Vector geometry · demo + explainer

Diagonal squares = side squares

In parallelogram OACB, |OC|² + |AB|² equals the sum of the squares of the four sides. Drag A and B — both sides of the identity stay locked. Step the proof.

a = OA b = OB OC AB

Drag A and B · C = A + B · scroll zoom · drag to pan

Live identity

|OC|² + |AB|² = 2(|a|² + |b|²)

Vector proof