Origami

It is well-known that all straightedge-and-compass constructions can be done using paperfolding (origami).

Let’s verify the statement above by executing three tasks below using paperfolding (origami).

• Given four points $A, B, C,$ and $D$. Construct the intersection of the straight line $AB$ and the straight line $CD$ (if it exists).

• Given four points $E, F, G,$ and $H$. Construct the intersection of the straight line $EF$ and the circle $(G, GH)$ (if it exists).

• Given four points $M, N, P$ and $Q$. Construct the intersection of the circle $(M, MN)$ and the circle $(P, PQ)$ (if it exists).

Two Geogebra programs for solving cubics using Origami

• Lill & Beloch’s method
• Edwards & Shurman’s general parabol equation