Degrees vs. Radians

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 an hour.

Why do we do this? Because our Babylonian uncles used a base 60 number system, and we’ve been following their example ever since.

Babylon left another relic in our system of measurements, one that requires a little deeper explanation, and which lies at the heart of your question (yes, I’m getting there): the degree. Continue reading

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