 |
Post AncBDImUFKgmVBnGYy by [email protected] |
 |
More posts by [email protected] |
|
Post #AnN3kwMwMmVrpkyUbo by [email protected] |
|
0 likes, 0 repeats |
|
|
|
If you cut out the yellow shape here, you can fold it up along the red lines, a… |
|
|
|
Post #AnN66EdjpYLUUQ76Po by [email protected] |
|
0 likes, 0 repeats |
|
|
|
"A triangulation of the sphere where 5 or 6 triangles meet at each vertex&… |
|
|
|
Post #AnN6zsWxDgqg8RTOoy by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@johncarlosbaez For anyone who wants to play: Incompetech has equilateral trian… |
|
|
|
Post #AnN6zsieWCCqiiwk3U by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@anke - thanks! I will try this myself. |
|
|
|
Post #AnN8Rqi9g49sYTc6hU by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@johncarlosbaez Looks related to Goldberg polyhedra?https://en.wikipedia.org/wi… |
|
|
|
Post #AnNFBFZ4ickCOROlxA by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@johncarlosbaez I'm not familiar with this William Thurston, alas, but *How… |
|
|
|
Post #AnNFUBIgnVCufalGPA by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@johncarlosbaez > A super-genius could write a program where the user could … |
|
|
|
Post #AnNHYCHNIfBMlwBmmu by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@johncarlosbaez I thought I was good at visualizing things but I’m struggling… |
|
|
|
Post #AnNM9T4UEJB9NpBjlo by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@weekend_editor - I hadn't known about Goldberg polyhedra, thanks! I'v… |
|
|
|
Post #AnNakcRDlZIAVSQnya by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@dougmerritt - I'd never heard of Howard Thurston. But then I'm pretty… |
|
|
|
Post #AnNb3PaNm5qK9Eg4Uy by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@johncarlosbaez Wow, what an amazing answer. If he was generally like that, the… |
|
|
|
Post #AnNbTSbHBpA91gW5bs by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@johncarlosbaez Yes, that was clearly a loss to our world. |
|
|
|
Post #AnNbmsTnCAZWn8H76O by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@dougmerritt - he was generally like that, which is why he was so well loved.If… |
|
|
|
Post #AnNbroDkSNYf1z7cZs by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@dougmerritt - sorry, I deleted my last comment so you'd see the new enhanc… |
|
|
|
Post #AnNc5sIW5zV1jI3k4e by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@dougmerritt @johncarlosbaez It was an amazing answer indeed! But I'd argue… |
|
|
|
Post #AnNc5sPxeJSE6NXgg4 by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@TonyVladusich @dougmerritt - I guess just as nonmathematicians mistakenly thin… |
|
|
|
Post #AnNcDVjpr3Os4zTjpA by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@johncarlosbaez @TonyVladusich For that matter, I have met (a few) dry dehumani… |
|
|
|
Post #AnNdtCX1kq9cczvmvg by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@johncarlosbaez Well, cutting it out and glueing it together was successful. It… |
|
|
|
Post #AnNfbUjzVyBdnYgC3c by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@GerardWestendorp - cool, very nice! There's no promise that such shapes a… |
|
|
|
Post #AnNfeoZUF2BaAdLiHg by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@johncarlosbaez BTW I'm not surprised you haven't heard of him, since H… |
|
|
|
Post #AnOJfwU0JAtVADsRhA by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@johncarlosbaez Cute. But there appears to be a missing constraint in the descr… |
|
|
|
Post #AnORsEAp9ycT8fH72W by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@johncarlosbaez I tried to use ChatGPT o1-preview to do some coding (for a diff… |
|
|
|
Post #AnOvAyUwYwF2h8yeTQ by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@johncarlosbaez The "ordinary" icosahedron is not so obvious. I figur… |
|
|
|
Post #AnP25b5crlOEKIWB2u by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@johncarlosbaez I enjoyed that essay, thanks for the link!@dougmerritt |
|
|
|
Post #AnPMX6QMTIoAPVbsCO by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@johncarlosbaez Here's my go at it. I got lucky, and my mine ended up being… |
|
|
|
Post #AnPOKlOd1jwncv2k9Q by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@chessapig - nice, that's really interesting. I'm surprised that your … |
|
|
|
Post #AnPObZvGwFCIxuKWhM by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@11011110 @johncarlosbaez I thought the original yellow shape looked wrong, but… |
|
|
|
Post #AnPOba6cG4GtX5daNc by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@ngons @johncarlosbaez Now that I looked through Thurston's paper, I see th… |
|
|
|
Post #AnPObaHFcWmK44c4xM by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@11011110 - thanks! I hadn't known about the concept of 'star unfoldin… |
|
|
|
Post #AnPOuw8uY77tNhwMYi by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@4raylee @johncarlosbaez I just finished Thurston's essay, and yeah, it was… |
|
|
|
Post #AnPOuwGi57MfltaaiO by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@dougmerritt @4raylee - great! Definitely an interesting guy. |
|
|
|
Post #AnPPFVlzmmyNg924zg by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@anke @johncarlosbaez If you want to be able to customize your triangle graph p… |
|
|
|
Post #AnPPFVz701SsKpAYRE by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@duetosymmetry - Thanks! I want to draw my own example 11-gon in LaTeX / TikZ … |
|
|
|
Post #AnPPMOmoA4L42JhG2i by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@johncarlosbaez @anke @mcnees I have been getting more and more proficient at T… |
|
|
|
Post #AnPPa2MqJKFOYm3T1c by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@duetosymmetry - I'm bad at TikZ, but I use it a lot because there's a … |
|
|
|
Post #AnPPlsg2AJjDyqg9qK by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@johncarlosbaez I am supposed to be writing GR homework solutions today, but I&… |
|
|
|
Post #AnPTfQ1mAa0FCn1THc by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@johncarlosbaez @11011110 Not that odd really — if you allow the equilateral … |
|
|
|
Post #AnPWZVvTctbdcjx6h6 by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@GerardWestendorp - cool! Thanks!If you make a version of this without all the… |
|
|
|
Post #AnPXWhixPAF1IgJvhg by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@duetosymmetry - @GerardWestendorp has almost produced the picture I want. |
|
|
|
Post #AnPYRIuILZISpzc22y by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@4raylee - It's indeed trick to visualize this stuff. I believe first you … |
|
|
|
Post #AnPads9zInnDYZ4cWO by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@johncarlosbaez Thanks for the walkthrough! His example helped me understand my… |
|
|
|
Post #AnPcCllx8wPppq2GB6 by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@johncarlosbaez Here's a video of me spinning it around, maybe this makes i… |
|
|
|
Post #AnPewjoSxbvAzGG48W by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@chessapig - okay, great! |
|
|
|
Post #AnPfEVl1xNxibj7smG by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@johncarlosbaez @GerardWestendorp I figured out the cleanest way to do this wit… |
|
|
|
Post #AnQc6p91t2wriLxDdY by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@johncarlosbaez It would be cool to be on the AMS weblog!Here is the icosahedro… |
|
|
|
Post #AnQcpOqqUWivCMhj28 by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@johncarlosbaez It also works for Generalized cubes!I can’t visualize yet how… |
|
|
|
Post #AnRApVDMELZXNISF6m by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@johncarlosbaez I edited the green triangles by hand, but I could write a macro… |
|
|
|
Post #AnRApVL9lLoJlU6TGS by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@GerardWestendorp - I almost failed to see this reply of yours! (So if I igno… |
|
|
|
Post #AnRC1eTbih1lWuPdA0 by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@GerardWestendorp - by the way, your picture will appear, not on my AMS blog (w… |
|
|
|
Post #AnRJGfAi7IMHi0g8EC by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@johncarlosbaez Wow! |
|
|
|
Post #AnRfO0pwABVxv6s68e by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@GerardWestendorp - aargh, but it turns out I can't use the icosahedron as … |
|
|
|
Post #AnRfitGxTw08XdSwuO by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@johncarlosbaez @GerardWestendorp Order of operations may help here. Try puttin… |
|
|
|
Post #AnRkPlpDRktJiEBx3I by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@johncarlosbaez @duetosymmetry We could do the buckyball, AKA truncated icosahe… |
|
|
|
Post #AnSCcqWe4xyAluWrGi by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@johncarlosbaez @duetosymmetry Changing the icosahedron to the buckyball would … |
|
|
|
Post #AnSCcqenaeUXBCLMye by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@GerardWestendorp @duetosymmetry - someone on this thread pointed out "Gol… |
|
|
|
Post #AnSCyO0Eo3sGgHdqEq by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@GerardWestendorp - We can make your icosahedron example be a puzzle in my colu… |
|
|
|
Post #AnSQohr1XkWIiAbu6q by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@johncarlosbaez @GerardWestendorp one of the removed triangles is not equilater… |
|
|
|
Post #AnSgIuXcR7Ss3kOWcC by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@johncarlosbaez @duetosymmetry Ah, I can see how to easily generate a "Thu… |
|
|
|
Post #AnTEupWov41bxSH2QK by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@GerardWestendorp @johncarlosbaez @duetosymmetry As I said elsewhere in this th… |
|
|
|
Post #AnTEupmPz4VAjpZUjg by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@11011110 @GerardWestendorp @duetosymmetry - thanks, that's interesting! T… |
|
|
|
Post #AnTFSulPxcD22cM22C by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@GerardWestendorp wrote: "Hmm, but these Goldberg polyhedra also have a sl… |
|
|
|
Post #AnTGtPk3VWOnbKuvCK by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@duetosymmetry - yuck, you're right! I spent hours creating this and becam… |
|
|
|
Post #AnTH3sOBqtX7LSg7ii by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@GerardWestendorp - could you show me the icosahedron, done using your new prog… |
|
|
|
Post #AnTOIMewnumAxaN8HQ by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@johncarlosbaez FYI I just learned how to use the "decorations" engin… |
|
|
|
Post #AnTUSdD6iqE4ued3uS by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@johncarlosbaez Here is the latest version. It is now easy to change the colors… |
|
|
|
Post #AnTbjJ7ZMmRZD0wBbE by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@johncarlosbaez With the new code, outside and inside are programmed like this… |
|
|
|
Post #AnTbjJF0v6Ola6Q8Ce by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@duetosymmetry - please send me the code: that would be great! I may make a sm… |
|
|
|
Post #AnTjaVMXHcIACaFeZU by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@johncarlosbaez But by Alexandria again, a sphere with cone points is exactly e… |
|
|
|
Post #AnTkyxm3OvWRDtPiV6 by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@11011110 - wonderful stuff! |
|
|
|
Post #AncBDImUFKgmVBnGYy by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@johncarlosbaez I was thinking, Thurston’s method of defining a positive curv… |
|
|
|
Post #AncBDIuHmKvYtNRUie by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@GerardWestendorp - wow! Scary to look at!Btw, I have a puzzle for you here:ht… |
|
|
|
Post #AnclIKOHHo3nI9ALey by [email protected] |
|
0 likes, 0 repeats |
|
|
|
@johncarlosbaez @GerardWestendorp Find any vertex-to-vertex line segment in the… |
