You choose a random point within a regular pentagon having unit sides.
What is the average distance to the five sides?
It looks like the answer is sqrt((5+sqrt(20))/20) or about 0.6881909602
Approximation from this drawing
https://www.geogebra.org/geometry/tqwh2wnx
You can see the sum of the five distances appears to be invariant.
Then look that up on the inverse symbolic calculator
https://wayback.cecm.sfu.ca/cgi-bin/isc/lookup?number=0.6881909602&lookup_type=simple
The answer is almost certainly correct given the square roots of 5.
The proof would be more involved, but not too bad.
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Posted by Jer
on 2024-06-23 14:55:56 |
Solution by Geogebra
