Timeline for Packing rectangles: Does rotation ever help?
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 30, 2019 at 0:11 | vote | accept | Joseph O'Rourke | ||
| Apr 29, 2019 at 12:43 | comment | added | Tony Huynh | @JeppeStigNielsen: You can increase the length from $100$ to an arbitrarily large length, in which case it is clear that the bottom picture covers less area. | |
| Apr 29, 2019 at 11:52 | comment | added | Joseph O'Rourke | @JeppeStigNielsen: "more upright": Yes, about $65^\circ$. See added detail. | |
| Apr 29, 2019 at 11:51 | history | edited | Joseph O'Rourke | CC BY-SA 4.0 |
added 280 characters in body
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| Apr 29, 2019 at 10:07 | comment | added | Jeppe Stig Nielsen | The first packing is $100\cdot (10+1) = 1100$, but I think the second packing is $\left( \frac{10}{61}(11+6\sqrt{22})+100 \right)\cdot 10\approx 1064.2$, so the example is valid, but $1025$ from the original comment is not so precise. To me, it is hard to estimate visually by staring at the figure, which packing is better, but I can see that the "leaning" thin box is more upright than $45^\circ$. | |
| Apr 27, 2019 at 19:55 | comment | added | Joseph O'Rourke | @VictorProtsak: Thanks; corrected. | |
| Apr 27, 2019 at 19:54 | history | edited | Joseph O'Rourke | CC BY-SA 4.0 |
edited body
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| Apr 27, 2019 at 19:51 | comment | added | Victor Protsak | Actually, in the first packing the smaller rectangle should lie on the top of the larger one, giving the intended area of 11*100=1100. | |
| S Apr 27, 2019 at 19:16 | history | answered | Joseph O'Rourke | CC BY-SA 4.0 | |
| S Apr 27, 2019 at 19:16 | history | made wiki | Post Made Community Wiki by Joseph O'Rourke |