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Prince Rupert's cube

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Re: Prince Rupert's cube

#21

Post by anvandare »

wetha wrote: post #18

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

The 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) 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.

Re: Prince Rupert's cube

#22

Post by whatshisface »

TehCorwiz wrote: post #17
cousin_it wrote: post #11

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?…

Orthographic or perspective projection?

Cylinders only look like squares in orthographic projection, so my guess is that that's the intention.

Re: Prince Rupert's cube

#25

Post by echelon »

anvandare wrote: post #5

A video is worth a thousand words of theory: https://www.youtube.com/watch?v=-2jjgHsxEu4

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.

Re: Prince Rupert's cube

#26

Post by ttsda »

echelon wrote: post #25
anvandare wrote: post #5

A video is worth a thousand words of theory: https://www.youtube.com/watch?v=-2jjgHsxEu4

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.

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

Re: Prince Rupert's cube

#27

Post by WJW »

wetha wrote: post #18

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

I'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

Re: Prince Rupert's cube

#28

Post by mhei »

cousin_it wrote: post #11

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?…

(Rot13 as not to spoil the riddle)

Ubj nobhg n grgenurqeba? Begubtencuvp cebwrpgvba nybat gur yvar pbaarpgvat nal rqtr zvqcbvag gb gur bccbfvgr rqtr zvqcbvag tvirf n fdhner, lvryqvat 3 fhpu cebwrpgvbaf (cyhf gurve bccbfvgr pbhagrecnegf). Abg fher vs gurer ner bgure fhpu funcrf (vtabevat gevivny zbqvsvpngvbaf bs gur grgenurqeba) - qvq lbh znantr gb svther guvf cneg bhg?

Re: Prince Rupert's cube

#29

Post by octahedron »

cousin_it wrote: post #11

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?…

An octahedron?

Re: Prince Rupert's cube

#30

Post by cousin_it »

mhei wrote: post #28
cousin_it wrote: post #11

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?…

(Rot13 as not to spoil the riddle) Ubj nobhg n grgenurqeba? Begubtencuvp cebwrpgvba nybat gur yvar pbaarpgvat nal rqtr zvqcbvag gb gur bccbfvgr rqtr zvqcbvag tvirf n fdhner, lvryqvat 3 fhpu cebwrpgvbaf (cyhf gurve bccbfvgr pbhagrecnegf). Abg fher vs gurer ner bgure fhpu funcrf (vtabevat gevivny zbqvsvpngvbaf bs gur grgenurqeba) - qvq lbh znantr gb svther guvf cneg bhg?

A tetrahedron looks like a square from three orthogonal directions, same as a cube. It's possible to get more.
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