7 ms·
Prince Rupert's cube
- mrdmnd 9y agoInteresting that the optimal solution is not "slide it along the space diagonal" but rather "slide it parallel to a face".
- ThoAppelsin 9y agoI might be wrong about this, but as far as I can see the larger cube slides parallel to an edge and not a face. On top of that, I think the cube passing through would still be sliding parallel to an edge, even if it were to slide along a space diagonal, so those two wouldn't be mutually exclusive. Unless I have failed to visualize it right ok my head.
- shaded-enmity 9y agoAnother interesting thing named after Prince Rupert is the Prince Rupert's drop for anyone interested: https://www.youtube.com/watch?v=k5MORochIDw https://www.youtube.com/watch?v=k5MORochIDw
- newman8r 9y agoI recommend trying them with capillary tubes, you can melt them with a cigarette lighter
- anvandare 9y agoA video is worth a thousand words of theory: https://www.youtube.com/watch?v=-2jjgHsxEu4 https://www.youtube.com/watch?v=-2jjgHsxEu4
- jholman 9y agoThat was very good (thank you!), but it led me to this, which was even better: https://www.youtube.com/watch?v=rAHcZGjKVvg https://www.youtube.com/watch?v=rAHcZGjKVvg
- taneq 9y agoAfter watching the video, I feel like this follows intuitively from the fact that sqrt(2) > 1.
- cousin_it 9y agoThe biggest possible difference between Prince Rupert's cubes is 3%, which is much smaller than the difference between sqrt(2) and 1.
- a1369209993 9y agoFWIW, `(sqrt(2)-1)^3` is `0.071067831`, which while not equal to `(1.0606601-1)` is fairly close.
- deleted 9y ago[deleted]
- arturmakly 9y agodrop https://m.youtube.com/watch?v=lt-zvsGvtqg https://m.youtube.com/watch?v=lt-zvsGvtqg
- echelon 9y agoI wish more of mathematics was visual. That's the mode of thinking I employ the most, and I excel at spatial problems. I wish higher level mathematics and physics paid more attention to the use of visual schematics and diagrams. So much can be communicated with them. Words often pale in comparison.
- ttsda 9y agoI would like to recommend the 3b1b's[1] YouTube channel. His procedurally generated videos really make you think of certain math that looked unintuitive or hard to explain in a truly intuitive, visual way. His series on linear algebra was very eye opening to me, as well as many of his videos about subjects I was initially failing to understand. [1] https://www.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw https://www.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw
- echelon 9y agoThanks so much for sharing! This looks fantastic.
- mjlee 9y agoI reckon you could stretch this to a 30 minute whiteboard session to answer why (some) manhole covers are round.
- planteen 9y agoAnd then fall in the Reuleaux triangle rabbit hole.
- newman8r 9y agolooks like a fun model to 3d-print
- cousin_it 9y agoAnother nice puzzle: A cube looks like a square from three orthogonal directions. A cylinder can look like a square from infinitely many directions, but they are all coplanar. Can you find a convex shape that looks like a square from more than three directions, without all of them being coplanar? In particular, can you find a convex shape that looks like a square from two distinct sets of three orthogonal directions? Can you find all such shapes?
- no_identd 9y agoDo mathematicians consider this an open problem or does there exist a well known solution? And what about a name for this problem, does it have one already?
- cousin_it 9y agoNah, it's nothing as grand as that. I saw it on facebook a few months ago and solved it in about ten minutes, just wanted to share the fun.
- no_identd 9y ago...do you know the story of George Dantzig? https://en.wikipedia.org/wiki/George_Dantzig#Mathematical_statistics https://en.wikipedia.org/wiki/George_Dantzig#Mathematical_st... I don't mean to say that it seems applicable here - but I also don't mean to say that it doesn't seem applicable here.
- Avshalom 9y agoAm I allowed to invoke hypercubes because that would cut this knot nicely.
- TehCorwiz 9y agoOrthographic or perspective projection?
- cousin_it 9y ago
- wetha 9y agoI knew of Prince Rupert’s drop before[1]. Reading about Prince Rupert’s cube sent me down the rabbit-hole of reading up on Prince Rupert himself. Why do we no longer have Renaissance men/women today, contributing to the sciences, philosophy and the arts? What did we lose? [1] https://en.m.wikipedia.org/wiki/Prince_Rupert%27s_Drop https://en.m.wikipedia.org/wiki/Prince_Rupert%27s_Drop
- craftyguy 9y ago> Why do we no longer have Renaissance men/women today, contributing to the sciences, philosophy and the arts? What did we lose? A lot of the low-hanging fruit has already been claimed, and it's very difficult now for amateurs to make discoveries in mathematics and physics. There are people today doing amazing research, it just takes a career and a team (and in many cases expensive equipment) to do so. If by "Renaissance men/women" you mean "well-versed/engaged in many topics", well, you just need to open your eyes. There are many folks like this now, likely millions. It was a bit more of a rarity a few hundred years ago, so it was much easier for these individuals to be documented/preserved.
- anvandare 9y agoThe more complex (advanced) a society becomes, the more specialized its individual members have to become so the longer it takes to produce a unit for a specific function (basic education of people now takes 18 years of their life). With the exponential increase in scientific output (http://pespmc1.vub.ac.be/POS/turchFigs/IMG.FIG14.1.GIF http://pespmc1.vub.ac.be/POS/turchFigs/IMG.FIG14.1.GIF) it becomes ever harder for an individual to keep up with multiple fields (in fact, I suspect that as soon as a field becomes _too_ big it automatically branches into new fields because of this). It would have been possible to read every book in existence on mathematics in a lifetime in the 17th century, but not in the 21st century.
- WJW 9y agoI'd wager that there weren't all that many renaissance men/women back in the day either, but some of the ones that were there are now well known. In any case, there are plenty of people contributing in a wide array of fields who are alive today. How about Franklin Story Musgraves, who has academic degrees in six different fields, including medicine, computer programming and literature. He also went into space for NASA no less than six times, served in numerous conflicts while he was in the air force, was briefly employed as a mathematician for Kodak, practiced and taught clinical medicine and is/was a consultant for Disney. I found him with the briefest of google searches for "modern renaissance men" :) https://en.wikipedia.org/wiki/Story_Musgrave https://en.wikipedia.org/wiki/Story_Musgrave
- tritium 9y agoSo, cubes have a margin of 6% play, if you need to pass any other cube through a given cube.
- poopslide 9y ago11s video: https://www.youtube.com/watch?v=-2jjgHsxEu4 https://www.youtube.com/watch?v=-2jjgHsxEu4
- gowld 9y agoMathologer on Rupert's cube: https://www.youtube.com/watch?v=rAHcZGjKVvg https://www.youtube.com/watch?v=rAHcZGjKVvg