Felix Christian Klein was a German mathematician and mathematics educator, known for his work in group theory, complex analysis, non-Euclidean geometry, and the associations between geometry and group theory. His 1872 Erlangen program classified geometries by their basic symmetry groups and was an influential synthesis of much of the mathematics of the time.
In the geometry of triangles, the incircle and nine-point circle of a triangle are internally tangent to each other at the Feuerbach point of the triangle. The Feuerbach point is a triangle center, meaning that its definition does not depend on the placement and scale of the triangle. It is listed as X(11) in Clark Kimberling's Encyclopedia of Triangle Centers, and is named after Karl Wilhelm Feuerbach.
Mathematical Reviews is a journal published by the American Mathematical Society (AMS) that contains brief synopses, and in some cases evaluations, of many articles in mathematics, statistics, and theoretical computer science. The AMS also publishes an associated online bibliographic database called MathSciNet, which contains an electronic version of Mathematical Reviews.
In geometry, the Schiffler point of a triangle is a triangle center, a point defined from the triangle that is equivariant under Euclidean transformations of the triangle. This point was first defined and investigated by Schiffler et al. (1985).
MathSciNet is a searchable online bibliographic database created by the American Mathematical Society in 1996. It contains all of the contents of the journal Mathematical Reviews (MR) since 1940 along with an extensive author database, links to other MR entries, citations, full journal entries, and links to original articles. It contains almost 3.6 million items and over 2.3 million links to original articles.
In geometry, the Japanese theorem states that no matter how one triangulates a cyclic polygon, the sum of inradii of triangles is constant.
The Mathematics Subject Classification (MSC) is an alphanumerical classification scheme that has collaboratively been produced by staff of, and based on the coverage of, the two major mathematical reviewing databases, Mathematical Reviews and Zentralblatt MATH. The MSC is used by many mathematics journals, which ask authors of research papers and expository articles to list subject codes from the Mathematics Subject Classification in their papers. The current version is MSC2020.
The Mathematical Intelligencer is a mathematical journal published by Springer Science+Business Media that aims at a conversational and scholarly tone, rather than the technical and specialist tone more common among academic journals. Volumes are released quarterly with a subset of open access articles. Some articles have been cross-published in the Scientific American. Karen Parshall and Sergei Tabachnikov are currently the co-editors-in-chief.
In geometry, Euler's theorem states that the distance d between the circumcenter and incenter of a triangle is given by or equivalently where and denote the circumradius and inradius respectively. The theorem is named for Leonhard Euler, who published it in 1765. However, the same result was published earlier by William Chapple in 1746.
In mathematics, convex geometry is the branch of geometry studying convex sets, mainly in Euclidean space. Convex sets occur naturally in many areas: computational geometry, convex analysis, discrete geometry, functional analysis, geometry of numbers, integral geometry, linear programming, probability theory, game theory, etc.
In geometry, the nine-point center is a triangle center, a point defined from a given triangle in a way that does not depend on the placement or scale of the triangle. It is so called because it is the center of the nine-point circle, a circle that passes through nine significant points of the triangle: the midpoints of the three edges, the feet of the three altitudes, and the points halfway between the orthocenter and each of the three vertices. The nine-point center is listed as point X(5) in Clark Kimberling's Encyclopedia of Triangle Centers.
Geoffrey Charles Smith, MBE is a British mathematician. He is Senior Lecturer in Mathematics at the University of Bath and current professor in residence at Wells Cathedral School.
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. The result is named after June Lester, who published it in 1997, and the circle through these points was called the Lester circle by Clark Kimberling. Lester proved the result by using the properties of complex numbers; subsequent authors have given elementary proofs, proofs using vector arithmetic, and computerized proofs. The center of the Lester circle is also a triangle center. It is the center designated as X(1116) in the Encyclopedia of Triangle Centers. Recently, Peter Moses discovered 21 other triangle centers lie on the Lester circle. The points are numbered X(15535) – X(15555) in the Encyclopedia of Triangle Centers.
The Steiner–Lehmus theorem, a theorem in elementary geometry, was formulated by C. L. Lehmus and subsequently proved by Jakob Steiner. It states:
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 was identified in 1836 by Christian Heinrich von Nagel as the symmedian point of the excentral triangle of the given triangle.
The Journal of Differential Geometry is a peer-reviewed scientific journal of mathematics published by International Press on behalf of Lehigh University in 3 volumes of 3 issues each per year. The journal publishes an annual supplement in book form called Surveys in Differential Geometry. It covers differential geometry and related subjects such as differential equations, mathematical physics, algebraic geometry, and geometric topology. The editor-in-chief is Shing-Tung Yau of Harvard University.
In Euclidean geometry, Kosnita's theorem is a property of certain circles associated with an arbitrary triangle.
In Euclidean plane geometry, the van Lamoen circle is a special circle associated with any given triangle . It contains the circumcenters of the six triangles that are defined inside by its three medians.
The International Journal of Geometry is a peer-reviewed academic journal that covers Euclidean, Non-Euclidean and Discrete 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 quarter of the nineteenth century. Triangles and their properties were the subject of investigation since at least the time of Euclid. In fact, Euclid's Elements contains description of the four special points – centroid, incenter, circumcenter and orthocenter - associated with a triangle. Even though Pascal and Ceva in the seventeenth century, Euler in the eighteenth century and Feuerbach in the nineteenth century and many other mathematicians had made important discoveries regarding the properties of the triangle, it was the publication in 1873 of a paper by Emile Lemoine (1840–1912) with the title "On a remarkable point of the triangle" that was considered to have, according to Nathan Altschiller-Court, "laid the foundations...of the modern geometry of the triangle as a whole." The American Mathematical Monthly, in which much of Lemoine's work is published, declared that "To none of these [geometers] more than Émile-Michel-Hyacinthe Lemoine is due the honor of starting this movement of modern triangle geometry". The publication of this paper caused a remarkable upsurge of interest in investigating the properties of the triangle during the last quarter of the nineteenth century and the early years of the twentieth century. A hundred-page article on triangle geometry in Klein's Encyclopedia of Mathematical Sciences published in 1914 bears witness to this upsurge of interest in triangle geometry.
