Degrees vs. Radians

While re-exploring and relearning much of Geometry this year to teach it to my high school students, I myself wondered why we learn and use radians. This post captured my attention and is really interesting and insightful. Thanks Ben for the awesome work!

Math with Bad Drawings

An Open Letter to Students Wondering, “Why Do We Use Radians Instead of Degrees?”

Dear Student,

Let me start with a question of my own. Did you know that you speak Babylonian?

You may not think that you do – you can’t ask for directions to a Babylonian bathroom, or order lunch off of a Babylonian menu, or ask a good-looking Babylonian out for coffee. But you’ve inherited Babylon’s legacy nevertheless.

You’ve probably noticed that our systems of counting and measuring are largely base 10. There are 10 years in a decade, 10 decades in a century, and 10 centuries in a millennium. But take a look at shorter time lengths: We don’t carve up the day into 10 hours, each 100 minutes long, even though this would make perfect sense. Instead, we divide our time up by multiples of 60 – 60 seconds in a minute, 60 minutes in…

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