Four points are chosen at random inside a square. Each point is chosen by choosing a random x-coordinate and a random y-coordinate.
A convex quadrilateral is drawn with the the four random points as the vertices.
Determine the probability that the center of the square is inside this quadrilateral.
(In reply to
re(2): preliminary simulation results by Charlie)
As a sanity check these show situations where the random points were deemed as forming a quadrilateral that is either convex or non-conves, and if convex, whether it contains the center of the square.
The center of the square is marked with 4 x's (the square is 60 character positions high and 100 wide, so there's no center character). The random points are marked with *'s. There are some close calls, so the coarseness of the grid can make it difficult to see in some instances.
Found to be convex and to contain the center of the square:
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K>>
Found to be non-convex:
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K>>
Determined as convex but not containing center of square:
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Posted by Charlie
on 2023-01-13 08:27:53 |
Sanity check on classification
