
Prince Rupert's cube - enhray
https://en.wikipedia.org/wiki/Prince_Rupert%27s_cube
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anvandare
A video is worth a thousand words of theory:

[https://www.youtube.com/watch?v=-2jjgHsxEu4](https://www.youtube.com/watch?v=-2jjgHsxEu4)

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echelon
I 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.

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ttsda
I 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)

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echelon
Thanks so much for sharing! This looks fantastic.

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cousin_it
Another 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?

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TehCorwiz
Orthographic or perspective projection?

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cousin_it
I only know the solution for orthographic. But it seems like perspective would
be too easy, just make any shape with many square sides, and put the cameras
close to the sides.

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shaded-enmity
Another 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)

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newman8r
I recommend trying them with capillary tubes, you can melt them with a
cigarette lighter

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wetha
I 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)

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craftyguy
> 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.

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mrdmnd
Interesting that the optimal solution is not "slide it along the space
diagonal" but rather "slide it parallel to a face".

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ThoAppelsin
I 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.

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gowld
Mathologer on Rupert's cube:
[https://www.youtube.com/watch?v=rAHcZGjKVvg](https://www.youtube.com/watch?v=rAHcZGjKVvg)

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newman8r
looks like a fun model to 3d-print

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tritium
So, cubes have a margin of 6% play, if you need to pass any other cube through
a given cube.

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tritium
Wow, a downvote for paraphrasing a wikipedia article.

    
    
      Its side length is approximately 6% larger than 
      that of the unit cube through which it passes.
    

I fail to see any error, based on that verbatim quote.

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tritium
Good job. Keep downvoting.

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mjlee
I reckon you could stretch this to a 30 minute whiteboard session to answer
why (some) manhole covers are round.

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planteen
And then fall in the Reuleaux triangle rabbit hole.

