Why Base 60?

I believe 60 is special as it appears so much in our own daily lives. I believe that it may have been because of a few things. Time is the theory I would go with. The Babylonians would have had a system for time and calendar. It could have been coinvent for its factors. 1,2,3,4,5,6,10 all factor 6. Whereas 10 only has 1,2,5,10 as its factor. It could have also been related to finger counting. But time and maybe angles seem the most likely. 

60 is important for time and space, as we count seconds, minutes, hours, and days (Vecna, Stranger Things, 2022). We have 60 of that, 365 days (close to 360), and even 360 degrees in a circle. Also based on the factors, I would guess that 60 is convenient to use and apply. And maybe this is banian, but we use 6 and 12 for measurements as well. 

Hanson (2015), discusses that the numeric system based on 60 originated with the Sumerian civilization about 4500 years ago. It is thought that 60 could be related to the origin of the number 12, which is the number of joints on 4 fingers of a hand, not including the thumb. The Babylonians replaced the Sumerian civilization.  UofUtah( 2014), discusses many theories as to why base 60 was used. Theon of Alexandria originally presented a theory for the reason of base 60 as the maximation of factors as 60 is divisible by 1,2,3,4,5 and 6. Another is to do with shape. Babylonians used a standard ruler and compass to construct a hexagon inscribed in a circle. This hexagon allowed for 6 sections, each 60° in size. This theory was introduced by the historian of mathematics, Moritz Cantor. The rationale for choosing the hexagon is still unclear to me. 

In my research for the significance of 60, 60 has a big advantage over base 10 as 60 is divisible by 3, and 10 is not. I believe the significance of 60 is such that the sexagesimal system that may have been shadowed by our now use of base 10, we still use it to measure time and angles. The theory of astronomy, as Babylonian astronomy which counts a year as 360 days, divided into 12 months of 30 days and 60 factors seem the simplest and most easily understood as to why base 60 was chosen. 

References 

Hanson, R. (2015, August 19). Roger Hanson: The origins of the number 60 as a counting method. Stuff. Retrieved September 13, 2022, from https://www.stuff.co.nz/science/71273903/roger-hanson-the-origins-of-the-number-60-as-a-counting-method

Liadelp, Liadelp, & 1, J. J. (2014, September 7). Why base 60? 3010tangents. Retrieved September 13, 2022, from https://3010tangents.wordpress.com/2014/09/07/why-base-60/