Beautiful trigonometry

You would be forgiven if you had the misimpression that I don’t like trigonometry, because I hadn’t been clear, as I pointed out the very next day. I definitely do like trig.

In fact, I love trig!

To see one reason why you too might love trig, take a few minutes to watch the Numberphile video titled “Beautiful Trigonometry.” Trig is both beautiful and useful:

  • Useful, not so much for the “practical” reasons that we taught 50–60+ years ago, but as models of phenomena that rise and fall and rise and fall and rise and fall… There are so many such phenomena!
  • Beautiful, not so much because of triangles — despite the name trigono-metry, as the video points out — but because of circles.

To learn more about the beauties of trig, you should definitely read Trigonometric Delightsby Eli Maor. You will enjoy it, as I tell my students every year. Most of them roll their eyes. Some of them roll their eyes as soon as they see the title of the book. As you’ll notice from the image of the cover, there’s not a triangle in sight. And yet that’s the impression most people have of trig — not to mention the impression that it’s boring and difficult in their opinion.

Difficult, yes. Boring, no. But you can wrestle with difficult ideas and get a great sense of fulfillment from overcoming challenges, despite the sage advice of Homer Simpson: “If it’s too hard, don’t do it.”

Speaking of Eli Maor, his other books are also worth reading and enjoying. I’ve read five of them:

  • Beautiful Geometry (of course)
  • e: The Story of a Number
  • Music by the Numbers: From Pythagoras to Schoenberg
  • The Pythagorean Theorem: A 4,000-Year History
  • To Infinity and Beyond: A Cultural History of the Infinite

He also wrote one called Venus in Transitbut I don’t know anything about that one.

In any case, go watch the Numberphile video first:


Categories: Math, Teaching & Learning