Timeline for Tying knots with reflecting lightrays
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| May 23, 2019 at 10:10 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
minor typo
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| Apr 12, 2018 at 17:45 | comment | added | Pierre Dehornoy | What a coincidence, I am just reading some of your papers carefully these days. Here is an updated version www-fourier.ujf-grenoble.fr/~dehornop/maths/Billiard.pdf | |
| Mar 23, 2018 at 19:02 | comment | added | Lee Mosher | @PierreDehornoy: Do you (or does anyone else) have an updated link to that short note? The current link is dead. | |
| Sep 17, 2010 at 22:05 | history | edited | Bill Thurston | CC BY-SA 2.5 |
pointer to Joseph's pictures.
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| Sep 17, 2010 at 13:02 | comment | added | Joseph O'Rourke | @Pierre: Beautiful idea! I love the "church shapes" figures! You may recommend me as a referee. :-) Congratulations! | |
| Sep 17, 2010 at 2:34 | comment | added | Pierre Dehornoy | It looks like one can use Ghrist's template in order to construct a non convex polyhedron containing all knots. Here is a short note on this. umpa.ens-lyon.fr/~pdehorno/maths/BilliardKnots.pdf | |
| Sep 17, 2010 at 0:01 | history | edited | Bill Thurston | CC BY-SA 2.5 |
added 2948 characters in body
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| Sep 16, 2010 at 17:32 | comment | added | Bill Thurston | @Pierre Dehornoy: That sounds like a promising idea. Since it's a particular flow, it might actually be possible to construct a convex polyhedron, but I don't remember (if I once knew) the specific construction for the knotholder. One could simulate splits in a branched surface by adding a narrow beam at a corner of a polyhedron. Horizontal splits are similar. Shifter units should be installed that perform unknotted operations to shift beams so they don't intersect. If the dynamics is or can be made PL (seems likely), then a polyhedral billiard realization sounds very plausible. | |
| Sep 16, 2010 at 16:32 | comment | added | Joseph O'Rourke | @Bill: Both your sketch on 3(a), and Pierre's idea, sound plausible to me---cool! Sorry for conflating the two different problems; corrected now. | |
| Sep 16, 2010 at 15:55 | comment | added | Pierre Dehornoy | I wonder if one could use Ghrist template to construct a (non convex) tube containing all knots: Ghrist constructed a branched surface equipped with a flow in $\mathbb R^3$ such that every link appears as a collection of periodic orbits of this flow. Could we thicken this knot-holder to get a billiard (made of glued square boxes) containing all knots? | |
| Sep 16, 2010 at 15:27 | history | answered | Bill Thurston | CC BY-SA 2.5 |