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Home Q & A Board Science-Related Homework Help Mathematics
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sml0920 sml0920
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12 years ago
What is the Super Pythagorean Theorem? It was an SAT question... Find the distance from the center of a sphere to a corner of a cube if the sphere is inside the cube.
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#1
12 years ago
The super Pythagorean Theorem refers to the Law of Cosines which says for any triangle with sides a,b,c and opposite angles A,B, and C then

c^2 = a^2 + b^2 -2ab(cosC)

Notice that when C=90 degrees since cos90 = 0 the last term above goes to zero leaving the Pythagorean Theorem.

You can think of the law of cosines as the Pythagorean Theorem for any triangle with a correction factor for non-right triangles of -2ab(cosC).
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#2
12 years ago
It depends on  size and position of sphere in cube. assuming the sphere fits the cube, or even if the sphere is located at cube centre, let cube side be x. then the distance is x/2*Sqrt3
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