In my reply I made no mention of either 360 nor [TEX]2\pi [/TEX], let alone anything about their ontological status.

The statement was about

*radians and degrees*.

The idea of dividing one revelation into 360 parts (we now call

*degrees*) surely dates from a time the Babylonians of 2000-1600 BCE. As their astronomy matured and good records were kept, they found one complete revolution could be divided in 24 equal parts hence hours and 360 came out of the way they measured distance. So the 360 is an accident of history.

On the other hand,

*a radian* has a very precise definition. We know a great deal about measurement of arc length on a circle. We have long known that the whole circle has arc length [TEX]d\cdot\pi [/TEX] where [TEX]d[/TEX] is the distance across the circle through the center. [TEX]\tfrac{d}{2}=r [/TEX] is radius. So a

*radian* is the measure of the central

angle in circle which subtends an arc of length equal to the radius. Thus the length of the whole circle is [TEX]2\cdot\pi\cdot r [/TEX]

*radians*. There is nothing arbitrary (no accident) there.

As a sidebar, much has been made of the fact that the value of [TEX]\pi[/TEX] shows up in measurements in old Egypt, say the pyramids. Of course the mystery goes away when one realizes that ancient Egyptians used a wheel with a peg in it to measure distance.

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