Timeline for Can you fold a square into a square of one-third the area
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 4, 2020 at 18:39 | comment | added | Paul Panzer | If I understand the "rules" of folding correctly once you have one of the four main folds the others can be made without any auxiliary folds because folding through a given point perpendicular to a given crease or edge is an allowed operation. | |
| Oct 4, 2020 at 18:30 | comment | added | Retudin | I did not show but need the 1/3 and 2/3 fold horizontally and vertically.. | |
| Oct 4, 2020 at 18:22 | comment | added | Paul Panzer | Generalization is a good point. Mine does generalize in principle but not as straight forward as yours. Re number of folds I count $9$ ($5$ auxiliary $4$ money folds) in both cases. | |
| Oct 4, 2020 at 18:10 | comment | added | Retudin | @PaulPanzer My solution needs more folds than yours, so in that sense yours is better. I think my solution is easier to understand, but if one understands Thales's theorem one probably understands your use of the golden ratio, so I might be wrong. I also like about my solution that it is easy to to generalize to any 1/Nth part of total, although that may also be true for yours.. | |
| Oct 4, 2020 at 17:11 | comment | added | Paul Panzer | I'd say this is up to a minor detail the same as my construction. Which is more elegant is very much a matter of taste. Number of auxiliary folds is the same. Btw. the thing you do with the right angled triangle is called Thales's Theorem. | |
| Oct 4, 2020 at 16:07 | comment | added | Retudin | Seems that adds something to the existing answers, so please post. | |
| Oct 4, 2020 at 16:04 | comment | added | Bubbler | I thought, by you mentioning the 1/5 problem, you wanted a solution where you can prove the 1/3-ness by dividing the paper into multiple areas and reassembling into three same-sized squares. I do have such a solution right now, though it doesn't place the square at the center. If you're interested, I'll post it when I get to my PC. | |
| Oct 4, 2020 at 15:47 | history | edited | Retudin | CC BY-SA 4.0 |
added 173 characters in body
|
| Oct 4, 2020 at 15:38 | history | answered | Retudin | CC BY-SA 4.0 |