Euclid

Greek mathematician active in Alexandria around 300 BCE, whose Elements organized geometry into an axiomatic system that ruled mathematics for over two millennia.

The Elements derived geometry from a handful of definitions, postulates, and common notions — the dimensionless point, the breadthless line, the infinite plane — a deductive edifice that became the model of rigorous knowledge in the West.

Relationship to Fuller

Relationship: forebear. Euclid is the predecessor R. Buckminster Fuller defined his own geometry against. Fuller rejected the Euclidean abstractions — the imaginary point with no size, the plane extending to infinity, the 90°/180° framing of space — as fictions no experiment could produce, and offered instead an operational, experience-based geometry coordinated on 60° angles and closest-packed spheres (synergetics). In the corpus's discussion of the subjectivity of mathematics, Euclid stands for exactly the inherited, a priori geometry Fuller sought to replace with one grounded in energetic events.

See Also

• Introduction to Geometry — Coxeter's modern survey of the geometry Euclid founded
• Regular Polytopes — the classical solids in their modern geometric treatment
• Plato — the philosopher of the regular solids Euclid catalogued
• Archimedes — the geometer of the semiregular solids in the same lineage

Sources

• Subjectivity in Mathematics — Implications of R. Buckminster Fuller (source reference) — situates Fuller's operational geometry against the Euclidean tradition