11–20 of 43 posts
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?
A video is worth a thousand words of theory: https://www.youtube.com/watch?v=-2jjgHsxEu4
After watching the video, I feel like this follows intuitively from the fact that sqrt(2) > 1.
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?…
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?…
Do 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?
Earlier quoted context omitted.
Do 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?
Nah, 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.
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.
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?…
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?…
Why do we no longer have Renaissance men/women today, contributing to the sciences, philosophy and the arts? What did we lose?
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?
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
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.