Geometry

Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems.

the Pythagorean theorem or Pythagoras's theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle.

In the mathematical field of geometric topology, the Poincaré conjecture (UK: , US: , French: [pwɛ̃kaʁe]) is a theorem about the characterization of the 3-sphere (the hypersphere that bounds the 4-ball in four-dimensional space).

the Hodge conjecture is a major unsolved problem in algebraic geometry and complex geometry

In geometry, a heptadecagon, septadecagon or 17-gon is a seventeen-sided polygon.

The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies.

The subject is part of differential geometry since Lie groups are differentiable manifolds.

Henri Brocard was a French mathematician best known for his discovery of the so-called Brocard points of a triangle.

Zimmer's conjecture is a statement in mathematics "which has to do with the circumstances under which geometric spaces exhibit certain kinds of symmetries." It was named after the mathematician Robert Zimmer.

In Euclidean geometry, the tangent-secant theorem describes the relation of line segments created by a secant and a tangent line with the associated circle.

In geometry, the kissing number of a mathematical space is defined as the greatest number of non-overlapping unit spheres (i.e., o

In geometry, a torus (pl.: tori or toruses) is a surface of revolution generated by revolving a circle in three-dimensional space

In geometry, a dodecahedron or duodecahedron is any polyhedron with twelve flat faces.

In geometry, an icosahedron ( or ) is a polyhedron with 20 faces.

In geometry, a tetrahedron (pl.: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four

A cube is a three-dimensional solid object in geometry.

In geometry, an octahedron (pl.: octahedra or octahedrons) is any polyhedron with eight faces.

In geometry, the truncated icosahedron is a polyhedron that can be constructed by truncating all of the regular icosahedron's vert

In geometry, the rhombic dodecahedron is a convex polyhedron with 12 congruent rhombic faces.

In geometry, an icosidodecahedron or pentagonal gyrobirotunda is a polyhedron with twenty (icosi-) triangular faces and twelve (do

Miquel's theorem is a result in geometry, named after Auguste Miquel, concerning the intersection of three circles, each drawn thr

In geometry, Brianchon's theorem is a theorem stating that when a hexagon is circumscribed around a conic section, its principal d

he generalized Ptolemy's theorem, is a theorem in Euclidean geometry named after the Irish mathematician John Casey.

In Euclidean geometry, Carnot's theorem (English: kar-NOH, French: [kaʁno]) states that the sum of the signed distances from the c

In geometry, given a triangle ABC and a point P on its circumcircle, the three closest points to P on lines AB, AC, and BC are col

In geometry, Monge's theorem, named after Gaspard Monge, states that for any three circles in a plane, none of which is completely

In Euclidean geometry, the British flag theorem says that if a point P is chosen inside a rectangle ABCD then the sum of the squar

In geometry, the Japanese theorem states that no matter how one triangulates a cyclic polygon, the sum of inradii of triangles is

In geometry, Brahmagupta's theorem states that if a cyclic quadrilateral is orthodiagonal (that is, has diagonals that are perpend

In geometry, Euler's rotation theorem states that, in three-dimensional space, any displacement of a rigid body such that a point

In Euclidean geometry, Anne's theorem describes an equality of certain areas within a convex quadrilateral.

In geometry, Clifford's theorems, named after the English geometer William Kingdon Clifford, are a sequence of theorems relating t

In plane geometry, the Conway circle theorem states that when the sides meeting at each vertex of a triangle are extended by the l

In geometry, the crossbar theorem states that if ray AD is between ray AC and ray AB, then ray AD intersects line segment BC.

In geometry, the equal incircles theorem derives from a Japanese Sangaku, and pertains to the following construction: a series of

In geometry, the five circles theorem states that, given five circles centered on a common sixth circle and intersecting each othe

In Euclidean geometry, the right triangle altitude theorem or geometric mean theorem is a relation between the altitude on the hyp

In geometry, the hinge theorem (sometimes called the open mouth theorem) states that if two sides of one triangle are congruent to

In geometry, Hjelmslev's theorem, named after Johannes Hjelmslev, is the statement that if points P, Q, R...

In geometry, an inscribed angle is the angle formed in the interior of a circle when two chords intersect on the circle.

er theorem, is an important theorem in elementary geometry about the ratios of various line segments that are created if two rays

In Euclidean geometry, the intersecting chords theorem, or just the chord theorem, is a statement that describes a relation of the

In Euclidean geometry, the intersecting secants theorem or just secant theorem describes the relation of line segments created by

In geometry, the Japanese theorem states that the centers of the incircles of certain triangles inside a cyclic quadrilateral are

Pompeiu's theorem is a result of plane geometry, discovered by the Romanian mathematician Dimitrie Pompeiu.

In geometry, the six circles theorem relates to a chain of six circles together with a triangle, such that each circle is tangent

In geometry, the spiral of Theodorus (also called the square root spiral, Pythagorean spiral, or Pythagoras's snail) is a spiral c

In Euclidean geometry, a translation is a geometric transformation that moves every point of a figure, shape or space by the same

In geometry, an apeirogon (from Ancient Greek ἄπειροv apeiron 'infinite, boundless' and γωνία gonia 'angle') or infinite polygon i

In geometry, a point at infinity or ideal point is an idealized limiting point at the "end" of each line.

In geometry, a point reflection (also called a point inversion or central inversion) is a geometric transformation of affine space

In plane geometry, a shear mapping is an affine transformation that displaces each point in a fixed direction by an amount proport

In four-dimensional geometry, the spherinder, or spherical cylinder or spherical prism, is a geometric object, defined as the Cart

In hyperbolic geometry, angle of parallelism Π ( a ) is the angle at the non-right angle vertex of a right hyperbolic triangle hav

In Euclidean plane geometry, a rectangle is a rectilinear convex polygon or a quadrilateral with four right angles.

Taxicab geometry or Manhattan geometry is geometry where the familiar Euclidean distance is ignored, and the distance between two

In geometry, a square is a regular quadrilateral.

In geometry, the isogonal conjugate of a point P with respect to a triangle △ABC is constructed by reflecting the lines PA, PB, PC

In geometry, the Dehn invariant is a value used to determine whether one polyhedron can be cut into pieces and reassembled ("disse

In geometry, the neusis (νεῦσις; from Ancient Greek νεύειν (neuein) 'incline towards'; plural: νεύσεις, neuseis) is a geometric co

In geometry, the hyperboloid model, also known as the Minkowski model after Hermann Minkowski, is a model of n-dimensional hyperbo

In hyperbolic geometry, an ideal point, omega point or point at infinity is a well-defined point outside the hyperbolic plane or s

adwiger theorem is a statement in Euclidean plane geometry that describes a third square derived from any two squares that share a

e Toeplitz conjecture, is an unsolved question in geometry: Does every plane simple closed curve contain all four vertices of some

In geometry, the Tammes problem is a problem in packing a given number of points on the surface of a sphere such that the minimum

In geometry, a hypercube is an n-dimensional analogue of a square (n = 2) and a cube (n = 3); the special case for n = 4 is known

In geometry, the convex hull, convex envelope or convex closure of a shape is the smallest convex set that contains it.

In geometry, Boy's surface is an immersion of the real projective plane in three-dimensional space.

In plane geometry, Van Aubel's theorem describes a relationship between squares constructed on the sides of a quadrilateral.

In geometry, Routh's theorem determines the ratio of areas between a given triangle and a triangle formed by the pairwise intersec

The Pitot theorem in geometry states that in a tangential quadrilateral the two pairs of opposite sides have the same total length

In geometry, Radon's theorem on convex sets, published by Johann Radon in 1921, states that:Any set of d + 2 points in Rd can be p

Cauchy's theorem is a theorem in geometry, named after Augustin Cauchy.

one of the most important theorems in symplectic geometry.

well-studied visibility problem in computational geometry.

In geometry, the angle bisector theorem is concerned with the relative lengths of the two segments that a triangle's side is divid

In geometry, Bretschneider's formula is a mathematical expression for the area of a general quadrilateral.

In Euclidean plane geometry, Lester's theorem states that in any scalene triangle, the two Fermat points, the nine-point center, a

In geometry, Pasch's theorem, stated in 1882 by the German mathematician Moritz Pasch, is a result in plane geometry which cannot

In computational geometry, a Delaunay triangulation or Delone triangulation of a set of points in the plane subdivides their conve

geometry

In mathematics Rodrigues is remembered for Rodrigues' rotation formula for vectors

a Swiss mathematician who worked primarily in geometry

a Treatise on Solid Geometry was published in 1863

used synthetic geometry to provide a foundation for arithmetic

known for Barbier's theorem on the perimeter of curves of constant width

Möbius was the first to introduce homogeneous coordinates into projective geometry.

His earliest mathematical work was on projective geometry; he wrote a significant treatise on the subject of conic sections at the age of 16.

Today he is best known for Pick's theorem for determining the area of lattice polygons.

Bretschneider worked in geometry, number theory, and history of geometry.

Niels Fabian Helge von Koch (Swedish pronunciation: [ˈhɛ̂lɡe fɔ̌nː ˈkɔ̌kː]; 25 January 1870-11 March 1924) was a Swedish mathematician who gave his name to the famous fractal known as the Koch snowflake, one of the earliest fractal curves to be described.

Pierre Laurent Wantzel (5 June 1814-21 May 1848) was a French mathematician who proved that several ancient geometric problems were impossible to solve using only compass and straightedge.

Giovanni Ceva (September 1, 1647, May 13, 1734) was an Italian mathematician widely known for proving Ceva's theorem in elementary geometry.

Mikhael Leonidovich Gromov (also Mikhail Gromov, Michael Gromov or Misha Gromov; Russian: Михаи́л Леони́дович Гро́мов; born 23 December 1943) is a Russian-French mathematician known for his work in geometry, analysis and group theory.

Frank Morley (September 9, 1860, October 17, 1937) was a leading mathematician, known mostly for his teaching and research in the fields of algebra and geometry.

Heinz Hopf (19 November 1894-3 June 1971) was a German mathematician who worked on the fields of dynamical systems, topology and geometry. == Early life and education == Hopf was born in Gräbschen, German Empire (now Grabiszyn, part of Wrocław, Poland), the son of Elizabeth (née Kirchner) and Wilh

Darboux made several important contributions to geometry and mathematical analysis (see, for example, linear PDEs).

In mathematics, he wrote a commentary on Euclid's Elements and a work on applied geometry known as the Metrica.

Max Wilhelm Dehn (November 13, 1878, June 27, 1952) was a German mathematician most famous for his work in geometry, topology and geometric group theory.

In geometry, more specifically in polytope theory, Kalai's 3d conjecture is a conjecture on the polyhedral combinatorics of centrally symmetric polytopes, made by Gil Kalai in 1989.

It is the setting for planar projective geometry, in which the relationships between objects are not considered to change under projective transformations.

In geometry, shape excludes information about the object's position, size, orientation and chirality.

The study of geometry may be approached by the study of these transformations, such as in transformation geometry.

This is a fundamental result in absolute geometry because its proof does not depend upon the parallel postulate.

Pappus is the last of the great Greek geometers

whose work was mainly on projective and algebraic geometry

Geometry Plane Geometry

Geometry Solid Geometry

Geometry Plane Geometry

Geometry Solid Geometry

Geometry Line Geometry

Geometry Projective Geometry

Geometry Line Geometry

Geometry Curves

Geometry Transformations

Geometry Transformations

Geometry Transformations

Geometry Projective Geometry

Geometry Plane Geometry

Geometry Coordinate Geometry

Geometry Distance

Geometry Coordinate Geometry

Geometry Solid Geometry

Geometry Coordinate Geometry

Geometry Plane Geometry

Geometry Plane Geometry

Geometry Transformations

Geometry Computational Geometry

Geometry Surfaces

Geometry Plane Geometry

Geometry Distance

Geometry Solid Geometry

Geometry Points

Euclidean transformation or Euclidean isometry) is a geometric transformation of a Euclidean space that preserves

The Sierpiński carpet is a plane fractal first described by Wacław Sierpiński in 1916.

universal curve, Sierpiński cube, or Sierpiński sponge) is a fractal curve. It is a three-dimensional generalization of

(also known as the Koch curve, Koch star, or Koch island is a fractal curve and one of the earliest fractals to have been

gasket, Apollonian net, or Apollonian circle packing is a fractal generated by starting with a triple of circles, each tangent to the other two, and successively

is an unproven conjecture on the ratio of lengths of Steiner trees and Euclidean minimum spanning trees for the

A Penrose tiling is an example of an aperiodic tiling. Here, a tiling is a covering of the plane by

Garfield's proof of the Pythagorean theorem is an original proof of the Pythagorean theorem

restriction theorem characterizes the possible orders of rotational symmetry in a lattice. In 2 or 3 dimensions, the rotational symmetries

Euler's quadrilateral theorem or Euler's law on quadrilaterals, named after Leonhard Euler (1707-1783), describes

The theorem of the gnomon states that certain parallelograms occurring in a gnomon have areas of equal si

Geometry Plane Geometry

George Szekeres was a Hungarian-born mathematician who worked for most of his life in Australia on geometry and combinatorics.

Menelaus was one of the later Greek geometers who applied spherical geometry to astronomy. He is best known for the so-called Menelaus's theorem.

Moritz Pasch was a German mathematician who worked on the foundations of geometry. He found a number of assumptions in Euclid that nobody had noticed before.

Piero della Francesca was an Italian artist who pioneered the use of perspective in Renaissance art and went on to write several mathematical treatises.

Reinhold Baer 's mathematical work was wide ranging; topology, abelian groups and geometry. His most important work, however, was in group theory, on the extension problem for groups, finiteness conditions, soluble and nilpotent groups.

Stefan Cohn-Vossen was a mathematician, born in what is now Poland, who is known for his collaboration with David Hilbert on a geometry book.

During his time in Göttingen, he lectured on mathematics, mechanics and optics, and introduced projective methods into astronomy and geography.

Wilhelm Blaschke was an Austrian mathematician whose research was on various aspects of geometry. He also initiated the study of topological differential geometry.

Al-Haytham is also known as Alhazen . He was an Islamic mathematician who wrote early works on optics as well as geometry and number theory.

Robert Simson was a Scottish mathematician best known for the Simson line of a triangle, even though he was not the first discoverer of it.

Benoit Mandelbrot was largely responsible for the present interest in Fractal Geometry. He showed how Fractals can occur in many different places in both Mathematics and elsewhere in Nature.

Lazare Carnot is best known as a geometer. In 1803 he published Géométrie de position in which sensed magnitudes were first systematically used in geometry.