Posts tagged 'problems'

F.41 Geometric Problems and Extremal Loci

Among all triangles with longest side c = |AB| = 1, the acute locus inside the vesica piscis above the semicircle on AB has area A = int_0^{sqrt(3)} (sqrt(4 - x^2) - 1) dx - pi/4 = (5 pi - 6 sqrt(3))/12 approx 0.44297 (for c = 2), and maximizing d_IO over acute triangles approaches the degenerate right-isosceles limit C -> (0, 1).