Timeline for Tiling the plane with incongruent isosceles triangles
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Jun 11, 2020 at 16:21 | comment | added | Nandakumar R | A further variant one can think of is: to tile the plane with mutually non-congruent ACUTE isosceles triangles ( without or with area/perimeter constraints), | |
| Jun 10, 2020 at 12:24 | comment | added | Nandakumar R | Indeed, we can tile plane with non-congruent isosceles triangles with bounds only on edge lengths: perturb each vertex of an equilateral triangle tiling infinitesimally in a unique direction, to get a tiling with non-congruent acute triangles.with every side unique and with both upper and lower bounds on max edge length.. Then, divide each triangle into isosceles triangles by joining its circumcenter with the vertices - as in one of the constructions given above. That should be it. However, it looks like further constraints such as equality of area/perimeter would make the problem harder. | |
| Jun 9, 2020 at 18:21 | comment | added | Nandakumar R | Both constructions shown above appear to use arbitrarily large isosceles triangles. Can one have tilings with incongruent isosceles triangles with bounds on the size of tiles? One can also further constrain the question with requirements such as "all tiles should have same area(same perimeter)" . | |
| Nov 24, 2017 at 4:23 | comment | added | domotorp | Wouldn't it make more sense to ask Noam if this figure could be included in his answer? After reading his answer and understanding it, it's little use to find this figure after scrolling down to the bottom... | |
| S Oct 21, 2015 at 19:37 | history | answered | Joseph O'Rourke | CC BY-SA 3.0 | |
| S Oct 21, 2015 at 19:37 | history | made wiki | Post Made Community Wiki by Joseph O'Rourke |