This list of triangle

Triangle

A triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three sides or edges which are line segments. A triangle with vertices A, B, and C is denoted ....

 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

Pascal's triangle

In mathematics, Pascal's triangle is a triangular array of the binomial coefficients in a triangle. It is named after the French mathematician, Blaise Pascal...

 or triangular matrices

Triangular matrix

In the mathematical discipline of linear algebra, a triangular matrix is a special kind of square matrix where either all the entries below or all the entries above the main diagonal are zero...

, or concretely in physical space. It does not include metaphors like "love triangle" in which the word has no reference to the geometric shape.

Geometry

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• Triangle
  Triangle
  A triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three sides or edges which are line segments. A triangle with vertices A, B, and C is denoted ....
  
   
• Altern base
  Altern base
  In trigonometry, the altern base is distinguished from the true base. Thus, in oblique triangles, the true base is the sum of the sides, and then the difference of the sides is the altern base; or the true base is the difference of the sides, and then the sum of the side is the altern base....
  
   
• Altitude (triangle)
  Altitude (triangle)
  In geometry, an altitude of a triangle is a straight line through a vertex and perpendicular to a line containing the base . This line containing the opposite side is called the extended base of the altitude. The intersection between the extended base and the altitude is called the foot of the...
  
   
• Angle bisector theorem
  Angle bisector theorem
  In geometry, the angle bisector theorem is concerned with the relative lengths of the two segments that a triangle's side is divided into by a line that bisects the opposite angle. It equates their relative lengths to the relative lengths of the other two sides of the triangle.Consider a triangle...
  
   
• Apollonius' theorem
  Apollonius' theorem
  In geometry, Apollonius' theorem is a theorem relating the length of a median of a triangle to the lengths of its side.Specifically, in any triangle ABC, if AD is a median, thenAB^2 + AC^2 = 2\,...
  
   
• Automedian triangle
  Automedian triangle
  In plane geometry, an automedian triangle is a triangle in which the lengths of the three medians are proportional to the lengths of the three sides, in a different order...
  
   
• Barycentric coordinates (mathematics)
  Barycentric coordinates (mathematics)
  In geometry, the barycentric coordinate system is a coordinate system in which the location of a point is specified as the center of mass, or barycenter, of masses placed at the vertices of a simplex . Barycentric coordinates are a form of homogeneous coordinates...
  
  
• Brianchon point 
• Brocard circle
  Brocard circle
  In geometry, the Brocard circle for a triangle is a circle having a diameter of the line segment between the circumcenter and symmedian. It contains the Brocard points. The Brocard circle is named for Henri Brocard....
  
   
• Brocard points 
• Brocard triangle
  Brocard triangle
  In geometry, the Brocard triangle of a triangle is a triangle formed by the intersection of line from a vertex to its corresponding Brocard point and a line from another vertex to its corresponding Brocard point and the other two points constructed using different combinations of vertices and...
  
   
• Carnot's theorem
  Carnot's theorem
  In Euclidean geometry, Carnot's theorem, named after Lazare Carnot , is as follows. Let ABC be an arbitrary triangle. Then the sum of the signed distances from the circumcenter D to the sides of triangle ABC is...
  
   
• Centroid
  Centroid
  In geometry, the centroid, geometric center, or barycenter of a plane figure or two-dimensional shape X is the intersection of all straight lines that divide X into two parts of equal moment about the line. Informally, it is the "average" of all points of X...
  
   
• Ceva's theorem
  Ceva's theorem
  Ceva's theorem is a theorem about triangles in plane geometry. Given a triangle ABC, let the lines AO, BO and CO be drawn from the vertices to a common point O to meet opposite sides at D, E and F respectively...
  
   
• Cevian
  Cevian
  In geometry, a cevian is any line segment in a triangle with one endpoint on a vertex of the triangle and the other endpoint on the opposite side. Medians, altitudes, and angle bisectors are special cases of cevians...
  
   
• Circumconic and inconic
  Circumconic and inconic
  In triangle geometry, a circumconic is a conic section that passes through three given points, and an inconic is a conic section inscribed in the triangle whose vertices lie at three given points....
  
   
• Circumscribed circle
  Circumscribed circle
  In geometry, the circumscribed circle or circumcircle of a polygon is a circle which passes through all the vertices of the polygon. The center of this circle is called the circumcenter....
  
   
• Cleaver (geometry)
  Cleaver (geometry)
  In geometry, a cleaver of a triangle is a line segment that bisects the perimeter of the triangle and has one endpoint at the midpoint of one of the three sides.* Each cleaver is parallel to one of the angle bisectors of the triangle....
  
   
• Congruence (geometry)
  Congruence (geometry)
  In geometry, two figures are congruent if they have the same shape and size. This means that either object can be repositioned so as to coincide precisely with the other object...
  
   
• Contact triangle 
• Conway triangle notation
  Conway triangle notation
  In geometry, the Conway triangle notation, named after John Horton Conway, allows trigonometric functions of a triangle to be managed algebraically...
  
   
• CPCTC
  CPCTC
  In geometry, CPCTC is the abbreviation of a theorem involving congruent triangles. CPCTC stands for Corresponding Parts of Congruent Triangles are Congruent. CPCTC states that if two or more triangles are proven congruent by: ASA, AAS, SSS, HL, or SAS, then all of their corresponding parts are...
  
   
• Delaunay triangulation
  Delaunay triangulation
  In mathematics and computational geometry, a Delaunay triangulation for a set P of points in a plane is a triangulation DT such that no point in P is inside the circumcircle of any triangle in DT. Delaunay triangulations maximize the minimum angle of all the angles of the triangles in the...
  
   
• de Longchamps point
  De Longchamps point
  In geometry, the de Longchamps point of a triangle is the reflection of its orthocenter about its circumcenter. It is listed as X in the Encyclopedia of Triangle Centers. Its trilinear coordinates are\displaystyle\cos A - \cos B \cos C : \cos B - \cos C \cos A : \cos C - \cos A \cos BThe point is...
  
   
• Desargues' theorem
  Desargues' theorem
  In projective geometry, Desargues' theorem, named in honor of Gérard Desargues, states:Denote the three vertices of one triangle by a, b, and c, and those of the other by A, B, and C...
  
   
• Encyclopedia of Triangle Centers
  Encyclopedia of Triangle Centers
  The Encyclopedia of Triangle Centers is an on-line list of more than 3,000 points or "centers" associated with the geometry of a triangle. It is maintained by Clark Kimberling, Professor of Mathematics at the University of Evansville....
  
   
• Equal incircles theorem
  Equal incircles theorem
  In geometry, the equal incircles theorem derives from a Japanese Sangaku, and pertains to the following construction: a series of rays are drawn from a given point to a given line such that the inscribed circles of the triangles formed by adjacent rays and the base line are equal...
  
   
• Equilateral triangle 
• Euler's line
  Euler's line
  In geometry, the Euler line, named after Leonhard Euler, is a line determined from any triangle that is not equilateral; it passes through several important points determined from the triangle...
  
   
• Euler's theorem in geometry
  Euler's theorem in geometry
  In geometry, Euler's theorem, named after Leonhard Euler, states that the distance d between the circumcentre and incentre of a triangle can be expressed as d^2=R \,...
  
   
• Exterior angle theorem
  Exterior angle theorem
  The exterior angle theorem can mean one of two things: Postulate 1.16 in Euclid's Elements which states that the exterior angle of a triangle is bigger than either of the remote interior angles, or a theorem in elementary geometry which states that the exterior angle of a triangle is equal to the...
  
   
• Fermat point
  Fermat point
  In geometry the Fermat point of a triangle, also called Torricelli point, is a point such that the total distance from the three vertices of the triangle to the point is the minimum possible...
  
   
• Fermat's right triangle theorem 
• Fuhrmann circle
  Fuhrmann circle
  In geometry, the Fuhrmann circle of a triangle is the circle with a diameter of the line segment between the orthocenter and the Nagel point. The radius of the Fuhrmann circle of a triangle with sides a, b, and c and circumradius R is...
  
   
• GEOS circle
  GEOS circle
  In geometry, the GEOS circle is derived from the intersection of four lines that are associated with a generalized triangle: the Euler line, the Soddy line, the orthic axis and the Gergonne line...
  
   
• Gergonne point 
• Golden triangle (mathematics) 
• Hadley's theorem 
• Hadwiger–Finsler inequality
  Hadwiger–Finsler inequality
  In mathematics, the Hadwiger–Finsler inequality is a result on the geometry of triangles in the Euclidean plane, named after the mathematicians Hugo Hadwiger and Paul Finsler...
  
   
• Heron's formula 
• Hyperbolic triangle
  Hyperbolic triangle
  In mathematics, the term hyperbolic triangle has more than one meaning.-Hyperbolic geometry:In hyperbolic geometry, a hyperbolic triangle is a figure in the hyperbolic plane, analogous to a triangle in Euclidean geometry, consisting of three sides and three angles...
  
   (non-Euclidean geometry)
• Hypotenuse
  Hypotenuse
  In geometry, a hypotenuse is the longest side of a right-angled triangle, the side opposite the right angle. The length of the hypotenuse of a right triangle can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse equals the sum of the squares of the...
  
   

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• Incircle and excircles of a triangle
  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 the three sides...
  
   
• Inertia tensor of triangle 
• Isosceles triangle 
• Isodynamic point
  Isodynamic point
  In Euclidean geometry, every triangle has two isodynamic points, usually denoted as S and S^'. These points are the common intersection points of the three circles of Apollonius associated with the triangle; hence, the line through these points is the common radical axis for these circles...
  
   
• Isogonal conjugate
  Isogonal conjugate
  In geometry, the isogonal conjugate of a point P with respect to a triangle ABC is constructed by reflecting the lines PA, PB, and PC about the angle bisectors of A, B, and C. These three reflected lines concur at the isogonal conjugate of P...
  
   
• Isosceles triangle theorem
  Isosceles triangle theorem
  In Euclidean geometry, the isosceles triangle theorem, also known as the pons asinorum, states that the angles opposite the two equal sides of an isosceles triangle are equal...
  
   
• Isotomic conjugate
  Isotomic conjugate
  In geometry, the isotomic conjugate of a point P not on a sideline of triangle ABC is constructed as follows: Let A, B, C be the points in which the lines AP, BP, CP meet the lines BC, CA, AB, respectively. Reflect ABC in the midpoints of sides BC, CA, AB to obtain points A", B", C", respectively...
  
   
• Isotomic lines
  Isotomic lines
  In geometry, the isotomic lines of a point in relation to a triangle are the cevians through the point from each polygon vertex which meet the opposite sides. The isotomic conjugate can be constructed from the iscotomic lines....
  
   
• Japanese theorem for concyclic polygons
• Johnson circles
  Johnson circles
  In geometry, a set of Johnson circles comprise three circles of equal radius r sharing one common point of intersection H. In such a configuration the circles usually have a total of four intersections : the common point H that they all share, and for each of the three pairs of circles one more...
  
   
• Kepler triangle 
• Kobon triangle problem
  Kobon triangle problem
  The Kobon triangle problem is an unsolved problem in combinatorial geometry first stated by Kobon Fujimura. The problem asks for the largest number N of nonoverlapping triangles that can be produced by k straight line segments....
  
   
• Leg (geometry) 
• Lester's theorem
  Lester's theorem
  In Euclidean plane geometry, Lester's theorem, named after June Lester, states that in any scalene triangle, the two Fermat points, the nine-point center, and the circumcenter are concyclic.- References :...
  
   
• Mandart inellipse 
• Medial triangle
  Medial triangle
  The medial triangle of a triangle ABC is the triangle with vertices at the midpoints of the triangle's sides AB, AC and BC....
  
   
• Median (geometry)
  Median (geometry)
  In geometry, a median of a triangle is a line segment joining a vertex to the midpoint of the opposing side. Every triangle has exactly three medians; one running from each vertex to the opposite side...
  
   
• Menelaus' theorem
  Menelaus' theorem
  Menelaus' theorem, named for Menelaus of Alexandria, is a theorem about triangles in plane geometry. Given a triangle ABC, and a transversal line that crosses BC, AC and AB at points D, E and F respectively, with D, E, and F distinct from A, B and C, thenThis equation uses signed lengths of...
  
   
• Miquel's theorem
  Miquel's theorem
  Miquel's theorem is a theorem in geometry, named after Auguste Miquel, about the intersection pattern of circles defined from six points on a triangle...
  
   
• Mittenpunkt
  Mittenpunkt
  In geometry, the mittenpunkt of a triangle is a triangle center: a point defined from the triangle that is invariant under Euclidean transformations of the triangle. It is defined as the symmedian point of the excentral triangle of the given triangle. It is also the centroid of the Mandart...
  
   
• Morley's trisector theorem
  Morley's trisector theorem
  In plane geometry, Morley's trisector theorem states that in any triangle, the three points of intersection of the adjacent angle trisectors form an equilateral triangle, called the Morley triangle. The theorem was discovered in 1899 by Anglo-American mathematician Frank Morley...
  
  
• Nagel point
  Nagel point
  In geometry, the Nagel point is a point associated with any triangle. Given a triangle ABC, let TA, TB, and TC be the extouch points in which the A-excircle meets line BC, the B-excircle meets line CA, and C-excircle meets line AB, respectively...
  
   
• Napoleon's theorem
  Napoleon's theorem
  In mathematics, Napoleon's theorem states that if equilateral triangles are constructed on the sides of any triangle, either all outward, or all inward, the centres of those equilateral triangles themselves form an equilateral triangle....
  
   
• Nine-point circle
  Nine-point circle
  In geometry, the nine-point circle is a circle that can be constructed for any given triangle. It is so named because it passes through nine significant points defined from the triangle...
  
   
• Nine-point hyperbola
  Nine-point hyperbola
  -Discovery:The nine-point hyperbola was first discovered by E.F. Allen and his work was published in a volume of The American Mathematical Monthly in December, 1941...
  
   
• One-seventh area triangle
  One-seventh area triangle
  In plane geometry, a triangle ABC contains a triangle of one-seventh area of ABC formed as follows: the sides of this triangle lie on lines p, q, r whereA more general result is known as Routh's theorem.-References:...
  
   
• Orthocenter 
• Orthocentric system
  Orthocentric system
  In geometry, an orthocentric system is a set of four points in the plane one of which is the orthocenter of the triangle formed by the other three....
  
   
• Pedal triangle
  Pedal triangle
  In geometry, a pedal triangle is obtained by projecting a point onto the sides of a triangle.More specifically, consider a triangle ABC, and a point P that is not one of the vertices A, B, C. Drop perpendiculars from P to the three sides of the triangle...
  
   
• Pompeiu's theorem
  Pompeiu's theorem
  Pompeiu's theorem is a result of plane geometry, discovered by the Romanian mathematician Dimitrie Pompeiu. The theorem is quite simple, but not classical. It states the following:...
  
   
• Pons asinorum
  Pons asinorum
  Pons asinorum is the name given to Euclid's fifth proposition in Book 1 of his Elements of geometry, also known as the theorem on isosceles triangles. It states that the angles opposite the equal sides of an isosceles triangle are equal...
  
   
• Pythagorean theorem
  Pythagorean theorem
  In mathematics, the Pythagorean theorem or Pythagoras' theorem is a relation in Euclidean geometry among the three sides of a right triangle...
  
   
• Reuleaux triangle
  Reuleaux triangle
  A Reuleaux triangle is, apart from the trivial case of the circle, the simplest and best known Reuleaux polygon, a curve of constant width. The separation of two parallel lines tangent to the curve is independent of their orientation...
  
   
• Regiomontanus
  Regiomontanus
  Johannes Müller von Königsberg , today best known by his Latin toponym Regiomontanus, was a German mathematician, astronomer, astrologer, translator and instrument maker....
  
   
• Regiomontanus' angle maximization problem
  Regiomontanus' angle maximization problem
  In mathematics, the Regiomontanus' angle maximization problem, is a famous optimization problem posed by the 15th-century German mathematician Johannes Müller...
  
   
• Right triangle
  Right triangle
  A right triangle or right-angled triangle is a triangle in which one angle is a right angle . The relation between the sides and angles of a right triangle is the basis for trigonometry.-Terminology:The side opposite the right angle is called the hypotenuse...
  
   
• Routh's theorem
  Routh's theorem
  In geometry, Routh's theorem determines the ratio of areas between a given triangle and a triangle formed by the intersection of three cevians...
  
   

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• Scalene triangle 
• Schwarz triangle
  Schwarz triangle
  In geometry, a Schwarz triangle, named after Hermann Schwarz is a spherical triangle that can be used to tile a sphere, possibly overlapping, through reflections in its edges. They were classified in ....
  
   
• Schiffler's theorem
  Schiffler's theorem
  In geometry, the Schiffler's theorem states that if the incenter of a triangle ABC is denoted by I, then the Euler lines of triangles BIC, CIA and AIB have a common point. The theorem can be proved by using trilinear coordinates....
  
   
• Sierpinski triangle
  Sierpinski triangle
  The Sierpinski triangle , also called the Sierpinski gasket or the Sierpinski Sieve, is a fractal and attractive fixed set named after the Polish mathematician Wacław Sierpiński who described it in 1915. However, similar patterns appear already in the 13th-century Cosmati mosaics in the cathedral...
  
    (fractal geometry)
• Similarity (geometry)
  Similarity (geometry)
  Two geometrical objects are called similar if they both have the same shape. More precisely, either one is congruent to the result of a uniform scaling of the other...
  
   
• Simson line
  Simson line
  In geometry, given a triangle ABC and a point P on its circumcircle, the three closest points to P on lines AB, AC, and BC are collinear. The line through these points is the Simson line of P, named for Robert Simson...
  
   
• Special right triangles
  Special right triangles
  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. For example, a right triangle may have angles that form simple relationships, such as 45-45-90. This is called an "angle-based" right triangle...
  
   
• Spieker circle
  Spieker circle
  In geometry, the incircle of the medial triangle of a triangle ABC is the Spieker circle. Its center, the Spieker center, is the center of mass of the boundary of triangle ABC as well as being the incenter of the medial triangle....
  
   
• Spiral of Theodorus
  Spiral of Theodorus
  In geometry, the spiral of Theodorus is a spiral composed of contiguous right triangles. It was first constructed by Theodorus of Cyrene.-Construction:...
  
   
• Splitter (geometry)
  Splitter (geometry)
  In plane geometry, a splitter of a triangle is a line segment having one endpoint at one of the three vertices of the triangle and the other so located on the perimeter as to bisect the perimeter.The three splitters concur at the Nagel point of the triangle....
  
   
• Steiner inellipse
  Steiner inellipse
  In geometry, the Steiner inellipse of a triangle is the unique ellipse inscribed in the triangle and tangent to the sides at their midpoints. It is an example of an inconic. By comparison the inscribed circle of a triangle is another inconic that is tangent to the sides, but not necessarily at the...
  
   
• Steiner–Lehmus theorem 
• Stewart's theorem
  Stewart's theorem
  In geometry, Stewart's theorem yields a relation between a lengths of the sides of the triangle and the length of a cevian of the triangle. Its name is in honor of the Scottish mathematician Matthew Stewart who published the theorem in 1746.- Theorem :...
  
   
• Symmedian
  Symmedian
  Symmedians are three particular geometrical lines associated with every triangle. They are constructed by taking a median of the triangle , and reflecting the line over the corresponding angle bisector...
  
   
• Tarry point
  Tarry point
  In geometry, the Tarry point for a triangle is a point of concurrency of the lines through the vertices of the triangle perpendicular to the corresponding sides of the triangle's first Brocard triangle. The Tarry point lies on the other endpoint of the diameter of the circumcircle drawn through...
  
   
• Ternary plot
  Ternary plot
  A ternary plot, ternary graph, triangle plot, simplex plot, or de Finetti diagram is a barycentric plot on three variables which sum to a constant. It graphically depicts the ratios of the three variables as positions in an equilateral triangle...
  
   
• Thales' theorem
  Thales' theorem
  In geometry, Thales' theorem states that if A, B and C are points on a circle where the line AC is a diameter of the circle, then the angle ABC is a right angle. Thales' theorem is a special case of the inscribed angle theorem...
  
   
• Thomson cubic
  Thomson cubic
  In geometry, the Thomson cubic of a triangle is the locus of centers of circumconics whose normals at the vertices are concurrent....
  
   
• Triangle center
  Triangle center
  In geometry a triangle center is a point in the plane that is in some sense a center of a triangle akin to the centers of squares and circles. For example the centroid, circumcenter, incenter and orthocenter were familiar to the ancient Greeks, and can be obtained by simple constructions. Each of...
  
   
• Triangle group
  Triangle group
  In mathematics, a triangle group is a group that can be realized geometrically by sequences of reflections across the sides of a triangle. The triangle can be an ordinary Euclidean triangle, a triangle on the sphere, or a hyperbolic triangle...
  
   
• Triangulation
  Triangulation
  In trigonometry and geometry, triangulation is the process of determining the location of a point by measuring angles to it from known points at either end of a fixed baseline, rather than measuring distances to the point directly...
  
  
• Triangular coordinates
  Triangular coordinates
  The term triangular coordinates may refer to any of at least three related systems of coordinates in the Euclidean plane:* a special case of barycentric coordinates for a triangle, in which case it is known as a ternary plot or areal coordinates, among other names,* trilinear coordinates, in which...
  
  
• Trilinear coordinates
  Trilinear coordinates
  In geometry, the trilinear coordinates of a point relative to a given triangle describe the relative distances from the three sides of the triangle. Trilinear coordinates are an example of homogeneous coordinates...
  
  
• Trisected perimeter point
  Trisected perimeter point
  In geometry, given a triangle ABC, there exist unique points A´, B´, and C´ on the sides BC, CA, AB respectively, such that:* A´, B´, and C´ partition the perimeter of the triangle into three equal-length pieces...
  
   
• Viviani's theorem
  Viviani's theorem
  Viviani's theorem, named after Vincenzo Viviani, states that the sum of the distances from a point to the sides of an equilateral triangle equals the length of the triangle's altitude....
  
   
• Wernau points 

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Trigonometry

• Law of cosines
  Law of cosines
  In trigonometry, the law of cosines relates the lengths of the sides of a plane triangle to the cosine of one of its angles. Using notation as in Fig...
  
   
• Law of sines
  Law of sines
  In trigonometry, the law of sines is an equation relating the lengths of the sides of an arbitrary triangle to the sines of its angles...
  
   
• Law of tangents
  Law of tangents
  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 opposite sides....
  
   
• Mollweide's formula
  Mollweide's formula
  In trigonometry, Mollweide's formula, sometimes referred to in older texts as Mollweide's equations, named after Karl Mollweide, is a set of two relationships between sides and angles in a triangle...
  
   
• Rational trigonometry
  Rational trigonometry
  Rational trigonometry is a recently introduced approach to trigonometry that eschews all transcendental functions and all proportional measurements of angles. In place of angles, it characterizes the separation between lines by a quantity called the "spread", which is a rational function of their...
  
   
• Solution of triangles
  Solution of triangles
  In trigonometry, to solve a triangle is to find the three angles and the lengths of the three sides of the triangle when given some, but not all of that information...
  
   
• Spherical trigonometry
  Spherical trigonometry
  Spherical trigonometry is a branch of spherical geometry which deals with polygons on the sphere and the relationships between the sides and the angles...
  
   
• Trigonometric functions 
• Trigonometry
  Trigonometry
  Trigonometry is a branch of mathematics that studies triangles and the relationships between their sides and the angles between these sides. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves...
  
   

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Triangular arrays of numbers

• Bell numbers
• Boustrophedon transform
  Boustrophedon transform
  In mathematics, the boustrophedon transform is a procedure which maps one sequence to another. The transformed sequence is computed by filling a triangular array in boustrophedon manner.-Definition:...
  
  
• Eulerian number
  Eulerian number
  In combinatorics the Eulerian number A, is the number of permutations of the numbers 1 to n in which exactly m elements are greater than the previous element...
  
  
• Floyd's triangle
  Floyd's triangle
  Floyd's triangle is a right-angled triangular array of natural numbers, used in computer science education. It is named after Robert Floyd. It is defined by filling the rows of the triangle with consecutive numbers, starting with a 1 in the top left corner:1...
  
  
• Lozanić's triangle
  Lozanic's triangle
  Lozanić's triangle is a triangular array of binomial coefficients in a manner very similar to that of Pascal's triangle...
  
  
• Narayana number
  Narayana number
  In combinatorics, the Narayana numbers N, n = 1, 2, 3 ..., 1 ≤ k ≤ n, form a triangular array of natural numbers, called Narayana triangle, that occur in various counting problems. They are named for T.V...
  
  
• Pascal's triangle
  Pascal's triangle
  In mathematics, Pascal's triangle is a triangular array of the binomial coefficients in a triangle. It is named after the French mathematician, Blaise Pascal...
  
  
• Rencontres numbers
• Romberg's method
  Romberg's method
  In numerical analysis, Romberg's method is used to estimate the definite integral \int_a^b f \, dx by applying Richardson extrapolation repeatedly on the trapezium rule or the rectangle rule . The estimates generate a triangular array...
  
  
• Stirling numbers of the first kind
  Stirling numbers of the first kind
  In mathematics, Stirling numbers of the first kind, together with the Stirling numbers of the second kind, are the two types of Stirling numbers. They commonly occur in combinatorics, where they appear in the study of permutations. The Stirling numbers of the first and second kind can be...
  
  
• Stirling numbers of the second kind

The (incomplete) Bell polynomials from a triangular array of polynomials (see also Polynomial sequence

Polynomial sequence

In mathematics, a polynomial sequence is a sequence of polynomials indexed by the nonnegative integers 0, 1, 2, 3, ..., in which each index is equal to the degree of the corresponding polynomial...

).

Integers in geometry

• Heronian triangle
  Heronian triangle
  In geometry, a Heronian triangle is a triangle whose sidelengths and area are all rational numbers. It is named after Hero of Alexandria. Any such rational triangle can be scaled up to a corresponding triangle with integer sides and area, and often the term Heronian triangle is used to refer to...
  
  
• Integer triangle
  Integer triangle
  An integer triangle or integral triangle is a triangle all of whose sides have lengths that are integers. A rational triangle can be defined as one having all sides with rational length; any such rational triangle can be integrally rescaled to obtain an integer triangle, so...
  
  
• Pythagorean triple
  Pythagorean triple
  A Pythagorean triple consists of three positive integers a, b, and c, such that . Such a triple is commonly written , and a well-known example is . If is a Pythagorean triple, then so is for any positive integer k. A primitive Pythagorean triple is one in which a, b and c are pairwise coprime...
  
  
• Triangular number
  Triangular number
  A triangular number or triangle number numbers the objects that can form an equilateral triangle, as in the diagram on the right. The nth triangle number is the number of dots in a triangle with n dots on a side; it is the sum of the n natural numbers from 1 to n...
  
  

Geography

• Bermuda Triangle
  Bermuda Triangle
  The Bermuda Triangle, also known as the Devil's Triangle, is a region in the western part of the North Atlantic Ocean where a number of aircraft and surface vessels allegedly disappeared under mysterious circumstances....
  
  
• Sunni Triangle
• Historic Triangle
  Historic Triangle
  The Historic Triangle is located on the Virginia Peninsula of the United States and includes the colonial communities of Jamestown, Colonial Williamsburg, and Yorktown, with many restored attractions linked by the Colonial Parkway in James City and York counties and the City of...
  
  
• Parliamentary Triangle, Canberra
  Parliamentary Triangle, Canberra
  The Parliamentary Triangle is the ceremonial precinct of Canberra, containing some of Australia's most significant buildings. The triangle is formed by Commonwealth, Kings and Constitution avenues...
  
  
• Research Triangle

Anatomy

• Submandibular triangle
• Triangle choke
  Triangle choke
  A triangle choke, or sankaku-jime in Judo, is a type of figure-four chokehold which strangles the opponent by encircling the opponent's neck and one arm with the legs in a configuration similar to the shape of a triangle...
  
  
• Arm triangle choke
  Arm triangle choke
  Arm triangle choke, side choke, or head and arm choke are generic terms describing blood chokeholds in which the opponent is strangled in between his or her own shoulder and the practitioner's arm. This is as opposed to the regular triangle choke, which denotes a chokehold using the legs, albeit...
  
  
• Submental triangle
• Carotid triangle