155 relations: Absolute value, Acute and obtuse triangles, Altitude (triangle), American Mathematical Monthly, Angle, Angle trisection, Apollonius's theorem, Architect, Aryabhata, Aryabhatiya, Astronomer, Astronomy, Barycentric coordinate system, Bisection, Brick, Broadway (Manhattan), Bronshtein and Semendyayev, Cantilever, Carnot's theorem, Cartesian coordinate system, Center of mass, Centroid, Ceva's theorem, Circle, Circumscribed circle, Concurrent lines, Congruence (geometry), Conic section, Construction, Cross product, Cyclic quadrilateral, Degeneracy (mathematics), Degree (angle), Desargues's theorem, Determinant, Dimension, Dot product, Dragon's Eye (symbol), Earthquake, Edge (geometry), Encyclopedia of Triangle Centers, Equilateral triangle, Euclid, Euclid's Elements, Euclidean geometry, Euclidean space, Euclidean vector, Euler line, Euler's theorem in geometry, Exterior angle theorem, ..., Extouch triangle, Fermat point, Flatiron Building, Geodesy, Geometric shape, Geometry, Great circle, Hadwiger–Finsler inequality, Heron's formula, Heronian triangle, Hexagon, Hyperbolic geometry, Hyperbolic triangle, Hypotenuse, If and only if, Incenter, Incircle and excircles of a triangle, Indian astronomy, Indian mathematics, Integer triangle, Internal and external angles, Inverse function, Inverse trigonometric functions, Isosceles triangle, Lattice graph, Law of cosines, Law of sines, Law of tangents, Lemoine hexagon, Lester's theorem, Lie algebra, Line integral, List of triangle inequalities, List of triangle topics, Mandart inellipse, Marden's theorem, Mathematician, Mathematics Magazine, Medial triangle, Median (geometry), Menelaus's theorem, Midpoint, Mnemonic, Multiplicative inverse, Napoleon points, Nature, Navigation, Necessity and sufficiency, New York City, Nine-point circle, Norway, Ono's inequality, Orthocentric system, Oxford University Press, Parallel postulate, Parallelogram, Pedal triangle, Pedoe's inequality, Pick's theorem, Plane (geometry), Polar coordinate system, Polygon, Polytope, Pons asinorum, Pythagorean addition, Pythagorean theorem, Pythagorean triple, Rectangle, Regular polygon, Right triangle, Saddle point, Semiperimeter, Shape, Shoelace formula, Similarity (geometry), Simplex, Space frame, Special right triangle, Sphere, Spherical geometry, Spherical trigonometry, Steiner ellipse, Steiner inellipse, Sum of angles of a triangle, Symmedian, Tally marks, Tangent, Tangential polygon, Tangential triangle, Tessellation, Tetrakis square tiling, Thales's theorem, The Mathematical Gazette, Theorem, Triangle, Triangle center, Triangle inequality, Triangular number, Triangulated category, Triangulation (topology), Trigonometric functions, Trigonometry, Trilinear coordinates, Two-dimensional space, Vertex (geometry). Expand index (105 more) » « Shrink index
In mathematics, the absolute value or modulus of a real number is the non-negative value of without regard to its sign.
An acute triangle is a triangle with all three angles acute (less than 90°).
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).
The American Mathematical Monthly is a mathematical journal founded by Benjamin Finkel in 1894.
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.
Angle trisection is a classical problem of compass and straightedge constructions of ancient Greek mathematics.
In geometry, Apollonius's theorem is a theorem relating the length of a median of a triangle to the lengths of its side.
An architect is a person who plans, designs, and reviews the construction of buildings.
Aryabhata (IAST) or Aryabhata I (476–550 CE) was the first of the major mathematician-astronomers from the classical age of Indian mathematics and Indian astronomy.
Aryabhatiya (IAST) or Aryabhatiyam, a Sanskrit astronomical treatise, is the magnum opus and only known surviving work of the 5th century Indian mathematician Aryabhata.
An astronomer is a scientist in the field of astronomy who concentrates their studies on a specific question or field outside the scope of Earth.
Astronomy (from ἀστρονομία) is a natural science that studies celestial objects and phenomena.
In geometry, the barycentric coordinate system is a coordinate system in which the location of a point of a simplex (a triangle, tetrahedron, etc.) is specified as the center of mass, or barycenter, of usually unequal masses placed at its vertices.
In geometry, bisection is the division of something into two equal or congruent parts, usually by a line, which is then called a bisector.
A brick is building material used to make walls, pavements and other elements in masonry construction.
Broadway is a road in the U.S. state of New York.
Bronshtein and Semendyayev (often just Bronshtein or Bronstein) is the informal name of a comprehensive handbook of fundamental working knowledge of mathematics and table of formulas originally compiled by the Russian mathematician Ilya Nikolaevich Bronshtein and engineer Konstantin Adolfovic Semendyayev.
A cantilever is a rigid structural element, such as a beam or a plate, anchored at one end to a (usually vertical) support from which it protrudes; this connection could also be perpendicular to a flat, vertical surface such as a wall.
In Euclidean geometry, Carnot's theorem states that the sum of the signed distances from the circumcenter D to the sides of an arbitrary triangle ABC is where r is the inradius and R is the circumradius of the triangle.
A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length.
In physics, the center of mass of a distribution of mass in space is the unique point where the weighted relative position of the distributed mass sums to zero, or the point where if a force is applied it moves in the direction of the force without rotating.
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.
Ceva's theorem is a theorem about triangles in Euclidean plane geometry.
A circle is a simple closed shape.
In geometry, the circumscribed circle or circumcircle of a polygon is a circle which passes through all the vertices of the polygon.
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, 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.
In mathematics, a conic section (or simply conic) is a curve obtained as the intersection of the surface of a cone with a plane.
Construction is the process of constructing a building or infrastructure.
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.
In Euclidean geometry, a cyclic quadrilateral or inscribed quadrilateral is a quadrilateral whose vertices all lie on a single circle.
In mathematics, a degenerate case is a limiting case in which an element of a class of objects is qualitatively different from the rest of the class and hence belongs to another, usually simpler, class.
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 projective geometry, Desargues's theorem, named after Girard Desargues, states: Denote the three vertices of one triangle by and, and those of the other by and.
In linear algebra, the determinant is a value that can be computed from the elements of a square matrix.
In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it.
In mathematics, the dot product or scalar productThe term scalar product is often also used more generally to mean a symmetric bilinear form, for example for a pseudo-Euclidean space.
The Dragon's Eye is an ancient Germanic symbol as collected by Rudolf Koch.
An earthquake (also known as a quake, tremor or temblor) is the shaking of the surface of the Earth, resulting from the sudden release of energy in the Earth's lithosphere that creates seismic waves.
In geometry, an edge is a particular type of line segment joining two vertices in a polygon, polyhedron, or higher-dimensional polytope.
The Encyclopedia of Triangle Centers (ETC) is an online list of thousands of points or "centers" associated with the geometry of a triangle.
In geometry, an equilateral triangle is a triangle in which all three sides are equal.
Euclid (Εὐκλείδης Eukleidēs; fl. 300 BC), sometimes given the name Euclid of Alexandria to distinguish him from Euclides of Megara, was a Greek mathematician, often referred to as the "founder of geometry" or the "father of geometry".
The Elements (Στοιχεῖα Stoicheia) is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt c. 300 BC.
Euclidean geometry is a mathematical system attributed to Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements.
In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.
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.
In geometry, Euler's theorem states that the distance d between the circumcentre and incentre of a triangle is given by.
The exterior angle theorem is Proposition 1.16 in Euclid's Elements, which states that the measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles.
In geometry, the extouch triangle of a triangle is formed by joining the points at which the three excircles touch the triangle.
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.
The Flatiron Building, originally the Fuller Building, is a triangular 22-story steel-framed landmarked building located at 175 Fifth Avenue in the borough of Manhattan, New York City, which is considered to be a groundbreaking skyscraper.
Geodesy, also known as geodetics, is the earth science of accurately measuring and understanding three of Earth's fundamental properties: its geometric shape, orientation in space, and gravitational field.
A geometric shape is the geometric information which remains when location, scale, orientation and reflection are removed from the description of a geometric object.
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.
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.
In mathematics, the Hadwiger–Finsler inequality is a result on the geometry of triangles in the Euclidean plane.
In geometry, Heron's formula (sometimes called Hero's formula), named after Hero of Alexandria, gives the area of a triangle by requiring no arbitrary choice of side as base or vertex as origin, contrary to other formulae for the area of a triangle, such as half the base times the height or half the norm of a cross product of two sides.
In geometry, a Heronian triangle is a triangle that has side lengths and area that are all integers.
In geometry, a hexagon (from Greek ἕξ hex, "six" and γωνία, gonía, "corner, angle") is a six-sided polygon or 6-gon.
In mathematics, hyperbolic geometry (also called Bolyai–Lobachevskian geometry or Lobachevskian geometry) is a non-Euclidean geometry.
In hyperbolic geometry, a hyperbolic triangle is a triangle in the hyperbolic plane.
In geometry, a hypotenuse (rarely: hypothenuse) is the longest side of a right-angled triangle, the side opposite of the right angle.
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 incenter of a triangle is a triangle center, a point defined for any triangle in a way that is independent of the triangle's placement or scale.
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.
Indian astronomy has a long history stretching from pre-historic to modern times.
Indian mathematics emerged in the Indian subcontinent from 1200 BC until the end of the 18th century.
An integer triangle or integral triangle is a triangle all of whose sides have lengths that are integers.
In geometry, an angle of a polygon is formed by two sides of the polygon that share an endpoint.
In mathematics, an inverse function (or anti-function) is a function that "reverses" another function: if the function applied to an input gives a result of, then applying its inverse function to gives the result, and vice versa.
In mathematics, the inverse trigonometric functions (occasionally also called arcus functions, antitrigonometric functions or cyclometric functions) are the inverse functions of the trigonometric functions (with suitably restricted domains).
In geometry, an isosceles triangle is a triangle that has two sides of equal length.
A lattice graph, mesh graph, or grid graph, is a graph whose drawing, embedded in some Euclidean space Rn, forms a regular tiling.
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.
In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of a triangle (any shape) to the sines of its angles.
In trigonometry, the law of tangents is a statement about the relationship between the tangents of two angles of a triangle and the lengths of the opposing sides.
In geometry, the Lemoine hexagon is a cyclic hexagon with vertices given by the six intersections of the edges of a triangle and the three lines that are parallel to the edges that pass through its symmedian point.
In Euclidean plane geometry, Lester's theorem states that in any scalene triangle, the two Fermat points, the nine-point center, and the circumcenter lie on the same circle.
In mathematics, a Lie algebra (pronounced "Lee") is a vector space \mathfrak g together with a non-associative, alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow \mathfrak g; (x, y) \mapsto, called the Lie bracket, satisfying the Jacobi identity.
In mathematics, a line integral is an integral where the function to be integrated is evaluated along a curve.
In geometry, triangle inequalities are inequalities involving the parameters of triangles, that hold for every triangle, or for every triangle meeting certain conditions.
This list of triangle topics includes things related to the geometric shape, either abstractly, as in idealizations studied by geometers, or in triangular arrays such as Pascal's triangle or triangular matrices, or concretely in physical space.
In geometry, the Mandart inellipse of a triangle is an ellipse inscribed within the triangle, tangent to its sides at the contact points of its excircles (which are also the vertices of the extouch triangle and the endpoints of the splitters).
In mathematics, Marden's theorem, named after Morris Marden but proven much earlier by Jörg Siebeck, gives a geometric relationship between the zeroes of a third-degree polynomial with complex coefficients and the zeroes of its derivative.
A mathematician is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems.
Mathematics Magazine is a refereed bimonthly publication of the Mathematical Association of America.
The medial triangle or midpoint triangle of a triangle ABC is the triangle with vertices at the midpoints of the triangle's sides AB, AC and BC.
In geometry, a median of a triangle is a line segment joining a vertex to the midpoint of the opposing side, bisecting it.
Menelaus's theorem, named for Menelaus of Alexandria, is a proposition about triangles in plane geometry.
In geometry, the midpoint is the middle point of a line segment.
A mnemonic (the first "m" is silent) device, or memory device, is any learning technique that aids information retention or retrieval (remembering) in the human memory.
In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x−1, is a number which when multiplied by x yields the multiplicative identity, 1.
In geometry, Napoleon points are a pair of special points associated with a plane triangle.
Nature, in the broadest sense, is the natural, physical, or material world or universe.
Navigation is a field of study that focuses on the process of monitoring and controlling the movement of a craft or vehicle from one place to another.
In logic, necessity and sufficiency are terms used to describe an implicational relationship between statements.
The City of New York, often called New York City (NYC) or simply New York, is the most populous city in the United States.
In geometry, the nine-point circle is a circle that can be constructed for any given triangle.
Norway (Norwegian: (Bokmål) or (Nynorsk); Norga), officially the Kingdom of Norway, is a unitary sovereign state whose territory comprises the western portion of the Scandinavian Peninsula plus the remote island of Jan Mayen and the archipelago of Svalbard.
In mathematics, Ono's inequality is a theorem about triangles in the Euclidean plane.
In geometry, an orthocentric system is a set of four points on a plane, one of which is the orthocenter of the triangle formed by the other three.
Oxford University Press (OUP) is the largest university press in the world, and the second oldest after Cambridge University Press.
In geometry, the parallel postulate, also called Euclid's fifth postulate because it is the fifth postulate in Euclid's ''Elements'', is a distinctive axiom in Euclidean geometry.
In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides.
In geometry, a pedal triangle is obtained by projecting a point onto the sides of a triangle.
In geometry, Pedoe's inequality (also Neuberg-Pedoe inequality), named after Daniel Pedoe (1910-1998) and Joseph Jean Baptiste Neuberg (1840-1926), states that if a, b, and c are the lengths of the sides of a triangle with area ƒ, and A, B, and C are the lengths of the sides of a triangle with area F, then with equality if and only if the two triangles are similar with pairs of corresponding sides (A, a), (B, b), and (C, c).
Given a simple polygon constructed on a grid of equal-distanced points (i.e., points with integer coordinates) such that all the polygon's vertices are grid points, Pick's theorem provides a simple formula for calculating the area of this polygon in terms of the number of lattice points in the interior located in the polygon and the number of lattice points on the boundary placed on the polygon's perimeter: In the example shown, we have interior points and boundary points, so the area is.
In mathematics, a plane is a flat, two-dimensional surface that extends infinitely far.
In mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction.
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 elementary geometry, a polytope is a geometric object with "flat" sides.
In geometry, the statement that the angles opposite the equal sides of an isosceles triangle are themselves equal is known as the pons asinorum, typically translated as "bridge of asses".
In mathematics, Pythagorean addition is the following binary operation on the real numbers: The name recalls the Pythagorean theorem, which states that the length of the hypotenuse of a right triangle is where a and b are the lengths of the other sides.
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.
A Pythagorean triple consists of three positive integers,, and, such that.
In Euclidean plane geometry, a rectangle is a quadrilateral with four right angles.
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).
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).
In mathematics, a saddle point or minimax point is a point on the surface of the graph of a function where the slopes (derivatives) of orthogonal function components defining the surface become zero (a stationary point) but are not a local extremum on both axes.
In geometry, the semiperimeter of a polygon is half its perimeter.
A shape is the form of an object or its external boundary, outline, or external surface, as opposed to other properties such as color, texture or material composition.
The shoelace formula or shoelace algorithm (also known as Gauss's area formula and the surveyor's formula) is a mathematical algorithm to determine the area of a simple polygon whose vertices are described by their Cartesian coordinates in the plane.
Two geometrical objects are called similar if they both have the same shape, or one has the same shape as the mirror image of the other.
In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions.
In architecture and structural engineering, a space frame or space structure is a rigid, lightweight, truss-like structure constructed from interlocking struts in a geometric pattern.
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.
A sphere (from Greek σφαῖρα — sphaira, "globe, ball") is a perfectly round geometrical object in three-dimensional space that is the surface of a completely round ball (viz., analogous to the circular objects in two dimensions, where a "circle" circumscribes its "disk").
Spherical geometry is the geometry of the two-dimensional surface of a sphere.
Spherical trigonometry is the branch of spherical geometry that deals with the relationships between trigonometric functions of the sides and angles of the spherical polygons (especially spherical triangles) defined by a number of intersecting great circles on the sphere.
In geometry, the Steiner ellipse of a triangle, also called the Steiner circumellipse to distinguish it from the Steiner inellipse, is the unique circumellipse (ellipse that touches the triangle at its vertices) whose center is the triangle's centroid.
In geometry, the Steiner inellipse,Weisstein, E. "Steiner Inellipse" — From MathWorld, A Wolfram Web Resource, http://mathworld.wolfram.com/SteinerInellipse.html.
In several geometries, a triangle has three vertices and three sides, where three angles of a triangle are formed at each vertex by a pair of adjacent sides.
In geometry, symmedians are three particular geometrical lines associated with every triangle.
Tally marks, also called hash marks, are a unary numeral system.
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 polygon, also known as a circumscribed polygon, is a convex polygon that contains an inscribed circle (also called an incircle).
In geometry, the tangential triangle of a reference triangle (other than a right triangle) is the triangle whose sides are on the tangent lines to the reference triangle's circumcircle at the reference triangle's vertices.
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, the tetrakis square tiling is a tiling of the Euclidean plane.
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.
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 mathematics, a theorem is a statement that has been proven on the basis of previously established statements, such as other theorems, and generally accepted statements, such as axioms.
A triangle is a polygon with three edges and three vertices.
In geometry, a triangle center (or triangle centre) is a point in the plane that is in some sense a center of a triangle akin to the centers of squares and circles, i.e. a point that is in the middle of the figure by some measure.
In mathematics, the triangle inequality states that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side.
A triangular number or triangle number counts objects arranged in an equilateral triangle, as in the diagram on the right.
In mathematics, a triangulated category is a category together with the additional structure of a "translation functor" and a class of "distinguished triangles".
In mathematics, topology generalizes the notion of triangulation in a natural way as follows: Triangulation is useful in determining the properties of a topological space.
In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are functions of an angle.
Trigonometry (from Greek trigōnon, "triangle" and metron, "measure") is a branch of mathematics that studies relationships involving lengths and angles of triangles.
In geometry, the trilinear coordinates x:y:z of a point relative to a given triangle describe the relative directed distances from the three sidelines of the triangle.
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).
In geometry, a vertex (plural: vertices or vertexes) is a point where two or more curves, lines, or edges meet.
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