0xDE ([info]11011110) wrote,
@ 2007-09-26 14:18:00
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Entry tags:visibility graph

Andy's triangles
Cute polygon visibility puzzler from Andy Drucker: how many equal-sized equilateral triangles can you place in the plane so that each triangle vertex is visible from each other triangle vertex?

If you're stuck, here's a spoilerific illustration...


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(Anonymous)
2007-09-30 06:15 pm UTC (link)
Thanks, David!
It can also be done with infinitely many triangles at once, but the picture is less pretty...
-Andy

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(Anonymous)
2007-09-30 06:18 pm UTC (link)
One additional thing I'd like to know, assuming readers agree with my last statement: must any such infinite arrangement have asymptotic density zero?
-A

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[info]11011110
2007-09-30 10:28 pm UTC (link)
Thanks yourself for a fun puzzle.

I assume the answer to your density question must be yes but I don't know how one would go about proving it.

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