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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, as described by René Descartes in his La Géométrie. See examples, proofs, generalizations and related topics.
Descartes' influence in mathematics is equally apparent, being the namesake of the Cartesian coordinate system. He is credited as the father of analytic geometry—used in the discovery of infinitesimal calculus and analysis. Descartes was also one of the key figures in the Scientific Revolution. Coat of arms of the Descartes family.
Cogito, ergo sum is the Latin phrase meaning "I think, therefore I am", which is the first principle of René Descartes's philosophy. It expresses the idea that the act of doubting one's own existence proves one's own existence as a thinking entity.
Cartesianism is the system of René Descartes and his followers, who emphasized reason and innate ideas over sensory experience. It influenced many thinkers in the 17th and 18th centuries, but also faced criticism and opposition.
Learn about Apollonius' problem, a famous geometric construction that involves finding circles tangent to three given circles. Explore the history, methods, solutions and applications of this problem in Euclidean plane geometry.
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.
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.