Integrating history of mathematics in a classroom

1) Think for yourself why 60 might be a convenient, significant or especially useful number to use as the base for a number notational system. What is special about the number 60? How is it different from 10?

2) Then think for yourself how we still use 60s in our own daily lives, in Canada, and across cultures if you have knowledge of other systems (like the Chinese zodiac and time-telling system, for example.) Why is 60 significant in so many situations involving time and/or space?

The Babylonian number system uses base sixty instead of 10.🆒

My first reaction was: what a lot of special number symbols they must have had to learn‼️

After a few minutes carefully exploring  a Babylonian table, I found out, surprisingly, that they used only two symbols to represent numbers. ✅
They also devised place value system that is very similar to what we use in our base 10 numeric system.✅

Are there other similarities or differences ⁉️🧐

It seems that both “1” and “60” were represented in a same way ‼️ Why⁉️ Didn’t they realize this problem⁉️Or they didn’t see this as a problem ‼️Weren’t they smart enough to devise a symbol for
“ nothing”😎
I assume they adapted to write each number under its specific place value to avoid confusion or they simply referred to context 🙈

Another question :
why Babylonians used base sixty⁉️ Why They didn’t consider other numbers such as 10, 20, 30 or so on⁉️
 They chose sixty maybe because a year is about 360 days and they divided a year to 6 parts( as we call month) to keep track of days or even seasons. In fact the legacy of Babylonian numerical system still can be seen today. Every hour is divided into sixty minutes and every minutes is divided into sixty seconds or we divide a circle ⭕️ into 360 degrees ✅

Another reason might be based on geometry.  An equilateral triangle was considered the fundamental geometrical building block by the Sumerians. Now an angle of an equilateral triangle is 60° so if this were divided into 10, an angle of 6° would become the basic angular unit. ✅

Or they chose sixty because, One can count up to 60 using  two hands. On your left hand there are three parts on each of four fingers (excluding the thumb). Now one can count up to 60 by pointing at one of the twelve parts of the fingers of the left hand with one of the five fingers of the right hand. This gives a way of finger counting up to 60 rather than to 10.✅

These are just some assumptions and Can be argued  for their validation.

we are still using base sixty in time system ,measuring angles, latitude and longitude system. It seems that base sixty partly survived over the centuries.