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/rɪˈsɪp.rə.kəl daɪˈæɡ.ən.əl/

Reciprocal diagonal

noun phrase · composition geometry

The line perpendicular to the main diagonal of a rectangle, drawn from a non-diagonal corner. The geometric heart of Jay Hambidge's dynamic symmetry composition system.

The construction

Given a rectangle with its main diagonal drawn corner-to-corner, the reciprocal is the line from one of the remaining two corners perpendicular to that diagonal. The reciprocal divides the rectangle into a smaller similar rectangle plus a square (in the case of the phi rectangle) or smaller similar rectangles plus shapes (for the other root rectangles).

Reciprocal diagonal constructionreciprocal
Reciprocal diagonal (orange) perpendicular to the main diagonal of a rectangle.

Why it matters

The reciprocal is what makes root rectangles self-similar. In a phi rectangle, the reciprocal slices off a square whose remaining rectangle is itself a phi rectangle — and this pattern continues indefinitely. Hambidge used reciprocal-diagonal armatures as the structural lines on which to plan compositions; placing major masses at intersections of the main diagonal and the reciprocal anchors the composition at structurally significant points.

See also: Dynamic symmetry · Armature · Dynamic symmetry overlays

References

  1. Hambidge, J. The Elements of Dynamic Symmetry. Yale (1920). Dover (1967). ISBN 0-486-21776-0.
  2. Bouleau, C. The Painter's Secret Geometry. Harcourt Brace (1963).

Sarah Chen

Founder of Grid Maker Pro. Classical portrait painter (BA Fine Arts). Writes about composition, drawing methods, and the art-history claims that don't survive measurement.

Updated · Methodology