Problem 59249. Compute the total length of lines between all vertices of a regular polygon

Created by ChrisR

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Write a function to compute the total length of between all vertices of a regular polygon inscribed in a unit circle. For example, a square in a unit circle would have side length of  and each of the two diagonals would have a length of 2. Therefore, for  the total length is . In the hexagon below, there are 6 lines of length 1 connecting adjacent points, 3 lines of length 2 connecting opposite points, and 6 lines of length  connecting points two away; therefore, for , the total length is . 

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Last Solution submitted on May 10, 2025

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William on 2 Dec 2023

The test suite seems suspicious to me. The length of the diagonals will add up to n, and the length of the edges will never be more than 2*pi*r = 6.28. Where are all the big values coming from?

ChrisR on 3 Dec 2023

"Diagonals" was confusing, so I changed the wording and added another example.

William on 3 Dec 2023

Oh, I see. The example of the square led me to believe that "diagonal" meant "diameter". Thanks for the clarification!

William on 3 Dec 2023

I am having precision problems with the first and third assert()'s in test 14. The relative precision on the first is about 1e-10 and it is getting a sum that is different by about 3 units. For the third, the error is much worse because if any of the elements of a() are off by even 1 unit, they don't trigger the isprime() and don''t get included in the sum.

Christian Schröder on 3 Dec 2023

I'm having the same problem as William: all tests pass except for test 14. I'm inclined to blame the test rather than my code (famous last words, I know).

ChrisR on 3 Dec 2023

OK, I reduced the number of terms in Test 14, and the three solutions submitted so far work.

Christian Schröder on 4 Dec 2023

Thanks, Chris!

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Problem 59249. Compute the total length of lines between all vertices of a regular polygon

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Last 200 Solutions

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Problem 59249. Compute the total length of lines between all vertices of a regular polygon

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Last 200 Solutions

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Problem Recent Solvers7

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