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Descartes' theorem generalizes to mutually tangent great or small circles in spherical geometry if the curvature of the th circle is defined as = , the geodesic curvature of the circle relative to the sphere, which equals the cotangent of the oriented intrinsic radius.
Learn how to count the roots of a polynomial by examining sign changes in its coefficients. See the proof, examples, generalizations and applications of this mathematical theorem by René Descartes.
Learn about the history, definition and properties of the Cartesian coordinate system, a geometric tool that specifies each point in a plane or space by a pair of real numbers. See examples, equations and applications of Cartesian coordinates in geometry, algebra, calculus and more.
Amicable numbers are pairs of natural numbers whose sum of proper divisors is equal to each other. Learn about their history, formula, properties, and examples from this comprehensive article.
René Descartes (/ d eɪ ˈ k ɑːr t / day-KART or UK: / ˈ d eɪ k ɑːr t / 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.
The folium of Descartes is an algebraic curve named after René Descartes, who challenged Pierre de Fermat to find its tangent line. Learn about its history, properties, graphing methods, and relation to the trisectrix of Maclaurin.
Learn the definition, examples, and properties of the Cartesian product of sets, a fundamental concept in set theory and mathematics. The Cartesian product of two sets A and B is the set of all ordered pairs (a, b) where a is in A and b is in B.
A comprehensive list of notable theorems from various fields of mathematics, physics, economics and other applied sciences. The list is organized alphabetically by theorems' names and includes links to their statements and proofs.