History of geometry
The development of geometric ideas and methods, from ancient measurement and Greek deductive proof to modern mathematical theories.
Egyptian mathematics: The mathematical practices of ancient Egypt, preserved chiefly in administrative and instructional texts. Egyptian surveying and construction required practical methods for measuring land and space.
Euclidean geometry: The geometry derived from Euclid’s postulates, including the parallel postulate. It became the central framework inherited from ancient Greek geometry.
Archimedes: An ancient Greek mathematician who developed rigorous results on areas, volumes, and mechanical principles. His exhaustion methods anticipated techniques later central to calculus.
Surveying: The measurement and mapping of land and other physical spaces. Land boundaries and field areas motivated some of geometry’s earliest practical procedures.
Differential geometry: The study of smooth curves, surfaces, and manifolds using calculus. It extends the study of curvature from classical surfaces to higher-dimensional spaces.
Babylonian mathematics: The mathematical tradition of ancient Mesopotamia, recorded on cuneiform tablets and including numerical problem-solving. Babylonian tablets preserve early solutions to problems involving lengths, areas, and right triangles.
Axiomatic method: A system of reasoning that derives theorems from explicit axioms and rules of inference. Euclid’s presentation made axiomatic deduction a defining geometric method.
Apollonius of Perga: A Hellenistic mathematician whose treatise systematically studied conic sections. His work established the classical treatment of ellipses, parabolas, and hyperbolas.
Perspective (graphical): A method for representing three-dimensional space on a flat surface through projected lines. Renaissance artists’ construction problems helped stimulate systematic projective geometry.
Algebraic geometry: The study of geometric objects defined by polynomial equations. It developed from analytic geometry into a major meeting point of geometry and algebra.