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The latter sort of properties are called invariants and studying them is the essence of geometry. Thales' theorem, named after Thales of Miletus states that if A, B, and C are points on a circle where the line AC is a diameter of the circle, then the angle ABC is a right angle. Cantor supposed that Thales proved his theorem by means of Euclid ...
Five circles theorem ; Five color theorem (graph theory) Fixed-point theorems in infinite-dimensional spaces; Flat torus theorem (geometric group theory) Floquet's theorem (differential equations) Fluctuation dissipation theorem ; Fluctuation theorem (statistical mechanics) Ford's theorem (number theory) Focal subgroup theorem (abstract algebra)
Absolute geometry is an extension of ordered geometry, and thus, all theorems in ordered geometry hold in absolute geometry. The converse is not true. Absolute geometry assumes the first four of Euclid's Axioms (or their equivalents), to be contrasted with affine geometry, which does not assume Euclid's third and fourth axioms. Ordered geometry ...
Pages in category "Theorems in geometry" The following 48 pages are in this category, out of 48 total. This list may not reflect recent changes. 0–9. 2π theorem; A.
Euler's theorem; Five color theorem; Five lemma; Fundamental theorem of arithmetic; Gauss–Markov theorem (brief pointer to proof) Gödel's incompleteness theorem. Gödel's first incompleteness theorem; Gödel's second incompleteness theorem; Goodstein's theorem; Green's theorem (to do) Green's theorem when D is a simple region; Heine–Borel ...
Fundamental theorem of projective geometry; Projective transformation. Möbius transformation; Cross-ratio; Duality; Homogeneous coordinates; Pappus's hexagon theorem; Incidence; Pascal's theorem; Affine geometry. Affine space; Affine transformation; Finite geometry; Differential geometry. Contact geometry; Riemannian geometry; Symplectic ...