Timeline for Partition of polygons into 'congruent sets of polygons'
Current License: CC BY-SA 4.0
6 events
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| Nov 8, 2021 at 9:58 | history | edited | Aaron Meyerowitz | CC BY-SA 4.0 |
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| Nov 8, 2021 at 2:16 | comment | added | Nandakumar R | Thank you Prof Meyerowitz. Let me restate the last question better: your algorithm yields (m-2)*n pieces in each congruent set when cutting an m-gon into n sets. Is that a tight lower bound on the number of pieces per set when partitioning any general m-gon into n sets? Basically, is the algorithm optimal in minimizing number of pieces per set? | |
| Nov 7, 2021 at 19:06 | comment | added | Aaron Meyerowitz | @NandakumarR Do you mean uniformly for all octagons? Certainly some octagons have solutions for $n=2$ or $4$ that only use $n$ pieces. Do you only want convex polygons? Use four small squares to make a larger one. Place a fifth small square centered on the top to get a (nonconvex) octagon from 5 squares | |
| Nov 7, 2021 at 9:36 | comment | added | Nandakumar R | Thanks very much. The idea of getting n^2 mutually congruent m-gons similar to P is a nice bonus! The only bit remaining would be to decide whether this also gives the least number of pieces in each congruent set - for ex, if one starts with an octagon that has to be cut into 5 congruent sets, the octagon goes into 6 triangles each of which goes into 25 self-similar triangles and the resulting 150 pieces get grouped into 5 sets of 30 pieces each. | |
| Nov 7, 2021 at 6:03 | history | edited | Aaron Meyerowitz | CC BY-SA 4.0 |
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| Nov 7, 2021 at 5:42 | history | answered | Aaron Meyerowitz | CC BY-SA 4.0 |