In mathematics, modern triangle geometry, or new triangle geometry, is the body of knowledge relating to the properties of a triangle discovered and developed...

expressions to geometric objects. He has been called a co-founder of modern triangle geometry, as many of its characteristics are present in his work. For most...

molecular geometry. An equilateral triangle is a triangle that has three equal sides. It is a special case of an isosceles triangle in the modern definition...

A triangle is a polygon with three corners and three sides, one of the basic shapes in geometry. The corners, also called vertices, are zero-dimensional...

Maxwell's theorem (geometry) Medial triangle Median (geometry) Menelaus' theorem Miquel's theorem Mittenpunkt Modern triangle geometry Monsky's theorem...

In geometry, an altitude of a triangle is a line segment through a given vertex (called apex) and perpendicular to a line containing the side or edge...

A'B'C'\\\triangle ABC&\nsim \triangle A'B'C'\end{aligned}}} There are several elementary results concerning similar triangles in Euclidean geometry: Any two...

Encyclopedia of Triangle Centers (ETC) is an online list of thousands of points or "centers" associated with the geometry of a triangle. This resource...

Lemoine and Joseph Neuberg, was one of the three co-founders of modern triangle geometry. He was awarded the Ordre des Palmes Académiques, and was an officer...

In geometry, an isosceles triangle (/aɪˈsɒsəliːz/) is a triangle that has two sides of equal length and two angles of equal measure. Sometimes it is specified...

In geometry, a triangle center or triangle centre is a point in the triangle's plane that is in some sense in the middle of the triangle. For example...

relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers (arithmetic). Classic geometry was focused...

issued: Cubic(A, B, C, 2) Modern triangle geometry Bernard Gibert. "Catalogue of Triangle Cubics". Cubics in the Triangle Plane. Bernard Gibert. Retrieved...

non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry. As Euclidean geometry lies at the...

In mathematics, affine geometry is what remains of Euclidean geometry when ignoring (mathematicians often say "forgetting") the metric notions of distance...

Absolute geometry Affine geometry Algebraic geometry Analytic geometry Birational geometry Complex geometry Computational geometry Conformal geometry Constructive...

Books I–IV and VI discuss plane geometry. Many results about plane figures are proved, for example, "In any triangle, two angles taken together in any...

geometry Altshiller-Court, Nathan (1952), College Geometry: An Introduction to the Modern Geometry of the Triangle and the Circle (2nd ed.), New York: Barnes...

In geometry, a transversal is a line that passes through two lines in the same plane at two distinct points. Transversals play a role in establishing whether...

, only assumes the modern equivalent of the first four postulates) is known as absolute geometry (or sometimes "neutral geometry"). Probably the best-known...

Synthetic geometry (sometimes referred to as axiomatic geometry or even pure geometry) is geometry without the use of coordinates. It relies on the axiomatic...

mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai–Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate...

are merely rounded triangles, with different geometry than the Reuleaux triangle. Another early application of the Reuleaux triangle, da Vinci's world...

non-Euclidean geometries. These are fundamental to the study and of historical importance, but there are a great many modern geometries that are not Euclidean...

Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side...

In geometry, Napoleon's theorem states that if equilateral triangles are constructed on the sides of any triangle, either all outward or all inward, the...

In Euclidean 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...

In geometry, two triangles are said to be orthologic if the perpendiculars from the vertices of one of them to the corresponding sides of the other are...

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...

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...