Degrees & Minutes: Explaining the 360º System

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DaveC426913
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A little birdy who is apparently too shy to post asks the following:

I have a doubt: considering the 360º for earth, and if it takes 24h to a complete rotation, why 1º corresponds to 60 min? It should be 4 min...
 
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I agree. It is a tradition as sensless and outdated as the mile and the pint.

I believe that the source of it is something along these lines: The word "minute" means small, and I guess a tradition is that 1/60 is a small fraction of something. A second is actually short for the "second minute" or the "second small fraction" so 1/60 of a minute. So 1/60 of anything is a "minute" fraction and 1/3600 of anything is a "second minute" fraction.
 
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So a degree is ten "second minutes" of a circle.
 
mks is such a beautiful system except the base-60 and base-24 time.

I had a fellow physics major who always asked why we are trying to unify science but we haven't bothered to unify the units yet.