## Saturday, January 25, 2014

### 6: Why 360?

Everyone knows that there are 360 degrees in a circle.

We can also take it as a given that people who did math back in the days of Babylon didn't mess around ... they must have had really good reasons for choosing that number.  They were logical and just as smart as we are now, even if we sometimes don't admit that.

How many good reasons can you think of for 360° in a circle?
How many ridiculous reasons can you think of for 360° in a circle?

Should we change to another number for doohickeys in a circle?

1. Typo last line.

2. Here's a potential "reason." The sun and moon have an angular diameter of about half-a-degree in the sky, so about 360 suns and 360 moons together fit around the horizon.

3. Which category are you including this in? Perhaps in the same one as the Platonic solids explanation of orbital diameter?

4. When I have this discussion with my students we chat a bit about why we kept 360deg around. One reason invariably is that 360 just has so many factors, which is a nice quality of life reason.

5. I heard that the Babylonians initially estimated the number of days in a year as 360, and since 360 is such a nice number with loads of factors it stuck. Much better than 365.25 but still very arbitrary!

6. In the military we sometimes used 6400 mils. http://en.wikipedia.org/wiki/Angular_mil

7. It's divisible by all whole numbers, except 7, from 1 to 10 (or from 1 to 12 excluding 7 and 11) This makes is very convenient to divide the circle into parts easily.