I01Available
The Law of Cosines
Move through the moduli space of triangle shapes, then translate a square grid across the two-colour tessellation.
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Tessellations
How much geometry can be made visible by superimposing periodic tilings and moving one layer across another?
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Tools & experiments
2 interactives
I02Available
Infinitely many “proofs” of Pythagoras
Slide one square tiling over another and visit the medieval, Perigal, and Ferrarese dissection phases.
The central question
How much geometry can be made visible by superimposing periodic tilings and moving one layer across another?
Tessellations turn a single area diagram into a family. A periodic pattern can be clipped by a movable square grid, and every grid position produces another dissection of the same identity.
For right triangles, two square tilings express Pythagoras. For a general triangle, the same architecture reveals cosine parallelograms as overlaps, gaps, or a right-angle transition.
GeometryTessellationsArea identities
Recent changes
The Pythagorean sandbox added a movable anchor, mirror orientation and historically distinguished phases.
All interactives last tested 29 July 2026.