Timeline for More on shadows of 3D convex bodies
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Aug 7, 2023 at 11:11 | comment | added | Nandakumar R | In above, 'girth' should be viewed not merely as parallel projection but orthogonal projection. The argument remains valid. | |
| Aug 6, 2023 at 12:27 | history | edited | Nandakumar R | CC BY-SA 4.0 |
added 85 characters in body
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| Aug 6, 2023 at 12:00 | comment | added | Nandakumar R | As given in en.wikipedia.org/wiki/Girth_(geometry), the girth of a geometric object, in a certain direction, is the perimeter of its parallel projection in that direction (perimeter of the shadow). From Hilbert and Cohn-Vossen's 'Geometry and the Imagination', page 216-7, Minkowski has proved that all convex surfaces of constant girth (ie. all its shadows have constant perimeter), then the surface is one of constant width - not necessarily a sphere. This answers question 2. | |
| Jul 7, 2023 at 1:51 | comment | added | Yoav Kallus | you're welcome. Feel free to write up an answer to #2 if you think it adds value | |
| Jul 6, 2023 at 19:38 | comment | added | Nandakumar R | Thank you for those pointers. I guess, despite the repetition, this post adds a little bit of value in the second claim (if you think otherwise, do comment). A further claim has also been posted: mathoverflow.net/questions/450310/… | |
| Jul 6, 2023 at 13:56 | comment | added | Yoav Kallus | and @alvarezpaiva's comment on my answer to that question should give you a good hint for question #2, if you replace the square of the radial function by the support function | |
| Jul 6, 2023 at 13:52 | comment | added | Yoav Kallus | your question #1 seems to be a duplicate of mathoverflow.net/questions/138525/… | |
| Jul 6, 2023 at 4:59 | history | asked | Nandakumar R | CC BY-SA 4.0 |