Timeline for Does existence of midpoints imply intrinsic?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Jan 20, 2017 at 22:08 | comment | added | Will Brian | That looks like it should work -- and I like the symmetry of your version! | |
| Jan 20, 2017 at 22:05 | comment | added | erz | yes, you are right, sorry. Something like this perhaps? postimg.org/image/3q0vavdhp | |
| Jan 20, 2017 at 15:48 | comment | added | Will Brian | @erz: If I'm understanding your idea correctly, then I don't think it works. The problem is that you will end up with holes that have points both directly above and directly below them. These pairs of points have a unique shortest path connecting them (and it crosses the hole. Their only chance at having a midpoint is if it's the midpoint of that path. If the points are equidistant from the hole, then you're out of luck. | |
| Jan 20, 2017 at 15:45 | history | edited | Will Brian | CC BY-SA 3.0 |
I fixed the picture
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| Jan 19, 2017 at 21:19 | vote | accept | erz | ||
| Jan 19, 2017 at 21:18 | comment | added | erz | That is a fantastic example! Please allow me to suggest a partial case, a more concrete construction, which is easier to visualize: Start with $B_0$ and a single holey bridge, which is based exactly in the middles of the corresponding sides. Now we have a rectangle with holes in the upper right and lower left corners. Each time we have such an object, divide it with a vertical and a horizontal "middle" lines in 4 smaller rectangles, and place a hole where these lines cross. Hence we obtain 2 "normal" rectangles and 2 rectangles with holes. Ultimately we will have something like a fractal grid. | |
| Jan 19, 2017 at 16:44 | history | answered | Will Brian | CC BY-SA 3.0 |