributed to the fact that it seems to be ubiquitous. It not only crops up with circles, spheres, arcs and pendulums, where it is expected, but also in places where there is no direct connection. The spiral of the DNA double helix, the ripples of light and sound, the shape of the universe and the pupil of our eyes are other places where it appears.

The river hypothesis And then in 1996, it was claimed in a paper that the average sinuosity of rivers around the world is pi. Sinuosity is the ratio of the river’s total length to the straight route from source to mouth as the crow flies and is an indicator of how bendy a river is. So straighter rivers have a sinuosity closer to 1, while there is no limit to how bendy it can get.

Albert Einstein, who incidentally was born on Pi Day in 1879, had used chaos theory and fluid dynamics to show that rivers have a tendency to bend into loops. Faster currents on the outer side of the river curve leads to more erosion, while soil deposits on the inside of the bend. This process continues and the bends become increasingly more wild until chaos leads the river to double back on itself.

So happens that this cuts the bend off on many occasions, forming an oxbow lake. This effectively lowers the sinuosity of the river as it suddenly becomes more straight. As a result, the true value of average river sinuosity is smaller than pi.

A crowdsourcing project that began as an attempt to substantiate the pi-hypothesis with regard to average river sinuosity now has data that suggests otherwise. After calculating 278 rivers, the average sinuosity was found to be 1.91, much closer to the golden ratio, or phi (1.62), another popular irrational number. In fact, pi/phi is 1.94…

As you digest all those pi facts, try and grab a piece of pie. And if you eat it at 1:59 p.m, you’ll end up with 3.14159!