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Can someone give a proof for this theorem?
The circle has the largest area of all shapes, given a fixed perimeter.
 one year ago
 one year ago
Can someone give a proof for this theorem? The circle has the largest area of all shapes, given a fixed perimeter.
 one year ago
 one year ago

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henpenBest ResponseYou've already chosen the best response.0
Not a formal proof, but here's the intuition. Imagine a cube, with a centre point. From this point radiate lines that touch the vertices of the cube. Sections such as thesedw:1350744197439:dw are formed. The area of any pyramid is 1/3 * base area * height. As you add sides to the polyhedron, the height increases, so the volume increases.
 one year ago

henpenBest ResponseYou've already chosen the best response.0
The total base area for the whole shape is held constant by the requirements of your question,
 one year ago

henpenBest ResponseYou've already chosen the best response.0
This proof is in 3D, 2D is much easier, but uses the same logic.
 one year ago

AndrasBest ResponseYou've already chosen the best response.0
Sorry but this didnt help much. How is this cube related to a circle or a sphere?
 one year ago

AndrasBest ResponseYou've already chosen the best response.0
I guess the proof for 3D + sphere is similar to the 2D and circle. But how does this cube section help?
 one year ago

henpenBest ResponseYou've already chosen the best response.0
It is the starting point: as you increace the number of faces, the volume goes up
 one year ago

estudierBest ResponseYou've already chosen the best response.1
http://www.math.utah.edu/~treiberg/isoperim/isop.pdf
 one year ago
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