Quadrilateral, the Glossary

Table of Contents

1. 94 relations: Alexander Bogomolny, Altitude (triangle), Angle, Antiparallelogram, Area, Arithmetic mean, Bicentric quadrilateral, Bisection, Bow tie, Brahmagupta's formula, Bretschneider's formula, British English, Butterfly, Carl Anton Bretschneider, Centroid, Circumcenter of mass, Circumcircle, Circumscribed circle, Collinearity, Complete quadrangle, Complex polygon, Concave polygon, Concurrent lines, Concyclic points, Congruence (geometry), Convex polygon, Corollary, Cross product, Cyclic quadrilateral, Cyclobutane, Degree (angle), Determinant, Diagonal, Dover Publications, Duality (mathematics), Edge (geometry), Equidiagonal quadrilateral, Euclidean geometry, Euclidean plane, Euclidean vector, Euler line, Euler's quadrilateral theorem, Ex-tangential quadrilateral, Fermat point, Forum Geometricorum, Harmonic quadrilateral, Homography, If and only if, Incircle and excircles, Internal and external angles, ... Expand index (44 more) »

2. 4 (number)
3. Quadrilaterals

Alexander Bogomolny

Alexander Bogomolny (January 4, 1948 July 7, 2018) was a Soviet-born Israeli-American mathematician.

See Quadrilateral and Alexander Bogomolny

Altitude (triangle)

In geometry, an altitude of a triangle is a line segment through a vertex and perpendicular to a line containing the side opposite the vertex.

See Quadrilateral and Altitude (triangle)

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 Quadrilateral and Angle

Antiparallelogram

In geometry, an antiparallelogram is a type of self-crossing quadrilateral.

See Quadrilateral and Antiparallelogram

Area

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

See Quadrilateral and Area

Arithmetic mean

In mathematics and statistics, the arithmetic mean, arithmetic average, or just the mean or average (when the context is clear) is the sum of a collection of numbers divided by the count of numbers in the collection.

See Quadrilateral and Arithmetic mean

Bicentric quadrilateral

In Euclidean geometry, a bicentric quadrilateral is a convex quadrilateral that has both an incircle and a circumcircle.

See Quadrilateral and Bicentric quadrilateral

Bisection

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

See Quadrilateral and Bisection

Bow tie

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

See Quadrilateral and Bow tie

Brahmagupta's formula

In Euclidean geometry, Brahmagupta's formula, named after the 7th century Indian mathematician, is used to find the area of any cyclic quadrilateral (one that can be inscribed in a circle) given the lengths of the sides.

See Quadrilateral and Brahmagupta's formula

Bretschneider's formula

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

See Quadrilateral and Bretschneider's formula

British English

British English is the set of varieties of the English language native to the island of Great Britain.

See Quadrilateral and British English

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 Quadrilateral and Butterfly

Carl Anton Bretschneider

Carl Anton Bretschneider (27 May 1808 – 6 November 1878) was a mathematician from Gotha, Germany.

See Quadrilateral and Carl Anton Bretschneider

Centroid

In mathematics and physics, the centroid, also known as geometric center or center of figure, of a plane figure or solid figure is the arithmetic mean position of all the points in the surface of the figure.

See Quadrilateral and Centroid

Circumcenter of mass

In geometry, the circumcenter of mass is a center associated with a polygon which shares many of the properties of the center of mass.

See Quadrilateral and Circumcenter of mass

Circumcircle

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

See Quadrilateral and Circumcircle

Circumscribed circle

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

See Quadrilateral and Circumscribed circle

Collinearity

In geometry, collinearity of a set of points is the property of their lying on a single line.

See Quadrilateral and Collinearity

Complete quadrangle

In mathematics, specifically in incidence geometry and especially in projective geometry, a complete quadrangle is a system of geometric objects consisting of any four points in a plane, no three of which are on a common line, and of the six lines connecting the six pairs of points.

See Quadrilateral and Complete quadrangle

Complex polygon

The term complex polygon can mean two different things.

See Quadrilateral and Complex polygon

Concave polygon

A simple polygon that is not convex is called concave, non-convex or reentrant.

See Quadrilateral and Concave polygon

Concurrent lines

In geometry, lines in a plane or higher-dimensional space are concurrent if they intersect at a single point.

See Quadrilateral and Concurrent lines

Concyclic points

In geometry, a set of points are said to be concyclic (or cocyclic) if they lie on a common circle.

See Quadrilateral and Concyclic points

Congruence (geometry)

In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.

See Quadrilateral and Congruence (geometry)

Convex polygon

In geometry, a convex polygon is a polygon that is the boundary of a convex set.

See Quadrilateral and Convex polygon

Corollary

In mathematics and logic, a corollary is a theorem of less importance which can be readily deduced from a previous, more notable statement.

See Quadrilateral and Corollary

Cross product

In mathematics, the cross product or vector product (occasionally directed area product, to emphasize its geometric significance) is a binary operation on two vectors in a three-dimensional oriented Euclidean vector space (named here E), and is denoted by the symbol \times.

See Quadrilateral and Cross product

Cyclic quadrilateral

In Euclidean geometry, a cyclic quadrilateral or inscribed quadrilateral is a quadrilateral whose vertices all lie on a single circle.

See Quadrilateral and Cyclic quadrilateral

Cyclobutane

Cyclobutane is a cycloalkane and organic compound with the formula (CH2)4.

See Quadrilateral and Cyclobutane

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 Quadrilateral and Degree (angle)

Determinant

In mathematics, the determinant is a scalar-valued function of the entries of a square matrix.

See Quadrilateral and Determinant

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 Quadrilateral and Diagonal

Dover Publications

Dover Publications, also known as Dover Books, is an American book publisher founded in 1941 by Hayward and Blanche Cirker.

See Quadrilateral and Dover Publications

Duality (mathematics)

In mathematics, a duality translates concepts, theorems or mathematical structures into other concepts, theorems or structures in a one-to-one fashion, often (but not always) by means of an involution operation: if the dual of is, then the dual of is.

See Quadrilateral and Duality (mathematics)

Edge (geometry)

In geometry, an edge is a particular type of line segment joining two vertices in a polygon, polyhedron, or higher-dimensional polytope.

See Quadrilateral and Edge (geometry)

Equidiagonal quadrilateral

In Euclidean geometry, an equidiagonal quadrilateral is a convex quadrilateral whose two diagonals have equal length.

See Quadrilateral and Equidiagonal quadrilateral

Euclidean geometry

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

See Quadrilateral and Euclidean geometry

Euclidean plane

In mathematics, a Euclidean plane is a Euclidean space of dimension two, denoted \textbf^2 or \mathbb^2.

See Quadrilateral and Euclidean plane

Euclidean vector

In mathematics, physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector or spatial vector) is a geometric object that has magnitude (or length) and direction.

See Quadrilateral and Euclidean vector

Euler line

In geometry, the Euler line, named after Leonhard Euler, is a line determined from any triangle that is not equilateral.

See Quadrilateral and Euler line

Euler's quadrilateral theorem

Euler's quadrilateral theorem or Euler's law on quadrilaterals, named after Leonhard Euler (1707–1783), describes a relation between the sides of a convex quadrilateral and its diagonals.

See Quadrilateral and Euler's quadrilateral theorem

Ex-tangential quadrilateral

In Euclidean geometry, an ex-tangential quadrilateral is a convex quadrilateral where the extensions of all four sides are tangent to a circle outside the quadrilateral.

See Quadrilateral and Ex-tangential quadrilateral

Fermat point

In Euclidean geometry, the Fermat point of a triangle, also called the Torricelli point or Fermat–Torricelli point, is a point such that the sum of the three distances from each of the three vertices of the triangle to the point is the smallest possible or, equivalently, the geometric median of the three vertices.

See Quadrilateral and Fermat point

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 Quadrilateral and Forum Geometricorum

Harmonic quadrilateral

In Euclidean geometry, a harmonic quadrilateral, or harmonic quadrangle, is a quadrilateral that can be inscribed in a circle (cyclic quadrilateral) in which the products of the lengths of opposite sides are equal.

See Quadrilateral and Harmonic quadrilateral

Homography

In projective geometry, a homography is an isomorphism of projective spaces, induced by an isomorphism of the vector spaces from which the projective spaces derive.

See Quadrilateral and Homography

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 Quadrilateral 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 Quadrilateral and Incircle and excircles

Internal and external angles

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

See Quadrilateral and Internal and external angles

Isoperimetric inequality

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

See Quadrilateral 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.

See Quadrilateral and Isosceles trapezoid

Kite (geometry)

In Euclidean geometry, a kite is a quadrilateral with reflection symmetry across a diagonal.

See Quadrilateral and Kite (geometry)

Law of cosines

In trigonometry, the law of cosines (also known as the cosine formula or cosine rule) relates the lengths of the sides of a triangle to the cosine of one of its angles.

See Quadrilateral and Law of cosines

Leonhard Euler

Leonhard Euler (15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, geographer, logician, and engineer who founded the studies of graph theory and topology and made pioneering and influential discoveries in many other branches of mathematics such as analytic number theory, complex analysis, and infinitesimal calculus.

See Quadrilateral and Leonhard Euler

Line segment

In geometry, a line segment is a part of a straight line that is bounded by two distinct end points, and contains every point on the line that is between its endpoints.

See Quadrilateral and Line segment

List of self-intersecting polygons

Self-intersecting polygons, crossed polygons, or self-crossing polygons are polygons some of whose edges cross each other.

See Quadrilateral and List of self-intersecting polygons

Maximum and minimum

In mathematical analysis, the maximum and minimum of a function are, respectively, the largest and smallest value taken by the function.

See Quadrilateral and Maximum and minimum

Midpoint

In geometry, the midpoint is the middle point of a line segment.

See Quadrilateral and Midpoint

Newton line

In Euclidean geometry the Newton line is the line that connects the midpoints of the two diagonals in a convex quadrilateral with at most two parallel sides. Quadrilateral and Newton line are quadrilaterals.

See Quadrilateral and Newton line

Nine-point circle

In geometry, the nine-point circle is a circle that can be constructed for any given triangle.

See Quadrilateral and Nine-point circle

North American English

North American English is the most generalized variety of the English language as spoken in the United States and Canada.

See Quadrilateral and North American English

Orthodiagonal quadrilateral

In Euclidean geometry, an orthodiagonal quadrilateral is a quadrilateral in which the diagonals cross at right angles.

See Quadrilateral and Orthodiagonal quadrilateral

Parallel (geometry)

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

See Quadrilateral and Parallel (geometry)

Parallelogram

In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides.

See Quadrilateral and Parallelogram

Parallelogram law

In mathematics, the simplest form of the parallelogram law (also called the parallelogram identity) belongs to elementary geometry.

See Quadrilateral and Parallelogram law

Pentagon

In geometry, a pentagon is any five-sided polygon or 5-gon.

See Quadrilateral and Pentagon

Perimeter

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

See Quadrilateral and Perimeter

Perpendicular

In geometry, two geometric objects are perpendicular if their intersection forms right angles (angles that are 90 degrees or π/2 radians wide) at the point of intersection called a foot.

See Quadrilateral and Perpendicular

Perpendicular bisector construction of a quadrilateral

In geometry, the perpendicular bisector construction of a quadrilateral is a construction which produces a new quadrilateral from a given quadrilateral using the perpendicular bisectors to the sides of the former quadrilateral. Quadrilateral and perpendicular bisector construction of a quadrilateral are quadrilaterals.

See Quadrilateral and Perpendicular bisector construction of a quadrilateral

Polygon

In geometry, a polygon is a plane figure made up of line segments connected to form a closed polygonal chain.

See Quadrilateral and Polygon

Ptolemy's inequality

In Euclidean geometry, Ptolemy's inequality relates the six distances determined by four points in the plane or in a higher-dimensional space.

See Quadrilateral and Ptolemy's inequality

Ptolemy's theorem

In Euclidean geometry, Ptolemy's theorem is a relation between the four sides and two diagonals of a cyclic quadrilateral (a quadrilateral whose vertices lie on a common circle).

See Quadrilateral and Ptolemy's theorem

Quadrangle (geography)

A "quadrangle" is a topographic map produced by the United States Geological Survey (USGS) covering the United States.

See Quadrilateral and Quadrangle (geography)

Rectangle

In Euclidean plane geometry, a rectangle is a quadrilateral with four right angles.

See Quadrilateral and Rectangle

Rhomboid

Traditionally, in two-dimensional geometry, a rhomboid is a parallelogram in which adjacent sides are of unequal lengths and angles are non-right angled.

See Quadrilateral and Rhomboid

Rhombus

In plane Euclidean geometry, a rhombus (rhombi or rhombuses) is a quadrilateral whose four sides all have the same length.

See Quadrilateral 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 Quadrilateral and Right angle

Right kite

In Euclidean geometry, a right kite is a kite (a quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are adjacent to each other) that can be inscribed in a circle.

See Quadrilateral and Right kite

Saccheri quadrilateral

A Saccheri quadrilateral is a quadrilateral with two equal sides perpendicular to the base.

See Quadrilateral and Saccheri quadrilateral

Simple polygon

In geometry, a simple polygon is a polygon that does not intersect itself and has no holes.

See Quadrilateral and Simple polygon

Square

In Euclidean geometry, a square is a regular quadrilateral, which means that it has four sides of equal length and four equal angles (90-degree angles, π/2 radian angles, or right angles). Quadrilateral and square are 4 (number).

See Quadrilateral and Square

Tangent

In geometry, the tangent line (or simply tangent) to a plane curve at a given point is, intuitively, the straight line that "just touches" the curve at that point.

See Quadrilateral and Tangent

Tangential quadrilateral

In Euclidean geometry, a tangential quadrilateral (sometimes just tangent quadrilateral) or circumscribed quadrilateral is a convex quadrilateral whose sides all can be tangent to a single circle within the quadrilateral.

See Quadrilateral and Tangential quadrilateral

Tangential trapezoid

In Euclidean geometry, a tangential trapezoid, also called a circumscribed trapezoid, is a trapezoid whose four sides are all tangent to a circle within the trapezoid: the incircle or inscribed circle.

See Quadrilateral and Tangential trapezoid

Taxonomy

Taxonomy is a practice and science concerned with classification or categorization.

See Quadrilateral and Taxonomy

Tessellation

A tessellation or tiling is the covering of a surface, often a plane, using one or more geometric shapes, called tiles, with no overlaps and no gaps.

See Quadrilateral and Tessellation

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 Quadrilateral and Tetrahedron

The Mathematical Gazette

The Mathematical Gazette is a triannual peer-reviewed academic journal published by Cambridge University Press on behalf of the Mathematical Association.

See Quadrilateral and The Mathematical Gazette

Trapezoid

In geometry, a trapezoid in North American English, or trapezium in British English, is a quadrilateral that has one pair of parallel sides.

See Quadrilateral and Trapezoid

Triangle

A triangle is a polygon with three corners and three sides, one of the basic shapes in geometry.

See Quadrilateral and Triangle

Van Aubel's theorem

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

See Quadrilateral and Van Aubel's theorem

Varignon's theorem

In Euclidean geometry, Varignon's theorem holds that the midpoints of the sides of an arbitrary quadrilateral form a parallelogram, called the Varignon parallelogram.

See Quadrilateral and Varignon's theorem

Vertex (geometry)

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

See Quadrilateral and Vertex (geometry)

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

Quadrilaterals

• Centered square number
• Happy ending problem
• Newton line
• Newton–Gauss line
• Orthocentric system
• Perpendicular bisector construction of a quadrilateral
• Polite number
• Quadrilateral
• Square number

References

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

Also known as 4-gon, Bimedian, Bimedians, Bowtie-quadrilateral, Butterfly-quadrilateral, Concave quadrilateral, Cross quadrilateral, Cross-quadrilateral, Crossed quadrilateral, Crossed-quadrilateral, Irregular quadrilateral, Maltitude, Maltitudes, Quadragon, Quadrialateral, Quadrilater, Quadrilateralness, Quadrilaterals, Skew quadrilateral, Tetragon.

, Isoperimetric inequality, Isosceles trapezoid, Kite (geometry), Law of cosines, Leonhard Euler, Line segment, List of self-intersecting polygons, Maximum and minimum, Midpoint, Newton line, Nine-point circle, North American English, Orthodiagonal quadrilateral, Parallel (geometry), Parallelogram, Parallelogram law, Pentagon, Perimeter, Perpendicular, Perpendicular bisector construction of a quadrilateral, Polygon, Ptolemy's inequality, Ptolemy's theorem, Quadrangle (geography), Rectangle, Rhomboid, Rhombus, Right angle, Right kite, Saccheri quadrilateral, Simple polygon, Square, Tangent, Tangential quadrilateral, Tangential trapezoid, Taxonomy, Tessellation, Tetrahedron, The Mathematical Gazette, Trapezoid, Triangle, Van Aubel's theorem, Varignon's theorem, Vertex (geometry).