Determine the largest area of an isosceles triangle that is enclosed within a unit cube.
What is the answer if the triangle is equilateral?
After a
lot of experimenting, I've come to the conclusion that the best you can do is cut off a corner. The equilateral triangle has sides of length sqrt(2) and area sqrt(3)/2=0.866
Other cross sections can yield quadrilaterals, pentagon and hexagons, but their largest embedded triangle (even ignoring isosceles) is smaller. I don't know that I haven't overlooked something, however.
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Posted by Jer
on 2025-03-30 13:26:57 |
probable solution
