Timeline for Billiard circuits in pentagons
Current License: CC BY-SA 4.0
16 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 2 at 18:42 | history | edited | Oscar Lanzi | CC BY-SA 4.0 |
edited body
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| Oct 6, 2023 at 11:15 | vote | accept | Joseph O'Rourke | ||
| Oct 6, 2023 at 0:53 | comment | added | Oscar Lanzi | @JosephO'Rourke maybe this isnit sufficient, though (so I add "am9ng other things"). Some further results with using different side nllengths in Case 2 suggest other criteria must be met. | |
| Oct 6, 2023 at 0:51 | history | edited | Oscar Lanzi | CC BY-SA 4.0 |
added 21 characters in body
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| Oct 6, 2023 at 0:36 | comment | added | Joseph O'Rourke | "the circumcenter of every triangle formed by three adjacent vertices lies inside the pentagon.": A very plausible conjecture. | |
| Oct 6, 2023 at 0:25 | history | edited | Oscar Lanzi | CC BY-SA 4.0 |
Added an angular criterion.
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| Oct 5, 2023 at 20:27 | history | edited | Oscar Lanzi | CC BY-SA 4.0 |
edited body
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| Oct 5, 2023 at 14:11 | history | edited | Oscar Lanzi | CC BY-SA 4.0 |
edited body
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| Oct 5, 2023 at 14:04 | history | edited | Oscar Lanzi | CC BY-SA 4.0 |
Summary sentence.
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| Oct 5, 2023 at 12:41 | comment | added | Oscar Lanzi | I have a proper billiard path now. | |
| Oct 5, 2023 at 12:41 | history | edited | Oscar Lanzi | CC BY-SA 4.0 |
Added a new figure.
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| Oct 5, 2023 at 11:10 | comment | added | Joseph O'Rourke | To answer why the definition: Tabachnikov calls it a "Fagnano" billiard path, analogous to the Fagnano path in a triangle. | |
| Oct 5, 2023 at 10:48 | comment | added | Oscar Lanzi | It turns out also that if you didn't require the consecutive order, then quadrilaterals woukd include all rhombi -> not necessarily cyclic. Frankly, I just like this pentagonal pattern! | |
| Oct 5, 2023 at 10:10 | comment | added | Joseph O'Rourke | Very nice! But you are right, the definition of billiard circuit requires reflections "from consecutive edges." | |
| Oct 5, 2023 at 1:01 | history | edited | Oscar Lanzi | CC BY-SA 4.0 |
Disagreement over the q!
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| Oct 5, 2023 at 0:49 | history | answered | Oscar Lanzi | CC BY-SA 4.0 |