Fermat's principle, also known as the principle of least time, is the link between ray optics and wave optics. Fermat's principle states that the path...

which he used to prove Fermat's right triangle theorem which includes as a corollary Fermat's Last Theorem for the case n = 4. Fermat developed the two-square...

1}={\frac {n_{2}}{n_{1}}}={\frac {v_{1}}{v_{2}}}} The law follows from Fermat's principle of least time, which in turn follows from the propagation of light...

Such solutions are known as geodesics. A related problem is posed by Fermat's principle: light follows the path of shortest optical length connecting two...

optico-mechanical analogy is closely related to Fermat's principle and thus to the Huygens–Fresnel principle. Fermat's principle states that the rays between wavefronts...

mathematician Pierre de Fermat engendered many theorems. Fermat's theorem may refer to one of the following theorems: Fermat's Last Theorem, about integer...

Fermat's Last Theorem is a popular science book (1997) by Simon Singh. It tells the story of the search for a proof of Fermat's Last Theorem, first conjectured...

progress is made, until a presentation of Fermat's Principle of Least Time is given. Gary explains the principle to Louise, giving the example of the refraction...

Knife-edge effect Fermat's principle Fourier optics Surface equivalence principle Wave field synthesis Kirchhoff integral theorem "Huygens' Principle". MathPages...

principle can be applied to optics. In 3D euclidean space the generalized coordinates are now the coordinates of euclidean space. Fermat's principle states...

are identical, and the variational principles become equivalent to Fermat's principle of least time:: 360  δ ( t 2 − t 1 ) = 0. {\displaystyle \delta (t_{2}-t_{1})=0...

a principle of least action, as a way of adapting Fermat's principle for waves to a corpuscular (particle) theory of light.: 96  Pierre de Fermat had...

pseudo-Riemannian manifold. Besides the geodesics principle in a classical field theory there exists Fermat's principle for stationary gravity fields. In case of...

threefold Fermat quotient Fermat's difference quotient Fermat's factorization method Fermat's Last Theorem Fermat's little theorem Fermat's method Fermat's method...

this reason this version of the theorem is sometimes called Fermat's Christmas theorem. Fermat's theorem on sums of two squares is strongly related with the...

design. Systems theory Principle of least action Principle of least interest Fermat's principle (of least time) Pareto principle The Long Tail Parsimony...

is based on a variational principle: light travels from one point in space to another in the shortest time. Fermat's principle In geometric optics laws...

propagation Fermat's principle in geometrical optics Hamilton's principle in classical mechanics Maupertuis' principle in classical mechanics The principle of...

the cycloid AMB in less time than any other curve ACB. According to Fermat’s principle, the actual path between two points taken by a beam of light (which...

interference and diffraction of light as it propagates. According to Fermat's principle, light rays can be characterized as those curves that optimize the...

the path integral formulation cleanly reproduces Hamilton's principle, and Fermat's principle in optics. In Lagrangian mechanics, the generalized coordinates...

variations Catenoid Cycloid Dirichlet principle Euler–Lagrange equation cf. Action (physics) Fermat's principle Functional (mathematics) Functional derivative...

change, the interference between the two waves can be calculated. Fermat's principle states that the path light takes between two points is the path that...

personal experience. He also stated the principle of least time for refraction which would later become Fermat's principle. He made major contributions to catoptrics...

mechanical principle of least action with Fermat's optical principle: "Fermat's principle applied to phase waves is identical to Maupertuis' principle applied...

A slightly more rigorous definition of a light ray follows from Fermat's principle, which states that the path taken between two points by a ray of light...

spheroid, because Huygens's construction leads to Fermat's principle, which becomes Maupertuis's principle if the ray speed is replaced by the reciprocal...

points on a ray (such as the point of entry and exit from the lens), Fermat's principle asserts that the path that the ray takes between them is that which...

method by Fermat's own example, consider the problem of finding the maximum of p ( x ) = b x − x 2 {\displaystyle p(x)=bx-x^{2}} (In Fermat's words, it...

material. The laws of reflection and refraction can be derived from Fermat's principle which states that the path taken between two points by a ray of light...