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In geometry, Descartes' theorem states that for every four kissing, or mutually tangent, circles, the radii of the circles satisfy a certain quadratic equation. By solving this equation, one can construct a fourth circle tangent to three given, mutually tangent circles. The theorem is named after René Descartes, who stated it in 1643.
René Descartes ( / deɪˈkɑːrt / day-KART or UK: / ˈdeɪkɑːrt / DAY-kart; French: [ʁəne dekaʁt] ⓘ; [note 3] [11] 31 March 1596 – 11 February 1650) [12] [13] [14] : 58 was a French philosopher, scientist, and mathematician, widely considered a seminal figure in the emergence of modern philosophy and science. Mathematics was ...
This diagram shows the main line of the Detroit, Lansing and Northern as of November 11, 1896, when it reformed as the Detroit, Grand Rapids and Western, including crossings by other lines as they were then constituted. For clarity, most minor stops omitted.
The folium of Descartes is related to the trisectrix of Maclaurin by affine transformation. To see this, start with the equation. and change variables to find the equation in a coordinate system rotated 45 degrees. This amounts to setting In the plane the equation is. If we stretch the curve in the direction by a factor of this becomes.
In mathematics, a Voronoi diagram is a partition of a plane into regions close to each of a given set of objects. It can be classified also as a tessellation. In the simplest case, these objects are just finitely many points in the plane (called seeds, sites, or generators). For each seed there is a corresponding region, called a Voronoi cell ...
Route diagram templates (RDTs) for lines and services of Amtrak. The pages listed in this category are templates. This page is part of Wikipedia's administration and not part of the encyclopedia. Further template category notes. This contains pages in the . It should not be used to categorize or pages in other . To add a template to this category:
This template takes two basic icon names ("ICON₁" and "ICON₂") to display all variants of a parallel lines compound icon (typically named "vICON₁-ICON₂"), with the following information in a row within a wikitable:
Doubling the cube is the construction, using only a straightedge and compass, of the edge of a cube that has twice the volume of a cube with a given edge. This is impossible because the cube root of 2, though algebraic, cannot be computed from integers by addition, subtraction, multiplication, division, and taking square roots.