Domain 04 · Mathematics Codex
Geometry
Shape, space, and structure — from Euclid's Elements to the geometry of curved spacetime.
Scope
Euclidean geometry, non-Euclidean geometry (hyperbolic, elliptic), projective geometry, differential geometry, algebraic geometry, fractal geometry, trigonometry, computational geometry.
Geometry is mathematics made visible. The discovery that non-Euclidean geometries are consistent — that parallel lines can meet — was one of the most revolutionary results in all of mathematics, and directly enabled Einstein's general relativity. Algebraic geometry connects the geometric study of curves and surfaces to the algebraic structure of polynomial equations.
Entries in this domain
Build status: This domain is in active build. Live entries are marked below. All other entries are planned and pending — see build status for the full picture.
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Euclidean Space
Pending
The familiar flat space of school geometry — the setting for Euclid's Elements and the geometry of everyday experience.
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Pythagorean Theorem
Pending
In a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides — known to Babylonian, Indian, Chinese, and Greek mathematicians independently.
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Conic Section
Pending
The curves formed by the intersection of a cone and a plane — circles, ellipses, parabolas, and hyperbolas, each describing planetary orbits, optics, and projectile motion.