National Pi Day: A slice of Pi?

3.141592…. and so on. Perhaps the most famous of mathematical constants, Pi dates all the way back to the ancient Babylonians.

Pi is a funny old thing and it is what mathematicians call an irrational number, albeit a perfectly reasonable one. The digits of Pi continue without repetition forever, that means that you are always writing down an approximation, no matter how many digits you calculate it to. In fact, that is why we use the Greek letter.

In essence it is the ratio of a circle’s circumference to its diameter. In non-mathematical speak, take any circle and divide the length of its circumference by its diameter and you will always get Pi.

Fine, it’s got something to do with circles but what use is it in the real world?

The thing about nature is that circles and arc length (a portion of a circle’s circumference) appear everywhere. For example, take the simple pendulum that swings back and forth, like the one in a Grandfather Clock.

The pendulum traces a portion of a circle (an arc) as it moves and it turns out that, for low angles of swing, the time that it takes to swing back and forth involves Pi. This is called Simple Harmonic Motion, a concept any Physics student would have come across.

In fact, it transpires that Pi appears in some of the great equations of physics that describe how nature works. It can be found in General Relativity, Electromagnetism, Quantum Mechanics and Cosmology. This means that Pi really is at the very heart of nature.

Pi can also be found in the fields of engineering, electronics, statistics and probability. It is used in drawing, machining, radio, TV, radar, telephones, aerospace and so much more.

History of Pi

Although approximations of Pi date back to as early as 1900 BC, the first recorded method is that of Greek mathematician Archimedes. In around 250 BC Archimedes proceeded to trap a circle between two polygons. He could then calculate the perimeter of the outer polygon and inner polygon, meaning the value of the circumference is somewhere between the two. Adding more sides to the polygons gave a better approximation. Repeat until you’re exhausted!

Approximations for Pi entered a new phase during the 16th and 17th centuries as Mathematicians developed the infinite series technique. Here you add a series of numbers that follow a pattern together, the more of the pattern you add the better the approximation. Below is the Leibniz formula for approximating Pi. Spot the pattern!

As a nod to a couple of my old Professors, a personal favourite of mine from this period was not actually aimed at approximating Pi, but at solving another problem. Like someone crashing your party, Pi turned up out of nowhere. The work done on this led to something called the Riemann Zeta Function and you can still earn yourself a nice cool $1,000,000 prize for solving a connected problem, the Riemann Hypothesis.

The modern quests for better approximations of Pi have arisen with the advent of modern computing. By 1949, using a desk calculator, D.F.Ferguson and J.Wrench had calculated Pi to 1,120 decimal places. This was quickly surpassed by the use of the first computer and the number of decimal places has been rising ever since. The number of decimal places that Pi has been calculated to, as of 11th November 2016, stands at a staggering 22,459,157,718,361. Wow!

Some fun facts

• If you write 3.14 as a mirror image, you spell out PIE

• Pi Day is on the 14th March. As an American date that is 3.14
• Albert Einstein was born in 1879 on 14th March
• The symbol was first used in print by William Jones in 1706
• The State of Indiana nearly passed a law which would have made Pi equal to 3.2 (Frankly ridiculous! Pi is Pi)

Pi in pop culture

• The book “Life of Pi” by Yann Martel, which also became a hit Hollywood movie
• Cult psychological thriller released in 1998, titled “Pi”
• In the Simpsons episode “Bye Bye Nerdie”, Professor Frink, in a desperate attempt to get the attention of an excited mob of scientists at a conference, shouts “Pi is exactly 3”. The stunned scientists fall silent and Professor Frink apologies, “I am sorry it had to come to that!”
• FBI agent, Robert Martz, misstated the value of Pi during the O.J. Simpson trial. This subsequently undermined his value as a witness

And finally

A short mnemonic can be used to remember the first 7 digits of Pi. Count the letters in each word in the following sentence, the length of each word represents a digit of Pi. “How I wish I could calculate pi”. And so we come full circle! 3.141592….