Rational Parametric Equation of a Circle From a Paper Fold.

Place a square sheet of paper with side length 1 into the first quadrant of a coordinate system in such a way that the lower-left corner coincides with the origin. Look at the set of points that are obtained by folding the lower-right corner of the sheet along a line passing through the origin. The points obtained in this fashion will lie on the unit circle whose center is the origin. By making use of two similar triangles, the illustration gives rise to a rational parametrization of the unit circle. The parameter t is the distance from the lower-right corner of the sheet to the point of intersection of the fold line with the right edge of the paper. [ABSTRACT FROM AUTHOR]