Base Sixty

Today we count using Base Ten (1-2-3-4-5-6-7-8-9-10, then 11-12-13-14-15-16-17-18-19-20, 21 to 30, 31 to 40, 41 to 50 and so on). Here’s something really interesting about the Sumerians. They counted numbers using Base Sixty! Fractions hadn’t been invented yet, so 60 was actually a handy base for counting. Sixty can be divided by 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60. Try it!

Base Sixty is natural, it occurs in the world around us. By watching the sky, the Sumerians saw the Moon make a complete cycle 12 times a year. Each cycle (month) takes about 30 days (one day = the time it takes Earth to completely revolve around her axis). That’s about 360 days per year (one year = the time it takes Earth to travel around the Sun). These numbers fit neatly into the Base Sixty way of counting.

Do we still use Base Sixty? You betcha! A ruler is 12 inches long—12 x 5 = 60. We buy eggs and doughnuts by the dozen. Can you think of any other examples?

How about a clock? There are 12 hours on the face of an analogue clock—12 x 5 = 60. Sixty minutes in an hour; sixty seconds in a minute. What about 24 hours in the day—does that work? Nope, sixty doesn’t evenly divide by 24. But a protractor uses Base Sixty—a circle is divided into 360 degrees. If you were to mark 24 hours around a protractor, each hour would use 15 degrees (hang onto that thought—it will become important later on in the show).

I bought this one at Protractor Supply.

I can hear you saying, “Hold on, Manders. Years aren’t 360 days long. They’re 365 days and six hours!” Okay, I have to admit, that’s a good point. Sumerian astronomers were fantastic at math and did mostly everything right—but they got one really important piece of information wrong. They thought the Earth was the center of the universe with the Sun, Moon and planets revolving around her. It’s impossible to make the lunar year (12 cycles of the Moon) agree exactly with the solar year (Earth’s trip around the Sun), so we had to add 5 extra days, plus one day every fourth year, to make it work on a calendar. That’s not really the best solution, as we will see.

2 responses to “Base Sixty

  1. Pingback: Egyptian sundials | John Manders' Blog

  2. Pingback: Egyptian calendar | John Manders' Blog

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