There are many ways to solve a problem. I decided to think in degrees. I pretended the square was a circle and there are 360 degrees in a circle. How do I remember that number? I remember it because a compass also has 360 degrees because it is based upon a circle. Why did mathematicians decide on 360? Here are some possible reasons:
- 360 can be divided by 2 or 3 or 4 or 5 or 6 or 8 or 9 or 10 or 12 without getting a remainder. That makes it very useful. Nobody wants to divide by 7 or 11 anyway.
- Ancient calendars were based upon 360 days. They followed a lunar month: twelve 30-day cycles of the moon. (In reality, the lunar month is 29.5 days.)
- The Babylonian number system was based on 60, instead of ten. You can fit six equilateral triangles with a side length of the radius into a circle. 6 x 60 = 360.