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Cartesian coordinate system with a circle of radius 2 centered at the origin marked in red. The equation of a circle is (x − a)2 + (y − b)2 = r2 where a and b are the coordinates of the center (a, b) and r is the radius. Cartesian coordinates are named for René Descartes, whose invention of them in the 17th century revolutionized ...
In mathematics, specifically set theory, the Cartesian product of two sets A and B, denoted A × B, is the set of all ordered pairs (a, b) where a is in A and b is in B. [1] In terms of set-builder notation, that is [2][3] A table can be created by taking the Cartesian product of a set of rows and a set of columns.
Snell's law (also known as the Snell–Descartes law, the ibn-Sahllaw, [ 1 ] and the law of refraction) is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing through a boundary between two different isotropic media, such as water, glass, or air.
René Descartes (/ deɪˈkɑːrt / day-KART or UK: / ˈdeɪkɑːrt / DAY-kart; French: [ʁəne dekaʁt] ⓘ; [ note 3 ][ 11 ] 31 March 1596 – 11 February 1650) [ 12 ][ 13 ]: 58 was a French philosopher, scientist, and mathematician, widely considered a seminal figure in the emergence of modern philosophy and science. Mathematics was paramount ...
Descartes' rule of signs. In mathematics, Descartes' rule of signs, described by René Descartes in his La Géométrie, counts the roots of a polynomial by examining sign changes in its coefficients. The number of positive real roots is at most the number of sign changes in the sequence of polynomial's coefficients (omitting zero coefficients ...
v. t. e. In mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts with synthetic geometry. Analytic geometry is used in physics and engineering, and also in aviation, rocketry, space science, and spaceflight. It is the foundation of most modern ...
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 which is ...
Here, as all three circles are tangent to each other at the same point, Descartes' theorem does not apply. Descartes' theorem is most easily stated in terms of the circles' curvatures . [ 25 ] The signed curvature (or bend ) of a circle is defined as k = ± 1 / r {\displaystyle k=\pm 1/r} , where r {\displaystyle r} is its radius.