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triangle/square bonding

Question

Suppose you have a unit square and a equilateral triangle of the same area. A vertex of the triangle shares location with the center of the square. What is the maximum possible overlap? What is the minimum possible overlap?

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1 answer to this question

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Extrema of areal overlap occur when median aligns with diagonal of square (max) or is perpendicular to edge of square (min).

Amax = 1/4 (1 - tan 15o) = 0.183012 ...

Amin = 1/4 (tan 30o) = 0.144337...

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