• Thumbnail for 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...
    29 KB (3,686 words) - 05:16, 14 February 2025
  • Thumbnail for Émile Lemoine
    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...
    22 KB (2,475 words) - 14:31, 25 August 2024
  • Thumbnail for Equilateral triangle
    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...
    25 KB (2,644 words) - 16:15, 29 May 2025
  • Thumbnail for Triangle
    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...
    55 KB (6,518 words) - 09:58, 5 June 2025
  • Maxwell's theorem (geometry) Medial triangle Median (geometry) Menelaus' theorem Miquel's theorem Mittenpunkt Modern triangle geometry Monsky's theorem...
    11 KB (634 words) - 12:01, 7 February 2025
  • Thumbnail for Altitude (triangle)
    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...
    9 KB (1,371 words) - 05:49, 27 May 2025
  • Thumbnail for Similarity (geometry)
    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...
    28 KB (3,581 words) - 12:34, 16 May 2025
  • Encyclopedia of Triangle Centers (ETC) is an online list of thousands of points or "centers" associated with the geometry of a triangle. This resource...
    6 KB (320 words) - 21:15, 19 May 2025
  • Thumbnail for Henri Brocard
    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...
    13 KB (1,270 words) - 10:29, 28 October 2024
  • Thumbnail for Isosceles triangle
    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...
    38 KB (4,157 words) - 08:26, 28 May 2025
  • Thumbnail for Triangle center
    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...
    32 KB (3,897 words) - 01:14, 27 May 2025
  • Thumbnail for History of geometry
    relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers (arithmetic). Classic geometry was focused...
    48 KB (6,300 words) - 05:58, 29 April 2025
  • issued: Cubic(A, B, C, 2) Modern triangle geometry Bernard Gibert. "Catalogue of Triangle Cubics". Cubics in the Triangle Plane. Bernard Gibert. Retrieved...
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  • Thumbnail for Euclidean geometry
    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...
    59 KB (7,198 words) - 13:24, 17 May 2025
  • non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry. As Euclidean geometry lies at the...
    45 KB (6,066 words) - 03:48, 14 May 2025
  • Thumbnail for Affine geometry
    In mathematics, affine geometry is what remains of Euclidean geometry when ignoring (mathematicians often say "forgetting") the metric notions of distance...
    20 KB (2,632 words) - 10:01, 21 October 2024
  • geometry Altshiller-Court, Nathan (1952), College Geometry: An Introduction to the Modern Geometry of the Triangle and the Circle (2nd ed.), New York: Barnes...
    30 KB (4,386 words) - 23:54, 25 May 2025
  • Absolute geometry Affine geometry Algebraic geometry Analytic geometry Birational geometry Complex geometry Computational geometry Conformal geometry Constructive...
    13 KB (914 words) - 10:26, 25 December 2024
  • Thumbnail for Transversal (geometry)
    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...
    11 KB (1,341 words) - 18:28, 21 April 2025
  • Thumbnail for Hyperbolic geometry
    mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai–Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate...
    56 KB (6,970 words) - 13:36, 7 May 2025
  • Synthetic geometry (sometimes referred to as axiomatic geometry or even pure geometry) is geometry without the use of coordinates. It relies on the axiomatic...
    14 KB (1,737 words) - 00:06, 27 December 2024
  • 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...
    76 KB (10,907 words) - 02:44, 15 June 2024
  • Thumbnail for Parallel postulate
    Parallel postulate (category Elementary geometry)
    , only assumes the modern equivalent of the first four postulates) is known as absolute geometry (or sometimes "neutral geometry"). Probably the best-known...
    26 KB (3,278 words) - 22:43, 19 April 2025
  • Thumbnail for Reuleaux triangle
    are merely rounded triangles, with different geometry than the Reuleaux triangle. Another early application of the Reuleaux triangle, da Vinci's world...
    57 KB (6,500 words) - 06:52, 2 June 2025
  • Geometry (from Ancient Greek γεωμετρία (geōmetría) 'land measurement'; from γῆ (gê) 'earth, land' and μέτρον (métron) 'a measure') is a branch of mathematics...
    102 KB (10,101 words) - 16:23, 8 May 2025
  • Thumbnail for Napoleon's theorem
    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...
    22 KB (2,901 words) - 16:24, 27 May 2025
  • Thumbnail for Pythagorean theorem
    Pythagorean theorem (category Euclidean plane geometry)
    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...
    94 KB (12,692 words) - 05:47, 14 May 2025
  • Thumbnail for Spherical trigonometry
    the branch of spherical geometry that deals with the metrical relationships between the sides and angles of spherical triangles, traditionally expressed...
    41 KB (6,784 words) - 13:26, 6 May 2025
  • Thumbnail for Orthologic triangles
    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...
    2 KB (250 words) - 01:05, 8 February 2025
  • Thumbnail for Angle bisector theorem
    Angle bisector theorem (category Theorems about triangles)
    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...
    13 KB (1,881 words) - 00:28, 22 May 2025