The Efficient Bug
A bug wants to walk from one vertex to the opposite vertex of an icosahedron in the most efficient way, and must stay on the surface.(i.e. At no time can it delve into the icosahedron's interior.)
The edges of the icosahedron have unit length.
If the minimum distance the bug must travel is , what is ?
Try more questions on Platonic Solids .
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The answer is 7.
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1 solution
If you flatten out the icosahedron, like this...
You can see that the minimum distance is from a point on the top, to a point on the bottom, which has an ( x , y ) offset of ( 0 . 5 , 1 . 5 3 ) . So the distance, x , is given by, x 2 = ( 0 . 5 ) 2 + ( 1 . 5 3 ) 2 = 7 .