Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

The World Record for the Shortest Math Article: 2 Words

openculture.com

Post reply on HN
Print view View original

11–20 of 39 posts

Re: The World Record for the Shortest Math Article: 2 Words

#11

Post by geofft »

Can someone explain Figure 2 from this paper? (If you didn't catch the link, it's inlined at http://www.wfnmc.org/mc20101.pdf .)

Figure 1 makes sense to me: it's (n-1)² unit equilateral triangles, plus a row at the bottom with (2n-1) + 2 equilateral triangles that causes coverage of a slightly larger triangle. (I assume the question posed is "for at least some tiny but nonzero ε".)

I don't know how to start interpreting figure 2. Where are the n²+2 triangles (or are they supposed to be there?)? What's the big empty space? Why 1 - ε, not 1 + ε?

Re: The World Record for the Shortest Math Article: 2 Words

#13

Post by raverbashing »

flashman wrote: post #7
Pinckney wrote: post #3

The paper doesn't make any sense without the title: "Can n^2 + 1 unit equilateral triangles cover an equilateral triangle of side >n, say n+\epsilon?"

Ah, this is like cheating on a compression test by encoding information in the filename.

Or splitting it into several files

Re: The World Record for the Shortest Math Article: 2 Words

#15

Post by madez »

hkmurakami wrote: post #12

Definitely not surprised that the author is John Conway (and his coauthor). I took his course on Linear Algebra back in the day -- the man is a veritable real life troll (in a good way)

That's typical for mathematicians - even more so with extroverted ones. They approach rules as a game one can use at will as long as the rules remain true. Thus, playing pranks with rules can become enjoyable. Coincidentally, surprise is the quintessence of humour, some say.

The original meaning of the word "hacker" is related to this thinking. However, the focus is different. The hackers tend to achieve their goal in whatever "hacky" way possible while mathematicians see the rules itself as the game.

Re: The World Record for the Shortest Math Article: 2 Words

#18

Post by artnep »

geofft wrote: post #11

Can someone explain Figure 2 from this paper? (If you didn't catch the link, it's inlined at http://www.wfnmc.org/mc20101.pdf .) Figure 1 makes sense to me: it's (n-1)² unit equilateral triangles, plus a row at the bottom with (2n-1) + 2 equilateral triangles that causes coverage of a slightly larger triangle. (I assume the question posed is "for at least some tiny but nonzero ε".) I don't know how to start interpret…

I think the idea is that the lower n-1 rows each have height (n-1)ε (by spreading them out horizontally), and at the top there's a big triangle with side length 1+(n-1)ε

Re: The World Record for the Shortest Math Article: 2 Words

#20

Post by rahimnathwani »

flashman wrote: post #7
Pinckney wrote: post #3

The paper doesn't make any sense without the title: "Can n^2 + 1 unit equilateral triangles cover an equilateral triangle of side >n, say n+\epsilon?"

Ah, this is like cheating on a compression test by encoding information in the filename.

http://www.patrickcraig.co.uk/other/compression.php
Post reply on HN