Prince Rupert's cube • Hacker News Board

Re: Prince Rupert's cube

#41

Post by darkmighty » Sun, Feb 18, 2018, 3:06 AM UTC

cousin_it wrote: post #30

mhei wrote: post #28

Earlier quoted context omitted.

(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.

I'm thoroughly impressed by your geometric abilities! I didn't know that, and took me a while to check. Any hints on the puzzle, and as a sidequestion, what tools do you use to figure this kind of question? Just imagination, vector algebra, elementary trigonometry?

Re: Prince Rupert's cube

#42

Post by cousin_it » Sun, Feb 18, 2018, 3:22 AM UTC

darkmighty wrote: post #41

cousin_it wrote: post #30

Earlier quoted context omitted.

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

I'm thoroughly impressed by your geometric abilities! I didn't know that, and took me a while to check. Any hints on the puzzle, and as a sidequestion, what tools do you use to figure this kind of question? Just imagination, vector algebra, elementary trigonometry?

Huh? There's nothing to be impressed about. You can stick a tetrahedron inside a cube so it creates the same square shadows in all three directions: https://i.stack.imgur.com/oAUnH.gif

I know a lot of math, but for this puzzle, drawing stuff on paper is enough. Here's a hint: if you cut off one corner of the cube, all shadows are still square. How much can you cut? Can you cut some corners strategically to make at least one new square shadow while keeping all the old ones? How many square shadows can you get?

Re: Prince Rupert's cube

#43

Post by echelon » Mon, Feb 19, 2018, 1:50 PM UTC

ttsda wrote: post #26

echelon wrote: post #25

Earlier quoted context omitted.

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

Thanks so much for sharing! This looks fantastic.