20 May 2008
Origami Pentagon, ctd.
Actually, I know one quick and dirty method (which my father had told me once): take a strip of paper of constant width w and tie a knot, as in the figure. Flatten the knot carefully so that it leaves no gaps--it should all fit nicely together. The result is a regular pentagon of edge length w.
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can you cross these dots with a single line?
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Yes I can.
ReplyDeleteI can't figure it out (the crossing of the dots with a single line)! Just curious (if you don't mind, and bother enlightening me), how so?
ReplyDeleteWan Yie
The question of the anonymous writer was ill-posed. Indeed, he/she did not define what "line" means. In which case, there are myriads of solutions!
ReplyDeleteNow, if we are talking about a single straight line, obviously, the answer is that it is not possible.
But if we are talking about a line which is continuous and piecewise straight, then the question is what is the smallest number of straight segments we can use. The answer is 4. And here is the line that achieves this minimum.
Or you could get a really fat sharpe marker and and make one straight line.
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