Timeline for Topological fun facts for high school students
Current License: CC BY-SA 4.0
34 events
| when toggle format | what | by | license | comment | |
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| Jan 10 at 15:48 | history | edited | bml64 | CC BY-SA 4.0 |
added 8 characters in body; edited title
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| Dec 30, 2023 at 10:47 | vote | accept | bml64 | ||
| Dec 30, 2023 at 10:47 | |||||
| Dec 23, 2023 at 19:44 | answer | added | Allen Knutson | timeline score: 5 | |
| Dec 22, 2023 at 17:31 | answer | added | Florian F | timeline score: 3 | |
| Dec 22, 2023 at 11:16 | answer | added | Arya_08 | timeline score: 4 | |
| Dec 22, 2023 at 3:51 | comment | added | JonathanZ | @JoelKeene - And I think Jyrki's suggestion to throw out more examples is pretty good too. After the $S^2$ "failure", you can show them a regular torus and a double torus, tell them one of them can be combed while the other can't, and get them to make their bets as to which one. After that, you could make vague hints about the Euler characteristic, and they'll be begging you for the details. :-) | |
| Dec 22, 2023 at 2:31 | comment | added | Joel Keene | @Jonathanz I second the hairy ball theorem. I can't imagine a better way to get them talking to their friends about topology (it still works for me to this day) | |
| Dec 21, 2023 at 22:05 | answer | added | Joshua Jurgensmeier | timeline score: 2 | |
| Dec 21, 2023 at 14:20 | comment | added | Michał Miśkiewicz | Be aware of certain issues with "inside and outside" of the Klein bottle. If it's only immersed (and not embedded) into $\mathbb{R}^3$, the question of having "inside and outside" is somewhat ill-posed. On the other hand, it is possible to embed the Klein bottle into a 3-dimensional (non-orientable) manifold in which it does have an inside and outside. Finally, the projective plane is different in that respect - it cannot be embedded with an inside and outside (otherwise it would be a boundary of some 3-manifold, which it isn't). | |
| Dec 21, 2023 at 13:59 | answer | added | A. Goodier | timeline score: 3 | |
| Dec 21, 2023 at 9:52 | comment | added | AccidentalTaylorExpansion | [sarcasm] so you know a donut and a coffee mug right? They are basically the same | |
| Dec 20, 2023 at 22:53 | answer | added | Daniel Shapero | timeline score: 3 | |
| Dec 20, 2023 at 13:32 | comment | added | Jyrki Lahtonen | Building upon Jonathan's suggestion of using the hairy ball theorem. The task is possible on a circle (and the sphere in 4D), and on a torus (combing east to west is non-problematic, when the poles have been replaced by circles). | |
| Dec 20, 2023 at 13:29 | comment | added | Jyrki Lahtonen | Fixed point theorem. Take two maps of their home state (or country). Fold, twist and whatnot the other (but do not tear it), and toss it randomly on top of the other. There exists at least one location in the state whose versions appear on the same spot (=on top of each other). | |
| Dec 20, 2023 at 13:24 | history | edited | Joseph O'Rourke |
edited tags
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| Dec 20, 2023 at 13:22 | history | became hot network question | |||
| Dec 20, 2023 at 13:21 | answer | added | Joseph O'Rourke | timeline score: 12 | |
| Dec 19, 2023 at 22:59 | answer | added | Michał Miśkiewicz | timeline score: 3 | |
| Dec 19, 2023 at 20:18 | answer | added | user1815 | timeline score: 6 | |
| Dec 19, 2023 at 16:54 | answer | added | Brendan W. Sullivan | timeline score: 7 | |
| Dec 19, 2023 at 12:58 | history | migrated | from math.stackexchange.com (revisions) | ||
| Dec 19, 2023 at 10:52 | comment | added | Vuk Jovovic | Stereographic projection metrics: The parallel lines intersect at infinity and number 2 is "closer" to infinity than to number 0, etc. | |
| Dec 19, 2023 at 1:11 | comment | added | Ethan Bolker | The spinor spanner: jstor.org/stable/2318771 | |
| Dec 19, 2023 at 1:06 | answer | added | Steven Clontz | timeline score: 5 | |
| Dec 18, 2023 at 23:31 | comment | added | Steven Clontz | The last time I taught topology, I used the Paper Mario Origami King ring battle system to motivate things. youtube.com/watch?v=R-zLCSgw_ao | |
| Dec 18, 2023 at 23:26 | comment | added | Taladris | How about unknotting knots: youtube.com/… (I remember some videos where they used it to do Houdini-style evasion magic tricks) | |
| Dec 18, 2023 at 22:58 | comment | added | JonathanZ | The hairy ball Theorem is great for this, because they can all go off and try to come up with a combing of their own. Even more fun when you reveal that it can be done with less than 2 singularities (although I wouldn't call that last point purely topological). | |
| Dec 18, 2023 at 14:06 | comment | added | Dave L Renfro | Relevant: Algebraic topology in high school? | |
| Dec 18, 2023 at 14:02 | comment | added | Mariusz Popieluch | See professor Tadashi Tokieda's videos on Numberphile :) | |
| Dec 18, 2023 at 12:18 | comment | added | marilou64 | knots are a great idea ! thanks | |
| Dec 18, 2023 at 10:11 | comment | added | Paul | Make a mobius band and draw on it with a pen. Cut the band along the middle length to create two bands. | |
| Dec 18, 2023 at 10:03 | comment | added | Julius J. | For some algebraic topology you could talk about knots and links, this is fairly hands-on (Let them tie the knots themselves!) | |
| Dec 18, 2023 at 9:44 | comment | added | Asaf Karagila | Topology fun fact: some people manage to get a permanent academic position by studying topology! :-) | |
| Dec 18, 2023 at 9:42 | history | asked | marilou64 | CC BY-SA 4.0 |