Happy Pi Day!
today is the high holy day for math nerds
This issue has many photos, so your email client may not handle it well. You can also read it at the Substack website.
Today is π Day!
In the US, where we tend to write dates in a month/day format, instead of a day/month format, today is written as 3/14 or 3.14.
The mathematical constant, π, has a value of approximately 3.14, so today is celebrated by math nerds everywhere as π day. Here is a page with 19 (a prime number, naturally) π Day memes.
I can only speak for myself, of course, but I suspect that people who truly love mathematics are so used to being weird in this respect that one reason why π Day took off as a meme is simply that it’s an excuse to geek out with minimal fear of social repercussions. That’s certainly a major reason why I love π Day!
But today I’m going to talk about more than π — I’m going to talk about the Unit Circle, which was a big part of what made me fall in love with mathematics.
What is π?
π is the ratio of a circle’s circumference (the measure of the perimeter—the distance fully around the outside of the circle) to its diameter (the distance from one side to the other; the line you would draw to cut a circle precisely in half).
This graphic is from the Math is Fun site, which I enjoy and recommend.
π is infinite, and memorizing the digits of π is a frequent arena for memory prodigies. Calculating more and more digits of π is also a constant pursuit of nerdy mathematicians who also program computers.
π is useful in matters of cybersecurity, as well as turning up in nature and many patterns of life, so it’s easy to answer the questions all math teachers and tutors are accustomed to answering regularly: “When am I ever going to use this?” and “Why should I care?” and “What relevance does this have to my life?”
π is also quite beautiful. Here is one of my favorite pieces of art, where some clever folks assigned a different shade to each digit, 0 to 9, and had a computer draw π.
The true and rightful President of the United States, Dr. Roller Gator, sent me a wine bottle with over a thousand digits of π as a graduation present:
And it makes for very cute decorations, from 3-D printed models to bookends:
The Unit Circle
The unit circle is used to teach trigonometry. It’s a circle with a radius of 1, which means its circumference is exactly 2π, as the formula for the circumference of a circle is: C = 2πr.
With the unit circle being 2π radians, the area of the unit circle is exactly π, as the formula for area of a circle is A = πr2 .
The angles of the circle are divided into radians, a way of measuring circles besides the more familiar degrees, and each angle has an (x, y) point on the usual (x, y) plane that gives you the (cosine, sine) of each angle.
For example: a 90 degree angle is one quarter of 2π, or half of π, which is why it’s written as π/2. It’s found at (0, 1) on the plane because its cosine is 0 and its sine is 1.
Or look at the 135 degree angle. A 135 degree angle is three quarters of the top half of the circle, so three quarters of π, which is why it’s written as 3π/4.
The other four major trigonometric values (tangent, secant, cosecant, and cotangent) are all easy to figure out if you have the sine and cosine. I memorized the entire unit circle and all the other trigonometric values for each angle, which was a major reason why I did well in calculus. It saved an enormous amount of time (and potential mistakes) to have fluency in my thinking between radians and degrees, and thus never need to derive any of those values, having absorbed them through constant repetition.
The Unit Circle is also ideal fodder for awesome math nerd decoration:
I’ve written before about how π helped me, as a little kid, to appreciate mathematics, and how mathematics being dependable and reliable was part of what helped me survive an unusually bad childhood.
The summer before I started college, when I was still trying to decide if it was worth the risk—since if I tried and failed to earn a degree in mathematics, I would have a nanny’s earning power with a mathematician’s level of debt—I spent upwards of ten hours a day on Khan Academy and other websites, working to remedy my “education” in a church basement. I have since lost it in a fire, but there was one used textbook I had ordered online for practice that had a fantastic explanation of the Unit Circle. It showed how this one neat construct taught many concepts at once and offered eager students a way to make rapid progress in their understanding by simply absorbing all it had to offer.
I’ve never quite understood why, but something about the unit circle is what made mathematics “click” for me. π was part of it, to be sure, and my previous love for π helped, but there was something more there.
I’ve thought about this a lot, and have in no way understood all of it, but part of it was this: the unit circle gave me a concrete way to take the trigonometric relationships, which I was starting to look for in the world around me, and frame them into a way of seeing physical reality. I started to learn the mathematical terms and ideas in a deeper way, a way that really used them to describe the world. That was part of what made this funny to me when I bought it to decorate my apartment:
Why I Love Mathematics
I’ve written about mathematics so much that I’m a little surprised any of you normies still read me, ha! But just some of my reasons are:
Mathematics is dependable and reliable. 2 + 2 = 4 and not 5, no matter how hard the Woke brigade may try to shatter the ability of people, especially children, to trust it.
The politics around women in mathematics has helped me clarify my own values and embrace both personality responsibility and realism.
Prime numbers are a particular fascination and love of mine, for reasons both big and small.
My take on Common Core mathematics has led to my doing a lot of tutoring, much of it for free, to help families who might otherwise not be able to homeschool.
I love tutoring. If teachers weren’t required to do Woke indoctrination of students, I would likely be a teacher. I’m tutoring a dyslexic teenage boy at present, and the light bulb moments he has during our work together provide me with enlightenment of my own.
If any of you non-math-nerds read this far, thank you! I am honored you indulged me and thank you for helping me celebrate this high and holy day for math nerds of all kinds.
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Wish could make a real pie for the festivities! I emailed you a couple though. Pies are the first thing I made on my own before attending pastry school many many years ago.
The concept of a prime number sounds lonely. Only two factors. Almost alone. Perhaps they keep company with the other primes, together in their rarity. "Hey, I know what it's like." Or perhaps its a badge of honor. They are each singular, after all.
Hi Holly:
I am an attorney and teach law and criminal justice at a community college, and have been practicing law for 28 years. However, my BS is in physics and mathematics and I, too, find the unit circle strangely comforting, even after all these years. I will still occasionally sketch it out and put all the coordinates in place just to see if I can do it.
I will also occasionally calculate the distance from home plate to second base on the baseball diamond. I had first learned it in a book about baseball as just a statement of fact, but later learned how to calculate it given the known distances between the bases.
I enjoy your writings, even the articles about math. Happy Pi Day!
Greg Perry