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A degree is one measure of angles. There are 360 degrees in a circle and that gives 360 its importance in relation to a circle.
The diameter of a circle determines all its characteristics.
It is important to know formulas of pi for circles like areas of a circle and its circumference
2*1673 = 3346 [don't forget that units are important].
I did not know it was lost! It is very important for the calculation of the area of a circle and such calculations were important to the ancient geometers (people who measured land/earth).