Wave surface

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In mathematics, Fresnel's wave surface, found by Augustin-Jean Fresnel in 1822, is a quartic surface describing the propagation of light in an optically biaxial crystal. Wave surfaces are special cases of tetrahedroids which are in turn special cases of Kummer surfaces.

Augustin-Jean Fresnel French civil engineer and optical physicist

Augustin-Jean Fresnel was a French civil engineer and physicist whose research in optics led to the almost unanimous acceptance of the wave theory of light, excluding any remnant of Newton's corpuscular theory, from the late 1830s  until the end of the 19th century. He is perhaps better known for inventing the catadioptric (reflective/refractive) Fresnel lens and for pioneering the use of "stepped" lenses to extend the visibility of lighthouses, saving countless lives at sea. The simpler dioptric stepped lens, first proposed by Count Buffon  and independently reinvented by Fresnel, is used in screen magnifiers and in condenser lenses for overhead projectors.

In mathematics, especially in algebraic geometry, a quartic surface is a surface defined by an equation of degree 4.

In algebraic geometry, a tetrahedroid is a special kind of Kummer surface studied by Cayley (1846), with the property that the intersections with the faces of a fixed tetrahedron are given by two conics intersecting in four nodes. Tetrahedroids generalize Fresnel's wave surface.

In projective coordinates (w:x:y:z) the wave surface is given by

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Fermats principle Principle of least time in physics

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Siméon Denis Poisson French mathematician, mechanician and physicist

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Quartic function Polynomial function of degree four

In algebra, a quartic function is a function of the form

Kummer surface irreducible nodal surface

In algebraic geometry, a Kummer quartic surface, first studied by Kummer (1864), is an irreducible nodal surface of degree 4 in with the maximal possible number of 16 double points. Any such surface is the Kummer variety of the Jacobian variety of a smooth hyperelliptic curve of genus 2; i.e. a quotient of the Jacobian by the Kummer involution x ↦ −x. The Kummer involution has 16 fixed points: the 16 2-torsion point of the Jacobian, and they are the 16 singular points of the quartic surface. Resolving the 16 double points of the quotient of a torus by the Kummer involution gives a K3 surface with 16 disjoint rational curves; these K3 surfaces are also sometimes called Kummer surfaces.

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Desmic system

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Digital object identifier Character string used as a permanent identifier for a digital object, in a format controlled by the International DOI Foundation

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Arthur Cayley English mathematician

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