[Background for those not getting it: what's touted as the world's shortest story is "For sale: baby shoes. Never worn." attributed to Ernest Hemingway. http://en.wikipedia.org/wiki/For_sale:_baby_shoes,_never_wor... Makes me tear up just recounting it.]
>John Conway and I accepted the “filler”, and in the January 2005 issue our paper [12] was published. The Monthly, however, invented the title without any consultation with the authors, and added our title to the body of the article! (p. 31, my emphasis)
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?
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
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.
Reminds me of the record for the shortest movie review. The movie in question is called "Isn't it Romantic?" which Leonard Maltin succinctly answered with "No".
I suppose the title of this submission is correct, but I would like to note that it's not "a new world record in the number of words in a paper". I believe that honour goes to:
Fiengo, Robert, and Howard Lasnik. 1972. “On Nonrecoverable Deletion in Syntax.” Linguistic Inquiry 3 (4): 528.
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[ 3.4 ms ] story [ 71.3 ms ] threadLet 2 words imply 6.
[Background for those not getting it: what's touted as the world's shortest story is "For sale: baby shoes. Never worn." attributed to Ernest Hemingway. http://en.wikipedia.org/wiki/For_sale:_baby_shoes,_never_wor... Makes me tear up just recounting it.]
"Can n^2 + 1 unit equilateral triangles cover an equilateral triangle of side >n, say n+\epsilon?"
>John Conway and I accepted the “filler”, and in the January 2005 issue our paper [12] was published. The Monthly, however, invented the title without any consultation with the authors, and added our title to the body of the article! (p. 31, my emphasis)
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?
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.
Unfortunately no better online source than Wikipedia: http://en.wikipedia.org/wiki/Isn%27t_It_Romantic%3F_%28film%...
Fiengo, Robert, and Howard Lasnik. 1972. “On Nonrecoverable Deletion in Syntax.” Linguistic Inquiry 3 (4): 528.
You can read the entire paper here: https://pbs.twimg.com/media/BmLQjz0CMAA-l28.jpg:large
Dennis Upper. 1974. The unsuccessful self-treatment of a case of "writer's block". Journal of Applied Behavior Analysis 7 (3): 497.
(Unfortunately it's paywalled: http://onlinelibrary.wiley.com/doi/10.1901/jaba.1974.7-497a/...)
Drawings and explanations go hand in hand.