Happy birthday mister Einstein, happy Pi Day to you!

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Π Day is the day on which we commemorate Albert Einstein’s (1879-1955) birthday. Also, people celebrate the existence of $ \pi $ as today is 3/14, forming the first three digits (at least) of the number $ \pi $ in the American date format. Some Western European critics—on Twitter, for example—have stated one oughtn’t as ‘we, here’ simply do not use the American date format. Of course, nearly the whole rest of the world do not use the American date format—hence, ‘American’—but it hasn’t stopped cheerful people from all over that same rest of the world to celebrate and put mathematics into the limelight once a year.


Larry Shaw (1939-2017), the founder of Pi Day, at the Exploratorium in San Francisco

In 1987 or 1988, a physicist named Larry Shaw (1939-2017), while working at the Exploratorium, museum for science, art, and human perception, came up with the idea of celebrating the mathematical constants on March 14th. What started out as eating pie with just his colleagues, the event became public the next year. At 1:59pm, a time notation predominantly used in the US and the Commonwealth, forming (at least) the fourth, fifth, and sixth digits, a parade would be held with each visitor holding a digit of pi while eating pie and singing happy birthday to Albert Einstein. Larry was pleased to see the younger visitors loving the museum’s festivities, which, furthermore, include pi poetry readings, pi-kus (haikus about pi) and pi limericks, a pizza-dough tossing lesson, and eating it.

Hidden pis

(Grow up, it’s not even spelt right.) One of the most fascinating things about pi is that it tends to come up in places where you would least expect it. For instance, Albert Einstein and pi have a relationship. His general theory of relativity pivots around the following field equations:

\[ R_{\mu\nu}-\frac{1}{2}Rg_{\mu\nu}=8\pi GT_{\mu\nu}. \]

We won’t get into the details, but it’s pretty delightful that a theory describing one of the most fundamental forces in our universe, called gravity, would need the ever so humble pi.

A long string of digits has been incorporated into the calçada portuguesa thanks to mathematics teacher and current chair of Faro’s city council Rogério Bacalhau. Credits: @kjrunia, licensed under CC BY 4.0.

And this one is even cooler. Mathematicians wondered what you would get when you sum the following series of terms to infinity:

\[ \frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+\dots \]

The genius mathematician Leonhard Euler solved this Basel problem and found that the sum would converge to $ \pi^2/6 $. Even when a series tends to infinity, the ever so humble pi appears.

Speaking of ‘humble pi’, recently, a great book with this very title has come out by my favourite stand-up mathematician and YouTuber Matt Parker. I recommend it. It’s great. In this video, he is trying to approximate pi by using classical mechanics. Do have a look! Over the years, he made a whole bunch of cool and funny videos calculating pi. If you find yourself trapped in the algorithmic funnel that its inventors called YouTube, you’re welcome.

Screenshot of Matt Parker’s YouTube video in which he is calculating pi using a balancing beam.

One of the most fascinating places where pi pops up is where billiard balls bounce against each other and the cushion on the inner rail of a billiard table. Gregory Galperin at the Department of Mathematics of the Eastern Illinois University wrote a paper demonstrating how pi could be obtained in a jaw-droppingly awesome way.

The New York Times published a blog post about it in 2014 but not before the YouTube channel Numberphile—another favourite—had professor Ed Copeland explain it already in 2012.

Recently, however, the YouTube channel 3Blue1Brown published a video about it too. (Yes, the channel is also a favourite and I realise that I am using the word in a contradictory manner.)

It features a gorgeous simulation and is somehow very pleasing to the ears. Also, Grant Sanderson, the mathematician behind the voice and videos, does a great job of visually deciphering the language of the universe. Do have a look. He then gives the answer as to ‘but how’ and ‘why at all’ in a second video.

If you haven’t seen it, do support your chin firmly with your hand while letting the video play out as it may gravitate towards the centre of Earth, radially.

A screenshot of 3Blue1Brown’s video on calculating pi using collisions.

Photo of Larry Shaw: credits: Ronhip, licensed under CC BY-SA 3.0.
Photo of digits of pi in the Portuguese streets: credits: @kjrunia, licensed under CC BY 4.0.