BMAD Posted October 14, 2014 Report Share Posted October 14, 2014 What is the largest circle you can construct in a unit cube? Quote Link to comment Share on other sites More sharing options...
0 k-man Posted October 15, 2014 Report Share Posted October 15, 2014 The largest circle inscribed in a cube will be in a plane that creates a cross section of the cube in a shape of a regular hexagon. The circle will be inscribed into that hexagon. The plane is perpendicular to the largest diagonal of a cube and cuts the cube at the midpoints of its edges. The side of the hexagon is 1/sqrt(2), so the inradius is sqrt(3)/2sqrt(2). Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted October 15, 2014 Report Share Posted October 15, 2014 It may be the inscribed circle of the largest square that fits inside the unit cube. Quote Link to comment Share on other sites More sharing options...
0 k-man Posted October 16, 2014 Report Share Posted October 16, 2014 Quote Link to comment Share on other sites More sharing options...
0 BMAD Posted October 16, 2014 Author Report Share Posted October 16, 2014 circle in the cube.png how would one construct this? Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted October 17, 2014 Report Share Posted October 17, 2014 circle in the cube.png how would one construct this? Take three points - for example the hypotenuse midpoints of the triangles in k-man's figure. They determine a circle: Quote Link to comment Share on other sites More sharing options...
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BMAD
What is the largest circle you can construct in a unit cube?
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