Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Consider a standard square sheet lying on the xy plane with edge length n. Is it possible to determine the coordinates (x, y, z) of the point where the vertices of the sheet will meet, when each of the four vertices are pulled upwards and inwards equally, at the same time?

The point will obviously lie right above the center of the sheet. The vertices will be pulled upwards until only a single point (theoretically speaking) of the sheet will be in contact with the xy plane, and then they will be pulled inwards until they meet above the center of the sheet.

share|improve this question

1 Answer 1

up vote 3 down vote accepted

If I understand the question properly, the answer depends on the flexibility of the sheet. A fine cloth napkin might crease almost like origami, in which case the height would be half the diagonal of the square, $\sqrt{2}/2$ for a unit square:
Square fold
For more realistic physical models, the shape would be more bag-like, and the analysis more difficult.

share|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.