Lab / Tessellations

The Law of Cosines

Move through the moduli space of triangle shapes, then translate a square grid across the two-colour tessellation.

Objective Explore a tessellation proof of the law of cosines for acute, right and obtuse triangles.

c^2=a^2+b^2-2ab\cos C

Shape space

Triangles up to similarity

78.8°

Representative

acute

Tessellation of the plane

a² squaresb² squaresoverlap

The softly shaded parallelograms are overlaps: the two square families cover the same area twice.

GeometryTessellationsModuli spaces