BMAD Posted March 6, 2014 Report Share Posted March 6, 2014 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? Quote Link to comment Share on other sites More sharing options...

0 bonanova Posted March 7, 2014 Report Share Posted March 7, 2014 Extrema of areal overlap occur when median aligns with diagonal of square (max) or is perpendicular to edge of square (min). A_{max} = 1/4 (1 - tan 15^{o}) = 0.183012 ... A_{min} = 1/4 (tan 30^{o}) = 0.144337... Quote Link to comment Share on other sites More sharing options...

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## BMAD

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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