Prince Rupert's cube • Hacker News Board

Re: Prince Rupert's cube

#31

Post by cousin_it » Sat, Feb 17, 2018, 10:04 PM UTC

octahedron wrote: post #29

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?

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

Re: Prince Rupert's cube

#32

Post by octahedron » Sat, Feb 17, 2018, 10:25 PM UTC

cousin_it wrote: post #31

octahedron wrote: post #29

Earlier quoted context omitted.

An octahedron?

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

Is the question posed only in relation to three dimensional space?

Re: Prince Rupert's cube

#33

Post by tritium » Sat, Feb 17, 2018, 11:06 PM UTC

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

Re: Prince Rupert's cube

#34

Post by poopslide » Sat, Feb 17, 2018, 11:38 PM UTC

11s video:

https://www.youtube.com/watch?v=-2jjgHsxEu4

Re: Prince Rupert's cube

#35

Post by cousin_it » Sun, Feb 18, 2018, 12:45 AM UTC

octahedron wrote: post #32

cousin_it wrote: post #31

Earlier quoted context omitted.

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

Is the question posed only in relation to three dimensional space?

Yeah, it's the kind of shape you can carve from a block of cheese in a minute.

Re: Prince Rupert's cube

#36

Post by a1369209993 » Sun, Feb 18, 2018, 2:01 AM UTC

cousin_it wrote: post #12

taneq wrote: post #10

Earlier quoted context omitted.

After watching the video, I feel like this follows intuitively from the fact that sqrt(2) > 1.

The biggest possible difference between Prince Rupert's cubes is 3%, which is much smaller than the difference between sqrt(2) and 1.

FWIW, `(sqrt(2)-1)^3` is `0.071067831`, which while not equal to `(1.0606601-1)` is fairly close.

Re: Prince Rupert's cube

#37

Post by gowld » Sun, Feb 18, 2018, 2:03 AM UTC

Mathologer on Rupert's cube: https://www.youtube.com/watch?v=rAHcZGjKVvg

Re: Prince Rupert's cube

#38

Post by [deleted] » Sun, Feb 18, 2018, 2:16 AM UTC

a1369209993 wrote: post #36

cousin_it wrote: post #12

Earlier quoted context omitted.

The biggest possible difference between Prince Rupert's cubes is 3%, which is much smaller than the difference between sqrt(2) and 1.

FWIW, `(sqrt(2)-1)^3` is `0.071067831`, which while not equal to `(1.0606601-1)` is fairly close.

[deleted]

Re: Prince Rupert's cube

#39

Post by tritium » Sun, Feb 18, 2018, 2:31 AM UTC

tritium wrote: post #33

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

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.

Re: Prince Rupert's cube

#40

Post by tritium » Sun, Feb 18, 2018, 2:32 AM UTC

tritium wrote: post #39

tritium wrote: post #33

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

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.

Good job. Keep downvoting.