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| Math Central | Quandaries & Queries |
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Question from cristina, a teacher: what is the formula for finding the number of angels that can be named by a given number of rays with the same endpoint? |
Cristina,
No, with angels the traditional question is how many can dance on the head of a pin.
If you mean angles (as Pope Gregory might have put it, "non angeli sed anguli") then every pair of rays determines two angles, one ordinary and one reflex (or both straight). If you are only interested in the nonreflex angle - and if we assume no two rays to be opposites - then the answer is the same as the number of pairs of distinct rays, n(n-1)/2. If reflex and straight angles are also acceptable the answer is twice that and we can drop the assumption.
Good Hunting!
RD
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