Angles in Our Midst

Matt Parker is a mathematician who does comedy. Or a comedian who does math. It’s as eccentric a combination as you’re likely to find, but the amazing thing about his new book, Love Triangle: How Trigonometry Shapes the World, is that he managed to find over 50 other people to join him in the math. And the comedy.

The purpose of Love Triangle, the author says, is to show that mathematics can be found in, and even defines, an endless number of the activities of everyday life—and that fact, he insists, is delightful. The book moves through the ways triangles appear all around. So, for example, he starts with something as easy as determining the height of a building from its shadow using the Pythagorean theorem we all learned in school.

But the complexity increases as the book goes on, from simple geometry to the trigonometry needed for something like identifying secret spy satellites from features in leaked photographs. Eventually we get to Fourier series and even quantum mechanics—since Parker, sounding like the ancient Greek mystic that Pythagoras was, proclaims, "Triangles are everything, and everything is triangles."

Parker wants everyone to see the beauty in mathematics, and he enlists his fellow eccentrics to speak with him about the triangles of their professions, from college professors to professional pool players, race-track operators to engineers. Part of the point of all these conversations is Parker’s notion that mathematics is not a solitary pursuit. But even more they demonstrate that Parker, an eccentric himself, attracts unique individuals into his orbit because of his infectious enthusiasm and quirky humor.

For instance, Tim Chartier, a sports analyst and statistician, gave Parker access to the NBA database for "all 4,678,387 shots taken during NBA games between 1997 and 2022." In discussing how the Pythagorean theorem can be used to calculate the distance between two points, he found that players make the same 1.12 points-per-shot average by standing just outside the three-point-line as they do by standing only 2 feet and 2 inches from the hoop. Along the way, he also discovered that some shots were mislabeled. The database has since been corrected, and Parker proudly claims to have added "some three-point shots to the NBA database."

Vincent Gallo, a retired software developer who "did a Ph.D. in bees," also pitched in to indulge Parker’s awe at honeycomb structures. The laying of wax into three-dimensional hexagonal shapes (called rhombic dodecahedrons, Parker delights in telling us) does not derive from the designs of genius bees. It comes from the equalizing of pressures from adjacent circular cells—and Parker is disappointed that bees are not the math-gods that he hoped for, since the rhombic dodecahedron is actually less efficient, using more wax for the same internal volume than as the more optimal truncated octahedron that a human mathematician would recommend. The bees, he finds, "have merely evolved a good-enough solution."

It isn’t until we meet Mark Bowler, a primate specialist, that Parker discusses Fourier series, his true love. The technique developed by the French mathematician Joseph Fourier (1768–1830) breaks complex signals down into a summation of discrete simple sine or cosine waves. With the help of Fourier series, Bowler tracks primate populations by identifying the unique sound signatures of each member. Parker, of course, had a different idea: He said his name aloud and mapped the sound waves using a spectrometer, so that he would have a "fun-but-tedious way" to "sine" his name. (He also, less forgivably, gives us the page numbers of Love Triangle as the sine of the page number in degrees, down to the millionth-decimal place.)

Part of what makes Love Triangle so enjoyable is that Matt Parker isn’t really writing it for us. He wrote it for himself. Sure, the Australian-born comedian living in the United Kingdom wants everyone to appreciate what he calls "maths" in the same way as he does, but Love Triangle is mostly an expression of his inner weirdness.

His earlier works, Things to Make and Do in the Fourth Dimension: A Mathematician’s Journey Through Narcissistic Numbers, Optimal Dating Algorithms, at Least Two Kinds of Infinity, and More (2015) and Humble Pi: A Comedy of Maths Errors (2019), were littered with selfies, sketches, and silly additions. And so with Love Triangle. Following his comically useless index, the phrase "Standard Triangle Language," for example, may be found by moving from the bottom-left corner of page 0.987688 a distance of 1.435 times the page width at an angle of 60.8 degrees counter-clockwise from the horizontal axis. Other such entries as "bit surprising, a" and "ran his code" can also be found and are just as useless. It ought to be annoying, but, like so much that Parker does, it adds to the funniness and quirkiness of the whole project.

However much Parker loves triangles, he’s wrong that we "are built of triangles" and that "reality is triangles." Yes, we can break complex solid objects down into models built from simple triangles, to approximate the ways in which they behave. And yes, we can describe the world with quantum mechanics, which is related to waves, which are related to sines and cosines, which are related to triangles. But to conclude from all this that the universe is triangles all the way down is as overstated as a Pythagorean notion that the universe is music all the way down. But, then, a lot of comedy runs on overstatement. And because Matt Parker is a comedian, we let him get away with it.

Love Triangle: How Trigonometry Shapes the World
by Matt Parker
Riverhead Books, 352 pp., $30

Matthew Phillips completed his doctorate in aerospace engineering at North Carolina State University this semester. He lives in the Triangle of North Carolina.

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