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Folding a Strip to Converge to an Equilateral Triangle

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photo
figure
ϵ
-0.3
k
4
show labels
Begin with a long strip of gummed tape. Fold it up in any way you like, then unfold it, fold it down, and repeat as in the photo. The number of steps can be selected with the
k
slider.
This gives a sequence of isosceles triangles with summits at
A
i
and
B
i
. The sequence of triangles converges to an equilateral triangle.
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