Why Base 60? Why 60 then? Why 10 now?

 1) As mentioned by some in class on Monday, Sept 8th, the number 60 has many factors—especially when compared to our base-10 system.

• 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
• 10: 1, 2, 5, 10

It makes me think that using 60 as a base would be much more efficient for working with fractions. When calculating measurements for cooking, feeding animals, taxes, or budgeting materials, 60 seems to offer more convenience. Like Susan pointed out:

• 1/3 of 60 is 20, while 1/3 of 10 is 0.33 (repeating).

• 1/4 of 60 is 15, while 1/4 of 10 is 2.5.

It makes mathematical sense that the larger the base number (like 60 compared to 10), the more divisibility options you get, and the less you rely on decimals—though decimals are still possible. Sixty seems to lead to more terminating decimals overall.

2) Our calendar year today is 365 days, but in the past, it was often calculated as 360 days—a number divisible by 60. Similarly, we measure angles in 360 degrees, and in trigonometry, our "special triangles" often feature angles that are fractions of 60:

• 15 (¼ of 60), 30 (½ of 60), 45 (¾ of 60), and 60 itself.

Another obvious place we see 60 is in time:

• 60 seconds in a minute

• 60 minutes in an hour

But then there's 24 hours in a day. That part has always made me wonder. Why 24? Sure, it’s 2/5 of 60—but why not 30 or even 60 hours in a day? This probably ties back to the historical and astronomical roots of timekeeping. Ancient mathematicians would study the sun, moon, and stars (especially the North Star) to find consistent patterns. I suspect that’s also how they came up with the idea of a 360-day year.

The earliest systems of cosmology, especially among the Babylonians, used base-60. They invented basic trigonometry, produced detailed star maps, and could even predict eclipses with surprising accuracy.

3) A little research on Google also shows that the number 60 holds spiritual and cultural significance. In the Bible, it appears numerous times, and some followers interpret it's frequency in the bible as the point where people enter the final stage of life.

In the Chinese zodiac, 60 marks the completion of a full sexagenary cycle: 12 zodiac signs × 5 elements. For example, I was born in the Year of the Dragon, which is also associated with the metal element—a combo that only happens once every 60 years.

BibleStudy. (n.d) Meaning of numbers in the bible: The number 60. https://www.biblestudy.org/bibleref/meaning-of-numbers-in-bible/60.html