Beloch folds originate in computational origami.

In origami, their are seven Huzita–Hatori axioms: 1. Fold through two points (line through two points). 2. Fold a point onto another point (perpendicular bisector). 3. Fold a line onto a line (angle bisector). 4. Fold through a point perpendicular to a line (line through a point perpendicular to a line). 5. Fold a point onto a line, passing the crease through another point (tangent to a parabola). 6. Fold a point onto a line and another point onto another line (common tangent to two parabolas). 7. Fold a point onto a line, making the crease perpendicular to another line (tangent to a parabola perpendicular to a line).

The sixth axiom was found in 1936 by Margherita Beloch. This fold is now named the Beloch fold, and can be used in origimi to solve various problems that cannot be solved with ruler and compass.

For a given set of two points and two lines, there can be 0, 1, 2 or 3 solutions. Most of the solutions arise from cubic equations.