given two triangles
1conjugate triangles — noun plural : two triangles in which the vertices of each are the poles with respect to a given curve of the sides of the other …
2Simson line — In geometry, given a triangle and a point on its circumcircle, the intersections formed when lines are constructed from the point perpendicular to each of the triangle s sides are collinear. The line through these points is the Simson line, named …
3Birkhoff's axioms — In 1932, G. D. Birkhoff created a set of four postulates of Euclidean geometry sometimes referred to as Birkhoff s axioms. These postulates are all based on basic geometry that can be confirmed experimentally with a scale and protractor. Since… …
4Pythagorean theorem — See also: Pythagorean trigonometric identity The Pythagorean theorem: The sum of the areas of the two squares on the legs (a and b) equals the area of the square on the hypotenuse (c) …
5Triangle — This article is about the basic geometric shape. For other uses, see Triangle (disambiguation). Isosceles and Acute Triangle redirect here. For the trapezoid, see Isosceles trapezoid. For The Welcome to Paradox episode, see List of Welcome to… …
6Collision detection — For collision detection on networks see CSMA/CD Collision detection typically refers to the computational problem of detecting the intersection of two or more objects. While the topic is most often associated with its use in video games and other …
7Euclidean geometry — geometry based upon the postulates of Euclid, esp. the postulate that only one line may be drawn through a given point parallel to a given line. [1860 65] * * * Study of points, lines, angles, surfaces, and solids based on Euclid s axioms. Its… …
8Logic and the philosophy of mathematics in the nineteenth century — John Stillwell INTRODUCTION In its history of over two thousand years, mathematics has seldom been disturbed by philosophical disputes. Ever since Plato, who is said to have put the slogan ‘Let no one who is not a geometer enter here’ over the… …
9Euclidean geometry — A Greek mathematician performing a geometric construction with a compass, from The School of Athens by Raphael. Euclidean geometry is a mathematical system attributed to the Alexandrian Greek mathematician Euclid, which he described in his… …
10Triangulated category — A triangulated category is a mathematical category satisfying some axioms that are based on the properties of the homotopy category of spectra, and the derived category of an abelian category. A t category is a triangulated category with a t… …
