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Geometry is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. Geometry is one of the oldest mathematical sciences. Geometry is one of the oldest mathematical sciences.
Shape Area Perimeter/Circumference Meanings of symbols Square: is the length of a side Rectangle (+)is length, is breadth Circle: or : where is the radius and is the diameter ...
Fulton–Hansen connectedness theorem (algebraic geometry) Fundamental theorem of algebra (complex analysis) Fundamental theorem of arbitrage-free pricing (financial mathematics) Fundamental theorem of arithmetic (number theory) Fundamental theorem of calculus ; Fundamental theorem on homomorphisms (abstract algebra)
Absolute geometry is a geometry based on an axiom system consisting of all the axioms giving Euclidean geometry except for the parallel postulate or any of its alternatives. [69] The term was introduced by János Bolyai in 1832. [70] It is sometimes referred to as neutral geometry, [71] as it is neutral with respect to the parallel postulate.
Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician who works in the field of geometry is called a geometer. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, [a] which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental ...
Genus (mathematics) Riemann surface; Riemann–Hurwitz formula; Riemann–Roch theorem; Abelian integral; Differential of the first kind; Jacobian variety. Generalized Jacobian; Moduli of algebraic curves; Hurwitz's theorem on automorphisms of a curve; Clifford's theorem on special divisors; Gonality of an algebraic curve; Weil reciprocity law ...
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems.Classically, it studies zeros of multivariate polynomials; the modern approach generalizes this in a few different aspects.
Foundations and Fundamental Concepts of Mathematics. Dover. Chpt. 4.2 covers the Hilbert axioms for plane geometry. Ivor Grattan-Guinness, 2000. In Search of Mathematical Roots. Princeton University Press. David Hilbert, 1980 (1899). The Foundations of Geometry, 2nd ed. Chicago: Open Court.