Marc Chamberland: Why π is important

On March 14, groups across the country will gather for Pi Day, a nerdy celebration of the number Pi, replete with fun facts about this mathematical constant, copious amounts pie, and of course, recitations of the digits of Pi. But why do we care about so many digits of Pi? How big is the room you want to wallpaper anyway? In 1706, 100 digits of Pi were known, and by 2013 over 12 trillion digits had been computed. I’ll give you five reasons why someone may claim that many digits of Pi is important, but they’re not all good.

Reason 1
It provides accuracy for scientific measurements

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This argument had merit when only a few digits were known, but today this reason is as empty as space. The radius of the universe is 93 billion light years, and the radius of a hydrogen atom is about 0.1 nanometers. So knowing Pi to 38 places is enough to tell you precisely how many hydrogen atoms you need to encircle the universe. For any mechanical calculations, probably 3.1415 is more than enough precision.

Reason 2
It’s neat to see how far we can go

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It’s true that great feats and discoveries have been done in the name of exploration. Ingenious techniques have been designed to crank out many digits of Pi and some of these ideas have led to remarkable discoveries in computing. But while this “because it is there” approach is beguiling, just because we can explore some phenomenon doesn’t mean we’ll find something valuable. Curiosity is great, but harnessing that energy with insight will take you farther.

Reason 3
Computer Integrity

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The digits of Pi help with testing and developing new algorithms. The Japanese mathematician Yasumasa Kanada used two different formulas to generate and check over one trillion digits of Pi. To get agreement after all those arithmetic operations and data transfers is strong evidence that the computers are functioning error-free. A spin-off of the expansive Pi calculations has been the development of the Fast Fourier Transform, a ground-breaking tool used in digital signal processing.

Reason 4
It provides evidence that Pi is normal

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A number is “normal” if any string of digits appears with the expected frequency. For example, you expect the number 4 to appear 1/10 of the time, or the string 28 to appear 1/100 of the time. It is suspected that Pi is normal, and this was evidenced from the first trillion digits when it was seen that each digit appears about 100 billion times. But proving that Pi is normal has been elusive. Why is the normality of numbers important? A normal number could be used to simulate a random number generator. Computer simulations are a vital tool in modeling any dynamic phenomena that involves randomness. Applications abound, including to climate science, physiological drug testing, computational fluid dynamics, and financial forecasting. If easily calculated numbers such as Pi can be proven to be normal, these precisely defined numbers could be used, paradoxically, in the service of generating randomness.

Reason 5
It helps us understand the prime numbers

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Pi is intimately connected to the prime numbers. There are formulas involving the product of infinitely numbers that connect the primes and Pi. The knowledge flows both ways: knowing many primes helps one calculate Pi and knowing many digits of Pi allows one to generate many primes. The Riemann Hypothesis—an unsolved 150-year-old mathematical problem whose solution would earn the solver one million dollars—is intimately connected to both the primes and the number Pi.

And you thought that Pi was only good for circles.

SingleMarc Chamberland is the Myra Steele Professor of Mathematics and Natural Science at Grinnell College. His research in several areas of mathematics, including studying Pi, has led to many publications and speaking engagements in various countries. His interest in popularizing mathematics resulted in the recent book Single Digits: In Praise of Small Numbers with Princeton University Press. He also maintains his YouTube channel Tipping Point Math that tries to make mathematics accessible to a general audience. He is currently working on a book about the number Pi.

Tipping Point Math Tuesdays with Marc Chamberland: How many guards are enough?

Today’s Tipping Point Tuesday gives us a behind the scenes look at how mathematics can be used in unique ways in the workplace.

Here’s the scenario: In busy museums, guards keep an eye on the priceless works of art. Suppose a museum wants to schedule the fewest number of guards per museum shift without leaving any art display unmonitored. Marc Chamberland explains how a museum manager could use mathematics to calculate the ideal number of guards per shift.

Continue exploring numbers with Chamberland in his book, Single Digits: In Praise of Small Numbers. Start by reading the first chapter here.

Tipping Point Math Tuesdays with Marc Chamberland: What’s the Pizza Theorem?

For the inaugural Tipping Point Math Tuesday, let’s find the math in something everyone loves, Pizza!

Have you ever opened your takeout pizza box and found that the slices were not cut evenly? What’s a party host to do? Marc Chamberland, author of Single Digits: In Praise of Small Numbers shows how mathematics can help you use the pizza theorem to evenly divide a pizza among yourself and your hungry friends:

 

Craving more math? Preview the first chapter of Chamberland’s book here.

Q&A with Marc Chamberland, author of Single Digits: In Praise of Small Numbers

Marc Chamberland is the Myra Steele Professor of Natural Science and Mathematics at Grinnell College. He is also the creator of the popular YouTube channel Tipping Point Math, which strives to make mathematics accessible to everyone. Continuing on his mathematics mission, Marc Chamberland has authored Single Digits: In Praise of Small Numbers, a book that looks at the vast numerical possibilities that can come from the single digits. j10437Over the course of the coming weeks, we will be exploring the single digits in real life math situations with the author himself by featuring a series of original videos from Tipping Point Math.

Recently Chamberland gave the press a look at the inspiration behind the book, along with some personal insights on being a mathematician, and more:

What was the motivation behind your Tipping Point Math website?

MC: I have long felt that many people are sour on math because they think it is all technical stuff that leads to nowhere. I felt that if they could be exposed to the rich ideas and beauty of mathematics presented in an interesting way, their negative opinion could change.

I had wondered for a while how YouTube could be used since it is such a popular medium. In 2013, I reconnected with Henry Reich, a former student of mine, who created the highly successful channels MinutePhysics and MinuteEarth. With his inspiration and advice, I was convinced that a similar channel for mathematics was possible. Thus the concept of Tipping Point Math was born.

What is the biggest misunderstanding people have about your mathematics profession?

MC: Besides my remarks about people thinking that math is only about technical stuff, there is also the misconception that all of mathematics is known. This is not the case at all. New mathematics is being developed every day. This ranges from very abstract ideas to applications such as signal processing, medical imaging, population modeling, and computer algorithms.

What would you have been if not a mathematician?

MC: In my last year of high school, I developed an unquenchable thirst to explore two academic areas: mathematics and music. Since I eventually became a mathematics professor, I suppose one could say that mathematics “won”. But music was also consuming. I would ask myself, “Why does that piece of music sound so good? Why does it produce particular emotional states? How can I compose music that affects people in different ways?” To this day I still ask some of these questions, I occasionally compose short pieces, and I play the piano, guitar, and sing. Would I have been a musician? Is it too late to change?

What are you reading right now?

MC: I’m reading “The Alchemist” (by Paulo Coelho) out loud to my wife. The simple language and overflowing spirituality is stunning.

Who do you see as the audience for your book, Single Digits?

MC: My audience: those who love beauty. I did not choose topics for their depth or their technical superiority. I principally chose vignettes that I thought are beautiful.