ユークリッド幾何学と非ユークリッド幾何学での長さ・面積・体積

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  • The length, area and volume in Euclidean and Non-Euclidean geometry

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The relations among perimeter, area and volume of convex polyhedron or convex polygons in Euclidean and non-Euclidean spaces are studied. They are parametrized by the radius of their inscribed circles. The derivative of the area of convex polyhedron with respect to the radius is equal to the perimeter of it. Similar relations hold for the volume and the area in Euclidean space and for the area and the perimeter in non-Euclidean space.

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