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In Euclidean plane geometry, a **quadrilateral** is a polygon with four edges (sides) and four vertices (corners). Sometimes, the term **quadrangle** is used, by analogy with triangle, and sometimes **tetragon** for consistency with pentagon (5-sided) and hexagon (6-sided), or **4-gon** for consistency with *k*-gons for arbitrary values of *k*.

**Christian Felix Klein** was a German mathematician and mathematics educator, known for his work with group theory, complex analysis, non-Euclidean geometry, and on the associations between geometry and group theory. His 1872 Erlangen program, classifying geometries by their basic symmetry groups, was an influential synthesis of much of the mathematics of the time.

In Euclidean plane geometry, a **rectangle** is a quadrilateral with four right angles. It can also be defined as an equiangular quadrilateral, since equiangular means that all of its angles are equal. It can also be defined as a parallelogram containing a right angle. A rectangle with four sides of equal length is a square. The term **oblong** is occasionally used to refer to a non-square rectangle. A rectangle with vertices *ABCD* would be denoted as *ABCD*.

In geometry, an **equilateral triangle** is a triangle in which all three sides are equal. In the familiar Euclidean geometry, an equilateral triangle is also equiangular; that is, all three internal angles are also congruent to each other and are each 60°. It is also a regular polygon, so it is also referred to as a **regular triangle**.

**Harold Scott MacDonald** "**Donald**" **Coxeter**, was a British-born Canadian geometer. Coxeter is regarded as one of the greatest geometers of the 20th century. He was born in London, received his BA (1929) and PhD (1931) from Cambridge, but lived in Canada from age 29. He was always called Donald, from his third name MacDonald. He was most noted for his work on regular polytopes and higher-dimensional geometries. He was a champion of the classical approach to geometry, in a period when the tendency was to approach geometry more and more via algebra.

In geometry, the **incenter** of a triangle is a triangle center, a point defined for any triangle in a way that is independent of the triangle's placement or scale. The incenter may be equivalently defined as the point where the internal angle bisectors of the triangle cross, as the point equidistant from the triangle's sides, as the junction point of the medial axis and innermost point of the grassfire transform of the triangle, and as the center point of the inscribed circle of the triangle.

In mathematics, **transformation geometry** is the name of a mathematical and pedagogic take on the study of geometry by focusing on groups of geometric transformations, and properties that are invariant under them. It is opposed to the classical synthetic geometry approach of Euclidean geometry, that focuses on proving theorems.

* 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

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 collaboratively 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.

In geometry, **Euler's theorem** states that the distance *d* between the circumcentre and incentre of a triangle is given by

**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.

The **Steiner–Lehmus theorem**, a theorem in elementary geometry, was formulated by C. L. Lehmus and subsequently proved by Jakob Steiner. It states:

**Geometry** is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. A mathematician who works in the field of geometry is called a geometer.

In geometry, two or more objects are said to be **concentric**, **coaxal**, or **coaxial** when they share the same center or axis. Circles, regular polygons and regular polyhedra, and spheres may be concentric to one another, as may cylinders.

**Joram Lindenstrauss** was an Israeli mathematician working in functional analysis. He was a professor of mathematics at the Einstein Institute of Mathematics, Hebrew University of Jerusalem, Israel.

**Károly Bezdek** is a Hungarian-Canadian mathematician. He is a professor as well as a Canada Research Chair of mathematics and the director of the Centre for Computational and Discrete Geometry at the University of Calgary in Calgary, Alberta, Canada. Also he is a professor of mathematics at the University of Pannonia in Veszprém, Hungary. His main research interests are in geometry in particular, in combinatorial, computational, convex, and discrete geometry. He has authored 3 books and more than 120 research papers. He is a founding Editor-in-Chief of the e-journal Contributions to Discrete Mathematics (CDM).

In Euclidean geometry, **Kosnita's theorem** is a property of certain circles associated with an arbitrary triangle.

**Wilhelm Ferdinand Fuhrmann** was a German mathematician. The Fuhrmann circle and the Fuhrmann triangle are named after him.

The * International Journal of Geometry* is a peer-reviewed academic journal that covers Euclidean, Non-Euclidean and Discrete geometry.

- ↑ Kimberling, Clark (2003),
*Geometry in Action: A Discovery Approach Using the Geometer's Sketchpad*, Springer, p. 111, ISBN 9781931914024 . - ↑ "Journal Information for "Forum Geometricorum. A Journal on Classical Euclidean Geometry and Related Areas"",
*MathSciNet*, American Mathematical Society, retrieved 2015-08-26. - ↑
*zbMath - Forum Geometricorum - A Journal on Classical Euclidean Geometry and Related Areas*, European Mathematical Society , retrieved 2020-05-28.

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