Finding the Ways to Put N Points on a Circle

Thread starter ehrenfest
Start date Oct 31, 2007
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Circle Points

AI Thread Summary

The problem of placing n points on a circle involves determining the distinct arrangements, which is calculated as n!/n to account for cyclic permutations. If reflections are allowed, an additional factor of 1/2 is included, resulting in the formula n!/(2n). This approach ensures that equivalent arrangements due to rotation and reflection are not counted multiple times. The discussion clarifies the importance of considering these factors in combinatorial geometry. Understanding these principles is essential for accurately solving related problems.

Oct 31, 2007

ehrenfest

Homework Statement

How many ways can you put n points on a circle? It is something like n!/2, right?

Homework Equations

The Attempt at a Solution

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Oct 31, 2007

Dick

Science Advisor

Homework Helper

No, it's n!/n. You have to identify cyclic permutations of a linear ordering. With an extra factor of 1/2 if you allow the circle to flip over.

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