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CTK Exchange
Mayuresh
guest
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Dec-04-08, 00:57 AM (EST) |
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"partioning 3 space into circles"
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Hello, I came across this problem of partitioning 3 space into circles (https://www.cut-the-knot.org/proofs/tessellation.shtml) For the life of me I cannot understand the solution at the end of that page :( I cannot see how each of the red spheres has only 2 points of intersection with a black circle. For eg consider the red sphere with radius 1. Surely it intersects the whole left half of the black circle centered at x = 1. I would greatly appreciate if someone could point me on the right path to understanding this. Thanks :) |
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alexb
Charter Member
2311 posts |
Dec-05-08, 01:09 AM (EST) |
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1. "RE: partioning 3 space into circles"
In response to message #0
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A shpere is a surface not a solid. The sphere in your example is x² + y² + z² = 1 while the circle is (x - 1)² + y² = 1, z = 0 Eliminating y and z gives x² = (x - 1)² from which x = 1/2. Then, for y, there is a quadratic equation: y² = 3/4. |
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