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Regular Hexagon and Mean Distance (Posted on 2022-10-14)

Part 1
Determine the mean distance between two random points on the perimeter of a unit (convex) regular hexagon.

Part 2
Determine the mean distance between two random points on the interior of a unit (convex) regular hexagon.

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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Part 2: Answer by internet search (spoiler)

| Comment 3 of 6 |

Internet Search finds the answer to part 2 at the following site:

The exact answer is given as

7*sqrt(3)/30 - 7/90 + (28*ln(2sqrt(3)+3) + 29*ln(2sqrt(3)-3))/60

Arriving at this answer has got to be way beyond a difficulty 3.

The expression is approximately 0.8262589495, which confirms Charlie's simulation

Posted by Steve Herman on 2022-10-14 10:49:52

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