Square, the Glossary

Table of Contents

1. 95 relations: Acute and obtuse triangles, Algebraic number, Alternation (geometry), Angle, Area, Ball (mathematics), Bisection, Bow tie, Butterfly, Circle, Circumcircle, Circumscribed circle, Classical antiquity, Coordinate system, Cross-polytope, Cube, Cyclic group, Degree (angle), Density (polytope), Diagonal, Digon, Dihedral group, Dihedron, Directed graph, Dual polygon, Equilateral triangle, Euclidean geometry, Euclidean tilings by convex regular polygons, Faceting, Forum Geometricorum, Great circle, Hexagon, Hyperbolic geometry, Hyperbolic space, Hypercube, If and only if, Incircle and excircles, 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 (group theory), Order-5 square tiling, ... Expand index (45 more) »

2. 4 (number)
3. Constructible polygons
4. Elementary shapes
5. Types of quadrilaterals

Acute and obtuse triangles

An acute triangle (or acute-angled triangle) is a triangle with three acute angles (less than 90°).

See Square and Acute and obtuse triangles

Algebraic number

An algebraic number is a number that is a root of a non-zero polynomial (of finite degree) in one variable with integer (or, equivalently, rational) coefficients.

See Square and Algebraic number

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.

See Square and Alternation (geometry)

Angle

In Euclidean 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.

See Square and Angle

Area

Area is the measure of a region's size on a surface.

See Square and Area

Ball (mathematics)

In mathematics, a ball is the solid figure bounded by a sphere; it is also called a solid sphere.

See Square and Ball (mathematics)

Bisection

In geometry, bisection is the division of something into two equal or congruent parts (having the same shape and size).

See Square and Bisection

Bow tie

The bow tie or dicky bow is a type of necktie.

See Square and Bow tie

Butterfly

Butterflies are winged insects from the lepidopteran suborder Rhopalocera, characterized by large, often brightly coloured wings that often fold together when at rest, and a conspicuous, fluttering flight.

See Square and Butterfly

Circle

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre. Square and circle are Elementary shapes.

See Square and Circle

Circumcircle

In geometry, the circumscribed circle or circumcircle of a triangle is a circle that passes through all three vertices.

See Square and Circumcircle

Circumscribed circle

In geometry, a circumscribed circle for a set of points is a circle passing through each of them.

See Square and Circumscribed circle

Classical antiquity

Classical antiquity, also known as the classical era, classical period, classical age, or simply antiquity, is the period of cultural European history between the 8th century BC and the 5th century AD comprising the interwoven civilizations of ancient Greece and ancient Rome known together as the Greco-Roman world, centered on the Mediterranean Basin.

See Square and Classical antiquity

Coordinate system

In geometry, a coordinate system is a system that 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.

See Square and Coordinate system

Cross-polytope

In geometry, a cross-polytope, hyperoctahedron, orthoplex, or cocube is a regular, convex polytope that exists in n-dimensional Euclidean space.

See Square and Cross-polytope

Cube

In geometry, a cube is a three-dimensional solid object bounded by six square faces. Square and cube are Elementary shapes.

See Square and Cube

Cyclic group

In abstract algebra, a cyclic group or monogenous group is a group, denoted Cn (also frequently \Zn or Zn, not to be confused with the commutative ring of p-adic numbers), that is generated by a single element.

See Square and Cyclic group

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 in which one full rotation is 360 degrees.

See Square and Degree (angle)

Density (polytope)

In geometry, the density of a star polyhedron is a generalization of the concept of winding number from two dimensions to higher dimensions, representing the number of windings of the polyhedron around the center of symmetry of the polyhedron.

See Square and Density (polytope)

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.

See Square and Diagonal

Digon

In geometry, a bigon, digon, or a 2-gon, is a polygon with two sides (edges) and two vertices.

See Square and Digon

Dihedral group

In mathematics, a dihedral group is the group of symmetries of a regular polygon, which includes rotations and reflections.

See Square and Dihedral group

Dihedron

A dihedron is a type of polyhedron, made of two polygon faces which share the same set of n edges.

See Square and Dihedron

Directed graph

In mathematics, and more specifically in graph theory, a directed graph (or digraph) is a graph that is made up of a set of vertices connected by directed edges, often called arcs.

See Square and Directed graph

Dual polygon

In geometry, polygons are associated into pairs called duals, where the vertices of one correspond to the edges of the other.

See Square and Dual polygon

Equilateral triangle

In geometry, an equilateral triangle is a triangle in which all three sides have the same length. Square and equilateral triangle are Constructible polygons.

See Square and Equilateral triangle

Euclidean geometry

Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry, Elements.

See Square and Euclidean geometry

Euclidean tilings by convex regular polygons

Euclidean plane tilings by convex regular polygons have been widely used since antiquity.

See Square and Euclidean tilings by convex regular polygons

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.

See Square and Faceting

Forum Geometricorum

Forum Geometricorum: A Journal on Classical Euclidean Geometry is a peer-reviewed open-access academic journal that specializes in mathematical research papers on Euclidean geometry.

See Square and Forum Geometricorum

Great circle

In mathematics, a great circle or orthodrome is the circular intersection of a sphere and a plane passing through the sphere's center point.

See Square and Great circle

Hexagon

In geometry, a hexagon (from Greek ἕξ, hex, meaning "six", and γωνία, gonía, meaning "corner, angle") is a six-sided polygon. Square and hexagon are Constructible polygons and Elementary shapes.

See Square and Hexagon

Hyperbolic geometry

In mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai–Lobachevskian geometry) is a non-Euclidean geometry.

See Square and Hyperbolic geometry

Hyperbolic space

In mathematics, hyperbolic space of dimension n is the unique simply connected, n-dimensional Riemannian manifold of constant sectional curvature equal to −1.

See Square and Hyperbolic space

Hypercube

In geometry, a hypercube is an ''n''-dimensional analogue of a square and a cube.

See Square and Hypercube

If and only if

In logic and related fields such as mathematics and philosophy, "if and only if" (often shortened as "iff") is paraphrased by the biconditional, a logical connective between statements.

See Square and If and only if

Incircle and excircles

In geometry, the incircle or inscribed circle of a triangle is the largest circle that can be contained in the triangle; it touches (is tangent to) the three sides.

See Square and Incircle and excircles

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.

See Square and Inscribed figure

Internal and external angles

In geometry, an angle of a polygon is formed by two adjacent sides.

See Square and Internal and external angles

Irrational number

In mathematics, the irrational numbers (in- + rational) are all the real numbers that are not rational numbers.

See Square and Irrational number

Isogonal figure

In geometry, a polytope (e.g. a polygon or polyhedron) or a tiling is isogonal or vertex-transitive if all its vertices are equivalent under the symmetries of the figure.

See Square and Isogonal figure

Isoperimetric inequality

In mathematics, the isoperimetric inequality is a geometric inequality involving the perimeter of a set and its volume.

See Square and Isoperimetric inequality

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. Square and isosceles trapezoid are types of quadrilaterals.

See Square and Isosceles trapezoid

John Horton Conway

John Horton Conway (26 December 1937 – 11 April 2020) was an English mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory.

See Square and John Horton Conway

Kite (geometry)

In Euclidean geometry, a kite is a quadrilateral with reflection symmetry across a diagonal. Square and kite (geometry) are Elementary shapes and types of quadrilaterals.

See Square and Kite (geometry)

Lindemann–Weierstrass theorem

In transcendental number theory, the Lindemann–Weierstrass theorem is a result that is very useful in establishing the transcendence of numbers.

See Square and Lindemann–Weierstrass theorem

List of geometers

A geometer is a mathematician whose area of study is geometry.

See Square and List of geometers

Octagon

In geometry, an octagon is an eight-sided polygon or 8-gon. Square and octagon are Constructible polygons and Elementary shapes.

See Square and Octagon

Order (group theory)

In mathematics, the order of a finite group is the number of its elements.

See Square and Order (group theory)

Order-5 square tiling

In geometry, the order-5 square tiling is a regular tiling of the hyperbolic plane.

See Square and Order-5 square tiling

Orthographic projection

Orthographic projection (also orthogonal projection and analemma) is a means of representing three-dimensional objects in two dimensions.

See Square and Orthographic projection

Parallel (geometry)

In geometry, parallel lines are coplanar infinite straight lines that do not intersect at any point.

See Square and Parallel (geometry)

Parallelogram

In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides. Square and parallelogram are Elementary shapes and types of quadrilaterals.

See Square and Parallelogram

Perimeter

A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length.

See Square and Perimeter

Pi

The number (spelled out as "pi") is a mathematical constant that is the ratio of a circle's circumference to its diameter, approximately equal to 3.14159.

See Square and Pi

Polynomial

In mathematics, a polynomial is a mathematical expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication and exponentiation to nonnegative integer powers, and has a finite number of terms.

See Square and Polynomial

Power of two

A power of two is a number of the form where is an integer, that is, the result of exponentiation with number two as the base and integer as the exponent.

See Square and Power of two

Pythagorean theorem

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

See Square and Pythagorean theorem

Quadrilateral

In geometry a quadrilateral is a four-sided polygon, having four edges (sides) and four corners (vertices). Square and quadrilateral are 4 (number).

See Square and Quadrilateral

Rational number

In mathematics, a rational number is a number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator.

See Square and Rational number

Rectangle

In Euclidean plane geometry, a rectangle is a quadrilateral with four right angles. Square and rectangle are Elementary shapes and types of quadrilaterals.

See Square and Rectangle

Reflection symmetry

In mathematics, reflection symmetry, line symmetry, mirror symmetry, or mirror-image symmetry is symmetry with respect to a reflection.

See Square and Reflection symmetry

Regular polygon

In Euclidean geometry, a regular polygon is a polygon that is direct equiangular (all angles are equal in measure) and equilateral (all sides have the same length).

See Square and Regular polygon

Rhombus

In plane Euclidean geometry, a rhombus (rhombi or rhombuses) is a quadrilateral whose four sides all have the same length. Square and rhombus are Elementary shapes and types of quadrilaterals.

See Square and Rhombus

Right angle

In geometry and trigonometry, a right angle is an angle of exactly 90 degrees or radians corresponding to a quarter turn.

See Square and Right angle

Right triangle

A right triangle or right-angled triangle, sometimes called an orthogonal triangle or rectangular triangle, is a triangle in which two sides are perpendicular forming a right angle (turn or 90 degrees).

See Square and Right triangle

Rotational symmetry

Rotational symmetry, also known as radial symmetry in geometry, is the property a shape has when it looks the same after some rotation by a partial turn.

See Square and Rotational symmetry

Schläfli symbol

In geometry, the Schläfli symbol is a notation of the form \ that defines regular polytopes and tessellations.

See Square and Schläfli symbol

Simplex

In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions.

See Square and Simplex

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.

See Square and Special right triangle

Spherical geometry

A sphere with a spherical triangle on it. Spherical geometry or spherics is the geometry of the two-dimensional surface of a sphere or the -dimensional surface of higher dimensional spheres.

See Square and Spherical geometry

Square (algebra)

In mathematics, a square is the result of multiplying a number by itself.

See Square and Square (algebra)

Square lattice

In mathematics, the square lattice is a type of lattice in a two-dimensional Euclidean space.

See Square and Square lattice

Square number

In mathematics, a square number or perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with itself.

See Square and Square number

Square root

In mathematics, a square root of a number is a number such that y^2.

See Square and Square root

Square root of 2

The square root of 2 (approximately 1.4142) is a real number that, when multiplied by itself or squared, equals the number 2.

See Square and Square root of 2

Square tiling

In geometry, the square tiling, square tessellation or square grid is a regular tiling of the Euclidean plane.

See Square and Square tiling

Squaring the circle

Squaring the circle is a problem in geometry first proposed in Greek mathematics.

See Square and Squaring the circle

Squaring the square

Squaring the square is the problem of tiling an integral square using only other integral squares.

See Square and Squaring the square

Squircle

A squircle is a shape intermediate between a square and a circle.

See Square and Squircle

Straightedge and compass construction

In geometry, straightedge-and-compass construction – also known as ruler-and-compass construction, Euclidean construction, or classical construction – is the construction of lengths, angles, and other geometric figures using only an idealized ruler and a pair of compasses.

See Square and Straightedge and compass construction

Symmetry group

In group theory, the symmetry group of a geometric object is the group of all transformations under which the object is invariant, endowed with the group operation of composition.

See Square and Symmetry group

Taxicab geometry

Taxicab geometry or Manhattan geometry is geometry where the familiar Euclidean distance is ignored, and the distance between two points is instead defined to be the sum of the absolute differences of their respective Cartesian coordinates, a distance function (or metric) called the taxicab distance, Manhattan distance, or city block distance.

See Square and Taxicab geometry

Tetrahedron

In geometry, a tetrahedron (tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertices.

See Square and Tetrahedron

Tetrahemihexahedron

In geometry, the tetrahemihexahedron or hemicuboctahedron is a uniform star polyhedron, indexed as U4.

See Square and Tetrahemihexahedron

Thales's theorem

In geometry, Thales's theorem states that if,, and are distinct points on a circle where the line is a diameter, the angle is a right angle.

See Square and Thales's theorem

Transcendental number

In mathematics, a transcendental number is a real or complex number that is not algebraic – that is, not the root of a non-zero polynomial with integer (or, equivalently, rational) coefficients.

See Square and Transcendental number

Trapezoid

In geometry, a trapezoid in North American English, or trapezium in British English, is a quadrilateral that has one pair of parallel sides. Square and trapezoid are Elementary shapes and types of quadrilaterals.

See Square and Trapezoid

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.

See Square and Truncation (geometry)

Uniform star polyhedron

In geometry, a uniform star polyhedron is a self-intersecting uniform polyhedron.

See Square and Uniform star polyhedron

Unit square

In mathematics, a unit square is a square whose sides have length. Square and unit square are types of quadrilaterals.

See Square and Unit square

Vertex (geometry)

In geometry, a vertex (vertices or vertexes) is a point where two or more curves, lines, or edges meet or intersect.

See Square and Vertex (geometry)

Vertex arrangement

In geometry, a vertex arrangement is a set of points in space described by their relative positions.

See Square and Vertex arrangement

Vertex figure

In geometry, a vertex figure, broadly speaking, is the figure exposed when a corner of a polyhedron or polytope is sliced off.

See Square and Vertex figure

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, the function f attains the value of 0 at x, or equivalently, x is a solution to the equation f(x).

See Square and Zero of a function

See also

4 (number)

• 4
• Final four
• Four Big Things
• Four Marks of the Church
• Four Modernizations
• Four Policemen
• Four Seas
• Four Worlds
• Four continents
• Four corners of the world
• Four kingdoms of Daniel
• Four last things
• Four-dimensional space
• Fourth Doctor
• Fourth television network
• Quadrilateral
• Quadrivium
• Quadrupedalism
• Quadruple Alliance (1815)
• Quartets
• Quartile
• Square
• Tetralogies
• Tetramers (chemistry)
• Tetrapods
• The four woes of Jesus

Constructible polygons

• 257-gon
• 4,294,967,295
• 65537-gon
• Carlyle circle
• Constructible polygon
• Decagon
• Dodecagon
• Equilateral triangle
• Fermat number
• Heptadecagon
• Hexadecagon
• Hexagon
• Icosagon
• Icositetragon
• Octagon
• Pentadecagon
• Pentagon
• Square
• Triacontagon

Elementary shapes

• Capsule (geometry)
• Circle
• Circles
• Cone
• Cube
• Cubes
• Cuboid
• Cuboids
• Cylinder
• Decagon
• Dodecagon
• Ellipse
• Hendecagon
• Heptagon
• Hexagon
• Kite (geometry)
• Nonagon
• Octagon
• Oval
• Parallelogram
• Pentagon
• Rectangle
• Rhombus
• Sphere
• Spheres
• Square
• Trapezoid
• Triangles

Types of quadrilaterals

• Ailles rectangle
• Antiparallelogram
• Bicentric quadrilateral
• Complete quadrangle
• Cyclic quadrilateral
• Dynamic rectangle
• Equidiagonal quadrilateral
• Ex-tangential quadrilateral
• Golden rectangle
• Golden rhombus
• Harmonic quadrilateral
• Isosceles trapezoid
• Kite (geometry)
• Lambert quadrilateral
• Levi-Civita parallelogramoid
• Lozenge (shape)
• Orthodiagonal quadrilateral
• Parallelogram
• Rectangle
• Rhomboid
• Rhombus
• Right kite
• Saccheri quadrilateral
• Square
• Tangential quadrilateral
• Tangential trapezoid
• Trapezoid
• Unit square

References

[1] https://en.wikipedia.org/wiki/Square

Also known as 2-cube, 2-hypercube, 2-orthoplex, 4 symmetry, Crossed square, Hypocube, Regular quadrilateral, Regular rectangle, Skew square, Sqare, Square (geometry), Square (mathematics), Square (shape), Square(geometry), Squarer, Squares, Squarest, .

, 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 number, Square root, Square root of 2, Square tiling, Squaring the circle, Squaring the square, Squircle, Straightedge and compass construction, Symmetry group, Taxicab geometry, Tetrahedron, Tetrahemihexahedron, Thales's theorem, Transcendental number, Trapezoid, Truncation (geometry), Uniform star polyhedron, Unit square, Vertex (geometry), Vertex arrangement, Vertex figure, Zero of a function.