Timeline for Maximizing the area of a region involving triangles
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Oct 23, 2021 at 0:15 | comment | added | user44143 | @JosephO’Rourke, I assumed $D_3$ symmetry, and the result is already mildly asymmetric in that the nonagon has no $\mathbb{Z}/9\mathbb{Z}$ symmetry. It would be hard to establish anything definitive about solutions with no symmetry, since the overall configuration space of three triangles (18 coordinates) with 3 specified areas and 6 specified centroid coordinates has 9 degrees of freedom. | |
| Oct 22, 2021 at 20:56 | comment | added | Joseph O'Rourke | Very nice! MattF, while working on this, did you get the sense that "the symmetric options" lead to the largest area? All rotational moves around your configuration are area-downward? Maybe your edit showing the explicit area answers this? Is your configuration at least a local max? | |
| Oct 22, 2021 at 7:39 | history | edited | user44143 | CC BY-SA 4.0 |
fixed units (the diagram was right), added more and less exact approaches
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| Oct 21, 2021 at 12:16 | comment | added | Stanley Yao Xiao | Certainly not the picture I was expecting! | |
| Oct 19, 2021 at 17:09 | history | edited | user44143 | CC BY-SA 4.0 |
shorter wording
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| Oct 19, 2021 at 16:59 | history | edited | user44143 | CC BY-SA 4.0 |
clearer lines in diagram
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| Oct 19, 2021 at 15:09 | history | answered | user44143 | CC BY-SA 4.0 |