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Do they gain anything by using base-60 that isn't gained by using radians or purely algebraic expressions, and that wasn't already known about?
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Late to the party and just saw this.
The point of the Babylonian base 60 was that they could do more precise geometric calculations earlier in history than other cultures, without developing algebra and so on.
The precision aspect is still relevant. Many calculations resolve perfectly in base 60 that never do in base 10.