Re:The World Record for the Shortest Math Article: 2 Words
by geofft on Tuesday April 21, 2015 @01:49AM
(#9412457)
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
by artnep on Tuesday April 21, 2015 @03:15AM
(#9412645)
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
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?