Folding a dollar bill into a triangle

There is some interesting geometry in this example of paper folding.

Start with a dollar bill (actually, most paper currency will do). For the classroom, I print fake dollars for the students.

Now, follow this sequence of folds:

foldingDollarBill_fold1

foldingDollarBill_fold2

foldingDollarBill_fold3

Repeat the last step as many times as you can, and insert whatever remains into the pocket formed by the triangle.

Is the triangle equilateral? Why?

If folded carefully, a real dollar bill seems be just the right length so that the last fold lines up with the edge of the bill. Do you think this is deliberate? What does this say about the ratio of the side lengths of the dollar bill?

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