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Nandakumar R
Nandakumar R
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Question: If within a convex solid body C there is a special point P such that every planar section of C passing through P has the same area, then, can we assert that C is a sphere and P its center? If not, is there any C such that there are more than one such P's?

Note 1: Same question can be asked with 'perimeter' (or moment of inertia or any other moment) replacing 'area'.

Note 2: If we rephrase the question with 'diameter' instead of 'area', the solid C could be an oblate spheroid and if we consider least width, it could be a prolate spheroid.

Question: If within a convex solid body C there is a special point P such that every planar section of C passing through P has the same area, then, can we assert that C is a sphere and P its center? If not, is there any C such that there are more than one such P's?

Note 1: Same question can be asked with 'perimeter' replacing 'area'.

Note 2: If we rephrase the question with 'diameter' instead, the solid C could be an oblate spheroid and if we consider least width, it could be a prolate spheroid.

Question: If within a convex solid body C there is a special point P such that every planar section of C passing through P has the same area, then, can we assert that C is a sphere and P its center? If not, is there any C such that there are more than one such P's?

Note 1: Same question can be asked with 'perimeter' (or moment of inertia or any other moment) replacing 'area'.

Note 2: If we rephrase the question with 'diameter' instead of 'area', the solid C could be an oblate spheroid and if we consider least width, it could be a prolate spheroid.

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Nandakumar R
Nandakumar R
  • 6k
  • 3
  • 7
  • 20

Question: If within a convex solid body C there is a special point P such that every planar section of C passing through P has the same area, then, can we assert that C is a sphere and P its center? If not, is there any C such that there are more than one such P's?

Note 1: Same question can be asked with 'perimeter' replacing 'area'.

Note 2: If we rephrase the question with 'diameter' instead, the solid C could be an oblate spheroid and if we consider least width, it could be a prolate spheroid.

Question: If within a convex solid body C there is a special point P such that every planar section of C passing through P has the same area, then, can we assert that C is a sphere and P its center? If not, is there any C such that there are more than one such P's?

Question: If within a convex solid body C there is a special point P such that every planar section of C passing through P has the same area, then, can we assert that C is a sphere and P its center? If not, is there any C such that there are more than one such P's?

Note 1: Same question can be asked with 'perimeter' replacing 'area'.

Note 2: If we rephrase the question with 'diameter' instead, the solid C could be an oblate spheroid and if we consider least width, it could be a prolate spheroid.

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Nandakumar R
Nandakumar R
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On special points within convex solids with all planar sections passing through them having equal area

Question: If within a convex solid body C there is a special point P such that every planar section of C passing through P has the same area, then, can we assert that C is a sphere and P its center? If not, is there any C such that there are more than one such P's?