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What is the largest possible value of the smallest angle between the diagonals of an $n$-gon for even $n$?
In this answer, I showed that the maximum value of the smallest angle between two diagonals of a $21-$gon is $8\frac{4}{7}$ degrees. The method given generalizes to all polygons with an odd number of ...
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Consider the diagonals of a 21-gon. Prove that at least one angle of less than 1 degree is formed.
I think it should be solved using the pigeonhole principle. The answer is:
A $21-$gon has $189$ diagonals. If through a point in the plane, we draw parallels to these diagonals, $2 × 189 = 378$ ...
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