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92 relations: Acute and obtuse triangles, Algebraic number, Alternation (geometry), Angle, Area, Bisection, Bow tie, Butterfly, Circle, Circumscribed circle, Classical antiquity, Compass-and-straightedge construction, Complete graph, Convex polygon, Coordinate system, Cross-polytope, Cube, Cyclic group, Degree (angle), Density (polytope), Diagonal, Digon, Dihedral group, Dihedron, Directed graph, Dual polygon, Equilateral triangle, Euclidean tilings by convex regular polygons, Faceting, Forum Geometricorum, Geometry, Gradian, Great circle, Hexagon, Hyperbolic geometry, Hyperbolic space, Hypercube, If and only if, Incircle and excircles of a triangle, Inscribed figure, Internal and external angles, Irrational number, Isogonal figure, Isoperimetric inequality, Isosceles trapezoid, John Horton Conway, Kite (geometry), Lindemann–Weierstrass theorem, List of geometers, Octagon, ..., Order-5 square tiling, Orthographic projection, Parallel (geometry), Parallelogram, Perimeter, Pi, Polynomial, Power of two, Pythagorean theorem, Quadrilateral, Rational number, Rectangle, Reflection symmetry, Regular polygon, Rhombus, Right angle, Right triangle, Rotational symmetry, Schläfli symbol, Simplex, Special right triangle, Spherical geometry, Square (algebra), Square lattice, Square root of 2, Square tiling, Squaring the circle, Squircle, Symmetry group, Tetrahedron, Tetrahemihexahedron, Thales's theorem, Transcendental number, Trapezoid, Truncation (geometry), Two-dimensional space, Uniform star polyhedron, Unit square, Vertex (geometry), Vertex arrangement, Vertex figure, Zero of a function. Expand index (42 more) »
Acute and obtuse triangles
An acute triangle is a triangle with all three angles acute (less than 90°).
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Algebraic number
An algebraic number is any complex number (including real numbers) that is a root of a non-zero polynomial (that is, a value which causes the polynomial to equal 0) in one variable with rational coefficients (or equivalently – by clearing denominators – with integer coefficients).
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Alternation (geometry)
In geometry, an alternation or partial truncation, is an operation on a polygon, polyhedron, tiling, or higher dimensional polytope that removes alternate vertices.
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Angle
In plane geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.
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Area
Area is the quantity that expresses the extent of a two-dimensional figure or shape, or planar lamina, in the plane.
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Bisection
In geometry, bisection is the division of something into two equal or congruent parts, usually by a line, which is then called a bisector.
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Bow tie
The bow tie is a type of traditional necktie.
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Butterfly
Butterflies are insects in the macrolepidopteran clade Rhopalocera from the order Lepidoptera, which also includes moths.
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Circle
A circle is a simple closed shape.
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Circumscribed circle
In geometry, the circumscribed circle or circumcircle of a polygon is a circle which passes through all the vertices of the polygon.
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Classical antiquity
Classical antiquity (also the classical era, classical period or classical age) is the period of cultural history between the 8th century BC and the 5th or 6th century AD centered on the Mediterranean Sea, comprising the interlocking civilizations of ancient Greece and ancient Rome, collectively known as the Greco-Roman world.
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Compass-and-straightedge construction
Compass-and-straightedge construction, also known as ruler-and-compass construction or classical construction, is the construction of lengths, angles, and other geometric figures using only an idealized ruler and compass.
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Complete graph
No description.
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Convex polygon
A convex polygon is a simple polygon (not self-intersecting) in which no line segment between two points on the boundary ever goes outside the polygon.
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Coordinate system
In geometry, a coordinate system is a system which uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.
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Cross-polytope
In geometry, a cross-polytope, orthoplex, hyperoctahedron, or cocube is a regular, convex polytope that exists in n-dimensions.
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Cube
In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.
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Cyclic group
In algebra, a cyclic group or monogenous group is a group that is generated by a single element.
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Degree (angle)
A degree (in full, a degree of arc, arc degree, or arcdegree), usually denoted by ° (the degree symbol), is a measurement of a plane angle, defined so that a full rotation is 360 degrees.
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Density (polytope)
In geometry, the density of a polytope represents the number of windings of a polytope, particularly a uniform or regular polytope, around its center.
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Diagonal
In geometry, a diagonal is a line segment joining two vertices of a polygon or polyhedron, when those vertices are not on the same edge.
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Digon
In geometry, a digon is a polygon with two sides (edges) and two vertices.
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Dihedral group
In mathematics, a dihedral group is the group of symmetries of a regular polygon, which includes rotations and reflections.
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Dihedron
A dihedron is a type of polyhedron, made of two polygon faces which share the same set of edges.
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Directed graph
In mathematics, and more specifically in graph theory, a directed graph (or digraph) is a graph that is a set of vertices connected by edges, where the edges have a direction associated with them.
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Dual polygon
In geometry, polygons are associated into pairs called duals, where the vertices of one correspond to the edges of the other.
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Equilateral triangle
In geometry, an equilateral triangle is a triangle in which all three sides are equal.
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Euclidean tilings by convex regular polygons
Euclidean plane tilings by convex regular polygons have been widely used since antiquity.
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Faceting
Stella octangula as a faceting of the cube In geometry, faceting (also spelled facetting) is the process of removing parts of a polygon, polyhedron or polytope, without creating any new vertices.
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Forum Geometricorum
Forum Geometricorum: A Journal on Classical Euclidean Geometry (often abbreviated Forum Geom.) is a peer-reviewed open-access academic journal that specializes in mathematical research papers on Euclidean geometry.
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Geometry
Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.
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Gradian
The gradian is a unit of measurement of an angle, equivalent to \frac of a turn, \frac of a degree, or \frac of a radian.
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Great circle
A great circle, also known as an orthodrome, of a sphere is the intersection of the sphere and a plane that passes through the center point of the sphere.
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Hexagon
In geometry, a hexagon (from Greek ἕξ hex, "six" and γωνία, gonía, "corner, angle") is a six-sided polygon or 6-gon.
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Hyperbolic geometry
In mathematics, hyperbolic geometry (also called Bolyai–Lobachevskian geometry or Lobachevskian geometry) is a non-Euclidean geometry.
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Hyperbolic space
In mathematics, hyperbolic space is a homogeneous space that has a constant negative curvature, where in this case the curvature is the sectional curvature.
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Hypercube
In geometry, a hypercube is an ''n''-dimensional analogue of a square and a cube.
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If and only if
In logic and related fields such as mathematics and philosophy, if and only if (shortened iff) is a biconditional logical connective between statements.
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Incircle and excircles of a triangle
In geometry, the incircle or inscribed circle of a triangle is the largest circle contained in the triangle; it touches (is tangent to) the three sides.
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Inscribed figure
An inscribed triangle of a circle In geometry, an inscribed planar shape or solid is one that is enclosed by and "fits snugly" inside another geometric shape or solid.
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Internal and external angles
In geometry, an angle of a polygon is formed by two sides of the polygon that share an endpoint.
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Irrational number
In mathematics, the irrational numbers are all the real numbers which are not rational numbers, the latter being the numbers constructed from ratios (or fractions) of integers.
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Isogonal figure
In geometry, a polytope (a polygon, polyhedron or tiling, for example) is isogonal or vertex-transitive if all its vertices are equivalent under the symmetries of the figure.
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Isoperimetric inequality
In mathematics, the isoperimetric inequality is a geometric inequality involving the surface area of a set and its volume.
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Isosceles trapezoid
In Euclidean geometry, an isosceles trapezoid (isosceles trapezium in British English) is a convex quadrilateral with a line of symmetry bisecting one pair of opposite sides.
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John Horton Conway
John Horton Conway FRS (born 26 December 1937) is an English mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory.
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Kite (geometry)
In Euclidean geometry, a kite is a quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are adjacent to each other.
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Lindemann–Weierstrass theorem
In transcendental number theory, the Lindemann–Weierstrass theorem is a result that is very useful in establishing the transcendence of numbers.
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List of geometers
A geometer is a mathematician whose area of study is geometry.
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Octagon
In geometry, an octagon (from the Greek ὀκτάγωνον oktágōnon, "eight angles") is an eight-sided polygon or 8-gon.
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Order-5 square tiling
In geometry, the order-5 square tiling is a regular tiling of the hyperbolic plane.
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Orthographic projection
Orthographic projection (sometimes orthogonal projection), is a means of representing three-dimensional objects in two dimensions.
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Parallel (geometry)
In geometry, parallel lines are lines in a plane which do not meet; that is, two lines in a plane that do not intersect or touch each other at any point are said to be parallel.
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Parallelogram
In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides.
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Perimeter
A perimeter is a path that surrounds a two-dimensional shape.
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Pi
The number is a mathematical constant.
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Polynomial
In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.
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Power of two
In mathematics, a power of two is a number of the form where is an integer, i.e. the result of exponentiation with number two as the base and integer as the exponent.
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Pythagorean theorem
In mathematics, the Pythagorean theorem, also known as Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle.
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Quadrilateral
In Euclidean plane geometry, a quadrilateral is a polygon with four edges (or sides) and four vertices or corners.
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Rational number
In mathematics, a rational number is any number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator.
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Rectangle
In Euclidean plane geometry, a rectangle is a quadrilateral with four right angles.
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Reflection symmetry
Reflection symmetry, line symmetry, mirror symmetry, mirror-image symmetry, is symmetry with respect to reflection.
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Regular polygon
In Euclidean geometry, a regular polygon is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length).
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Rhombus
In plane Euclidean geometry, a rhombus (plural rhombi or rhombuses) is a simple (non-self-intersecting) quadrilateral whose four sides all have the same length.
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Right angle
In geometry and trigonometry, a right angle is an angle of exactly 90° (degrees), corresponding to a quarter turn.
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Right triangle
A right triangle (American English) or right-angled triangle (British English) is a triangle in which one angle is a right angle (that is, a 90-degree angle).
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Rotational symmetry
Rotational symmetry, also known as radial symmetry in biology, is the property a shape has when it looks the same after some rotation by a partial turn.
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Schläfli symbol
In geometry, the Schläfli symbol is a notation of the form that defines regular polytopes and tessellations.
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Simplex
In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions.
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Special right triangle
A special right triangle is a right triangle with some regular feature that makes calculations on the triangle easier, or for which simple formulas exist.
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Spherical geometry
Spherical geometry is the geometry of the two-dimensional surface of a sphere.
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Square (algebra)
In mathematics, a square is the result of multiplying a number by itself.
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Square lattice
In mathematics, the square lattice is a type of lattice in a two-dimensional Euclidean space.
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Square root of 2
The square root of 2, or the (1/2)th power of 2, written in mathematics as or, is the positive algebraic number that, when multiplied by itself, gives the number 2.
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Square tiling
In geometry, the square tiling, square tessellation or square grid is a regular tiling of the Euclidean plane.
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Squaring the circle
Squaring the circle is a problem proposed by ancient geometers.
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Squircle
A squircle is a mathematical shape intermediate between a square and a circle.
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Symmetry group
In group theory, the symmetry group of an object (image, signal, etc.) is the group of all transformations under which the object is invariant with composition as the group operation.
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Tetrahedron
In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners.
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Tetrahemihexahedron
In geometry, the tetrahemihexahedron or hemicuboctahedron is a uniform star polyhedron, indexed as U4.
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Thales's theorem
In geometry, Thales's theorem states that if A, B, and C are distinct points on a circle where the line is a diameter, then the angle ∠ABC is a right angle.
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Transcendental number
In mathematics, a transcendental number is a real or complex number that is not algebraic—that is, it is not a root of a nonzero polynomial equation with integer (or, equivalently, rational) coefficients.
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Trapezoid
In Euclidean geometry, a convex quadrilateral with at least one pair of parallel sides is referred to as a trapezoid in American and Canadian English but as a trapezium in English outside North America.
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Truncation (geometry)
In geometry, a truncation is an operation in any dimension that cuts polytope vertices, creating a new facet in place of each vertex.
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Two-dimensional space
Two-dimensional space or bi-dimensional space is a geometric setting in which two values (called parameters) are required to determine the position of an element (i.e., point).
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Uniform star polyhedron
In geometry, a uniform star polyhedron is a self-intersecting uniform polyhedron.
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Unit square
In mathematics, a unit square is a square whose sides have length.
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Vertex (geometry)
In geometry, a vertex (plural: vertices or vertexes) is a point where two or more curves, lines, or edges meet.
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Vertex arrangement
In geometry, a vertex arrangement is a set of points in space described by their relative positions.
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Vertex figure
In geometry, a vertex figure, broadly speaking, is the figure exposed when a corner of a polyhedron or polytope is sliced off.
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Zero of a function
In mathematics, a zero, also sometimes called a root, of a real-, complex- or generally vector-valued function f is a member x of the domain of f such that f(x) vanishes at x; that is, x is a solution of the equation f(x).
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References
[1] https://en.wikipedia.org/wiki/Square
