1800 BCE — 2026 CE · Morphologium + Cartologium
The Lineage of Continuous Geometric Representation
The history of geometry is the progressive emancipation of continuous mathematical form from the constraints of discrete physical recording media.
1800 BCEMorphologium · Arithmetical Geometry
Discrete Pythagorean Triples
Babylonian Scribes (Plimpton 322)
Earliest recorded table of right-triangle hypotenuse proportions on cuneiform clay tablets.
1637Morphologium · Coordinate Algebra
Analytic Coordinate Geometry
René Descartes (*La Géométrie*)
Unification of algebra and geometry via the orthogonal Cartesian coordinate grid ($x, y, z$).
1827Morphologium · Differential Geometry
Intrinsic Surface Curvature
Carl Friedrich Gauss (*Theorema Egregium*)
Proof that Gaussian curvature is intrinsic to the 2-manifold metric and invariant under isometric bending.
1962Morphologium · CAD & Industrial Modeling
Polynomial Parametric Curves (Bézier)
Pierre Bézier & Paul de Casteljau
Bernstein polynomial control cages for smooth parametric car body tooling at Renault and Citroën.
1978Morphologium · Computer Graphics
Recursive Subdivision Surfaces
Edwin Catmull & Jim Clark
Generalizing bicubic B-splines over arbitrary polygonal meshes, foundational to Pixar's pipeline.
2026Morphologium · Continuous Neural Geometry
Volumetric Implicit Radiance Manifolds
Neural Radiance Fields & 3D Gaussian Splats
Continuous differentiable neural volume rendering replacing discrete triangle meshes.