# Category: Triangle geometry

Modern triangle geometry
In mathematics, modern triangle geometry, or new triangle geometry, is the body of knowledge relating to the properties of a triangle discovered and developed roughly since the beginning of the last q
Kiepert conics
In triangle geometry, the Kiepert conics are two special conics associated with the reference triangle. One of them is a hyperbola, called the Kiepert hyperbola and the other is a parabola, called the
Circumcevian triangle
In triangle geometry, a circumcevian triangle is a special triangle associated with the reference triangle and a point in the plane of the triangle. It is also associated with the circumcircle of the
Congruent number
In number theory, a congruent number is a positive integer that is the area of a right triangle with three rational number sides. A more general definition includes all positive rational numbers with
Mass point geometry
Mass point geometry, colloquially known as mass points, is a geometry problem-solving technique which applies the physical principle of the center of mass to geometry problems involving triangles and
Orthologic triangles
In geometry, two triangles are said to be orthologic triangles if the perpendiculars from the vertices of one of them to the corresponding sides of the other are concurrent. This is a symmetric proper
Hart circle
The Hart circle is externally tangent to and internally tangent to incircles of the associated triangles ,,, or the other way around. The Hart circle was discovered by Andrew Searle Hart. There are ei
Orthocentric system
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. If four points form an orthocentric system, then each
List of triangle topics
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 triangula
Triangular coordinates
No description available.
Circumgon
In mathematics and particularly in elementary geometry, a circumgon is a geometric figure which circumscribes some circle, in the sense that it is the union of the outer edges of non-overlapping trian
In triangle geometry, the Bernoulli quadrisection problem asks how to divide a given triangle into four equal-area pieces by two perpendicular lines. Its solution by Jacob Bernoulli was published in 1
Feuerbach hyperbola
In geometry, the Feuerbach hyperbola is a rectangular hyperbola passing through important triangle centers such as the Orthocenter, Gergonne point, Nagel point and Shiffler point. The center of the hy
The Secrets of Triangles
The Secrets of Triangles: A Mathematical Journey is a popular mathematics book on the geometry of triangles. It was written by Alfred S. Posamentier and , and published in 2012 by Prometheus Books.
Neuberg cubic
In mathematics, in triangle geometry, Neuberg cubic is a special cubic plane curve in the plane of the reference triangle having several remarkable properties. It is a triangle cubic in that it is ass
Eisenstein triple
Similar to a Pythagorean triple, an Eisenstein triple (named after Gotthold Eisenstein) is a set of integers which are the lengths of the sides of a triangle where one of the angles is 60 or 120 degre
Semiperimeter
In geometry, the semiperimeter of a polygon is half its perimeter. Although it has such a simple derivation from the perimeter, the semiperimeter appears frequently enough in formulas for triangles an
Trilinear polarity
In geometry, trilinear polarity is a certain correspondence between the points in the plane of a triangle not lying on the sides of the triangle and lines in the plane of the triangle not passing thro
Johnson circles
In geometry, a set of Johnson circles comprises 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 intersectio
Sum of angles of a triangle
In a Euclidean space, the sum of angles of a triangle equals the straight angle (180 degrees, π radians, two right angles, or a half-turn).A triangle has three angles, one at each vertex, bounded by a
Marching triangles
In computer graphics, the problem of transforming a cloud of points on the surface of a three-dimensional object into a polygon mesh for the object can be solved by a technique called marching triangl
Isotomic conjugate
In geometry, the isotomic conjugate of a point P with respect to a triangle ABC is another point, defined in a specific way from P and ABC: If the base points of the lines PA, PB, and PC on the sides
Triangle strip
In computer graphics, a triangle strip is a subset of triangles in a triangle mesh with shared vertices, and is a more memory-efficient method of storing information about the mesh. They are more effi
Soddy line
The Soddy line of a triangle is the line that goes through the centers of the two Soddy circles of that triangle. The Soody line intersects the Euler line in de Longchamps point und the in the Fletche
AA postulate
In Euclidean geometry, the AA postulate states that two triangles are similar if they have two corresponding angles congruent. The AA postulate follows from the fact that the sum of the interior angle
Catalogue of Triangle Cubics
The Catalogue of Triangle Cubics is an online resource containing detailed information about more than 1200 cubic curves in the plane of a reference triangle. The resource is maintained by Bernard Gil
Similarity (geometry)
In Euclidean geometry, two objects are similar if they have the same shape, or one has the same shape as the mirror image of the other. More precisely, one can be obtained from the other by uniformly
Triangle conic
In triangle geometry, a triangle conic is a conic in the plane of the reference triangle and associated with it in some way. For example, the circumcircle and the incircle of the reference triangle ar
Perspective (geometry)
Two figures in a plane are perspective from a point O if the lines joining corresponding points of the figures all meet at O. Dually, the figures are said to be perspective from a line if the points o
Trilinear coordinates
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. Trilinear coordinates are an exa
McCay cubic
In mathematics, in triangle geometry, McCay cubic (also called M'Cay cubic or Griffiths cubic) is a cubic plane curve in the plane of the reference triangle and associated with it, and having several
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 respectively. These three
Central triangle
In geometry, a central triangle is a triangle in the plane of the reference triangle the trilinear coordinates of whose vertices relative to the reference triangle are expressible in a certain cyclica
Ailles rectangle
The Ailles rectangle is a rectangle constructed from four right-angled triangles which is commonly used in geometry classes to find the values of trigonometric functions of 15° and 75°. It is named af
Conway triangle notation
In geometry, the Conway triangle notation, named after John Horton Conway, allows trigonometric functions of a triangle to be managed algebraically. Given a reference triangle whose sides are a, b and
Barycentric coordinate system
In geometry, a barycentric coordinate system is a coordinate system in which the location of a point is specified by reference to a simplex (a triangle for points in a plane, a tetrahedron for points
5-Con triangles
In geometry, two triangles are said to be 5-Con or almost congruent if they are not congruent triangles but they are similar triangles and share two side lengths (of non-corresponding sides). The 5-Co