In classical differential geometry, Clairaut's relation, named after Alexis Claude de Clairaut, is a formula that characterizes the great circle paths...

In mathematics, the differential geometry of surfaces deals with the differential geometry of smooth surfaces with various additional structures, most...

credited with Clairaut's equation and Clairaut's relation. Clairaut was born in Paris, France, to Jean-Baptiste and Catherine Petit Clairaut. The couple...

Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It...

Clairaut's formula may refer to: Clairaut's equation (mathematical analysis) Clairaut's relation (differential geometry) Clairaut's theorem (calculus)...

of quantities, which is how they enter differential equations. Specific mathematical fields include geometry and analytical mechanics. Scientific fields...

given by Schwarz's theorem, also called Clairaut's theorem or Young's theorem. In the context of partial differential equations, it is called the Schwarz...

list presents differential equations that have received specific names, area by area. Ablowitz-Kaup-Newell-Segur (AKNS) system Clairaut's equation Hypergeometric...

Foundations of geometry is the study of geometries as axiomatic systems. There are several sets of axioms which give rise to Euclidean geometry or to non-Euclidean...

Differential equations are prominent in many scientific areas. Nonlinear ones are of particular interest for their commonality in describing real-world...

phenomena. Hamiltonian mechanics has a close relationship with geometry (notably, symplectic geometry and Poisson structures) and serves as a link between classical...

particle system in 3 dimensions, there are 3N second order ordinary differential equations in the positions of the particles to solve for. Instead of...

latitude, β, using R = a cos ⁡ β , {\displaystyle R=a\cos \beta ,} and Clairaut's relation then becomes sin ⁡ α 1 cos ⁡ β 1 = sin ⁡ α 2 cos ⁡ β 2 . {\displaystyle...

displaying wikidata descriptions as a fallback Clairaut's relation – Formula in classical differential geometryPages displaying short descriptions of redirect...

geodesics on a surface of revolution. Other geodesics are governed by Clairaut's relation. A surface of revolution with a hole in, where the axis of revolution...

or a star system—a mathematical model is developed in the form of a differential equation. The model can be solved numerically or analytically to determine...

important variational problem in Riemannian geometry. However as a computational tool, the partial differential equations are notoriously complicated to...

closer than fifty paces to the reservoir. Vanity of vanities! Vanity of geometry! However, the disappointment was almost surely unwarranted from a technical...

procedure for the action principle of a gauge theory using the differential geometry of the gauge bundle on which the field theory lives. One then quantizes...

justified in concluding that they are not accelerating. Acceleration (differential geometry) Four-vector: making the connection between space and time explicit...

Katsumi Nomizu (2001). Geometry of Differential Forms. American Mathematical Society Bookstore. p. 12. ISBN 0-8218-1045-6. geometry axiom coordinate system...

development of analysis by Weierstrass and others, the reformulation of geometry in terms of analysis, and the invention of set theory by Cantor, eventually...

Laplace's five-volume Traité de mécanique céleste (1798–1825) forsook geometry and developed mechanics purely through algebraic expressions, while resolving...

(combinations of translations and rotations). Angular velocity Axes conventions Differential rotation Rigid body dynamics Infinitesimal rotations Euler's equations...

dynamics of a system is known, the equations are the solutions for the differential equations describing the motion of the dynamics. There are two main descriptions...

Karasëv, Mikhail V.; Maslov, Victor P. (1993). Nonlinear Poisson brackets, Geometry and Quantization. Translations of Mathematical Monographs. Vol. 119. Translated...

section). A conservative force can be expressed in the language of differential geometry as a closed form. As Euclidean space is contractible, its de Rham...

made by W. K. Clifford and Albert Einstein. The development used differential geometry to describe a curved universe with gravity; the study is called...

to move. Kinematics, as a field of study, is often referred to as the "geometry of motion" and is occasionally seen as a branch of mathematics. Dynamics...

stream, current or flood". Aquaculture – Farming of aquatic organisms Clairaut's theorem – Theorem about gravityPages displaying short descriptions of...