91 relations: 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, Circumscribed circle, Collinearity, Complete quadrangle, Complex polygon, Concave polygon, Concurrent lines, Concyclic points, Congruence (geometry), Convex polygon, Corollary, Cross product, Crux Mathematicorum, Cut-the-Knot, Cyclic quadrilateral, Cyclobutane, Degree (angle), Determinant, Diagonal, Dover Publications, Duality (mathematics), Edge (geometry), Equidiagonal quadrilateral, Euclidean geometry, Euclidean vector, Euler line, Euler's quadrilateral theorem, Ex-tangential quadrilateral, Fermat point, Hexagon, If and only if, Incircle and excircles of a triangle, Internal and external angles, Isoperimetric inequality, Isosceles trapezoid, Kite (geometry), ..., Law of cosines, Leonhard Euler, Line segment, List of self-intersecting polygons, Maxima and minima, 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 (general), Tessellation, Tetrahedron, The Mathematical Gazette, Trapezoid, Triangle, Van Aubel's theorem, Varignon's theorem, Vertex (geometry). Expand index (41 more) » « Shrink index
In geometry, an altitude of a triangle is a line segment through a vertex and perpendicular to (i.e., forming a right angle with) a line containing the base (the side opposite the vertex).
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.
In geometry, an antiparallelogram is a quadrilateral having, like a parallelogram, two opposite pairs of equal-length sides, but in which the sides of one pair cross each other.
Area is the quantity that expresses the extent of a two-dimensional figure or shape, or planar lamina, in the plane.
In mathematics and statistics, the arithmetic mean (stress on third syllable of "arithmetic"), or simply the mean or average when the context is clear, is the sum of a collection of numbers divided by the number of numbers in the collection.
In Euclidean geometry, a bicentric quadrilateral is a convex quadrilateral that has both an incircle and a circumcircle.
In geometry, bisection is the division of something into two equal or congruent parts, usually by a line, which is then called a bisector.
The bow tie is a type of traditional necktie.
In Euclidean geometry, Brahmagupta's formula is used to find the area of any cyclic quadrilateral (one that can be inscribed in a circle) given the lengths of the sides.
In geometry, Bretschneider's formula is the following expression for the area of a general quadrilateral: Here,,,, are the sides of the quadrilateral, is the semiperimeter, and and are two opposite angles.
British English is the standard dialect of English language as spoken and written in the United Kingdom.
Butterflies are insects in the macrolepidopteran clade Rhopalocera from the order Lepidoptera, which also includes moths.
Carl Anton Bretschneider (27 May 1808 – 6 November 1878) was a mathematician from Gotha, Germany.
In mathematics and physics, the centroid or geometric center of a plane figure is the arithmetic mean position of all the points in the shape.
In geometry, the circumcenter of mass is a center associated with a polygon which shares many of the properties of the center of mass.
In geometry, the circumscribed circle or circumcircle of a polygon is a circle which passes through all the vertices of the polygon.
In geometry, collinearity of a set of points is the property of their lying on a single line.
In mathematics, specifically 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.
The term complex polygon can mean two different things.
A simple polygon that is not convex is called concave, non-convex or reentrant.
In geometry, three or more lines in a plane or higher-dimensional space are said to be concurrent if they intersect at a single point.
In geometry, a set of points are said to be concyclic (or cocyclic) if they lie on a common circle.
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.
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.
A corollary is a statement that follows readily from a previous statement.
In mathematics and vector algebra, the cross product or vector product (occasionally directed area product to emphasize the geometric significance) is a binary operation on two vectors in three-dimensional space \left(\mathbb^3\right) and is denoted by the symbol \times.
Crux Mathematicorum is a scientific journal of mathematics published by the Canadian Mathematical Society.
Cut-the-knot is a free, advertisement-funded educational website maintained by Alexander Bogomolny and devoted to popular exposition of many topics in mathematics.
In Euclidean geometry, a cyclic quadrilateral or inscribed quadrilateral is a quadrilateral whose vertices all lie on a single circle.
Cyclobutane is a cycloalkane and organic compound with the formula (CH2)4.
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.
In linear algebra, the determinant is a value that can be computed from the elements of a square matrix.
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.
Dover Publications, also known as Dover Books, is an American book publisher founded in 1941 by Hayward Cirker and his wife, Blanche.
In mathematics, a duality, generally speaking, 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 A is B, then the dual of B is A. Such involutions sometimes have fixed points, so that the dual of A is A itself.
In geometry, an edge is a particular type of line segment joining two vertices in a polygon, polyhedron, or higher-dimensional polytope.
In Euclidean geometry, an equidiagonal quadrilateral is a convex quadrilateral whose two diagonals have equal length.
Euclidean geometry is a mathematical system attributed to Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements.
In mathematics, physics, and engineering, a Euclidean vector (sometimes called a geometric or spatial vector, or—as here—simply a vector) is a geometric object that has magnitude (or length) and direction.
In geometry, the Euler line, named after Leonhard Euler, is a line determined from any triangle that is not equilateral.
Euler's quadrilateral theorem or Euler's law on quadrilaterals, named after Leonhard Euler (1707–1783), describes a relation between the sides of an convex quadrilateral and its diagonals.
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.
In geometry, the Fermat point of a triangle, also called the Torricelli point or Fermat–Torricelli point, is a point such that the total distance from the three vertices of the triangle to the point is the minimum possible.
In geometry, a hexagon (from Greek ἕξ hex, "six" and γωνία, gonía, "corner, angle") is a six-sided polygon or 6-gon.
In logic and related fields such as mathematics and philosophy, if and only if (shortened iff) is a biconditional logical connective between statements.
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.
In geometry, an angle of a polygon is formed by two sides of the polygon that share an endpoint.
In mathematics, the isoperimetric inequality is a geometric inequality involving the surface area of a set and its volume.
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.
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.
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.
Leonhard Euler (Swiss Standard German:; German Standard German:; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, logician and engineer, who made important and influential discoveries in many branches of mathematics, such as infinitesimal calculus and graph theory, while also making pioneering contributions to several branches such as topology and analytic number theory.
In geometry, a line segment is a part of a line that is bounded by two distinct end points, and contains every point on the line between its endpoints.
Self-intersecting polygons, crossed polygons, or self-crossing polygons are polygons some of whose edges cross each other.
In mathematical analysis, the maxima and minima (the respective plurals of maximum and minimum) of a function, known collectively as extrema (the plural of extremum), are the largest and smallest value of the function, either within a given range (the local or relative extrema) or on the entire domain of a function (the global or absolute extrema).
In geometry, the midpoint is the middle point of a line segment.
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.
In geometry, the nine-point circle is a circle that can be constructed for any given triangle.
North American English (NAmE, NAE) is the most generalized variety of the English language as spoken in the United States and Canada.
In Euclidean geometry, an orthodiagonal quadrilateral is a quadrilateral in which the diagonals cross at right angles.
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.
In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides.
In mathematics, the simplest form of the parallelogram law (also called the parallelogram identity) belongs to elementary geometry.
In geometry, a pentagon (from the Greek πέντε pente and γωνία gonia, meaning five and angle) is any five-sided polygon or 5-gon.
A perimeter is a path that surrounds a two-dimensional shape.
In elementary geometry, the property of being perpendicular (perpendicularity) is the relationship between two lines which meet at a right angle (90 degrees).
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.
In elementary geometry, a polygon is a plane figure that is bounded by a finite chain of straight line segments closing in a loop to form a closed polygonal chain or circuit.
In Euclidean geometry, Ptolemy's inequality relates the six distances determined by four points in the plane or in a higher-dimensional space.
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).
In geology or geography, the word "quadrangle" usually refers to a United States Geological Survey (USGS) 7.5-minute quadrangle map, which are usually named after a local physiographic feature.
In Euclidean plane geometry, a rectangle is a quadrilateral with four right angles.
Traditionally, in two-dimensional geometry, a rhomboid is a parallelogram in which adjacent sides are of unequal lengths and angles are non-right angled.
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.
In geometry and trigonometry, a right angle is an angle of exactly 90° (degrees), corresponding to a quarter turn.
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.
A Saccheri quadrilateral (also known as a Khayyam–Saccheri quadrilateral) is a quadrilateral with two equal sides perpendicular to the base.
In geometry a simple polygon is a flat shape consisting of straight, non-intersecting line segments or "sides" that are joined pair-wise to form a closed path.
In geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, or (100-gradian angles or right angles). It can also be defined as a rectangle in which two adjacent sides have equal length. A square with vertices ABCD would be denoted.
In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point.
In Euclidean geometry, a tangential quadrilateral (sometimes just tangent quadrilateral) or circumscribed quadrilateral is a convex quadrilateral whose sides are all tangent to a single circle within the quadrilateral.
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.
Taxonomy is the practice and science of classification.
A tessellation of a flat surface is the tiling of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps.
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.
The Mathematical Gazette is an academic journal of mathematics education, published three times yearly, that publishes "articles about the teaching and learning of mathematics with a focus on the 15–20 age range and expositions of attractive areas of mathematics." It was established in 1894 by Edward Mann Langley as the successor to the Reports of the Association for the Improvement of Geometrical Teaching.
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.
A triangle is a polygon with three edges and three vertices.
In plane geometry, Van Aubel's theorem describes a relationship between squares constructed on the sides of a quadrilateral.
Varignon's theorem is a statement in Euclidean geometry, that deals with the construction of a particular parallelogram, the Varignon parallelogram, from an arbitrary quadrilateral (quadrangle).
In geometry, a vertex (plural: vertices or vertexes) is a point where two or more curves, lines, or edges meet.
4-gon, Bimedian, Bowtie-quadrilateral, Butterfly-quadrilateral, Cross quadrilateral, Cross-quadrilateral, Crossed quadrilateral, Crossed-quadrilateral, Irregular quadrilateral, Maltitude, Quadragon, Quadrialateral, Quadrilateralness, Quadrilaterals, Skew quadrilateral, Tetragon.