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Cosa (chi) è quartic$66083$ - definizione
Lamé's Special Quartic; Lame's special quartic; Lame special quartic; Lamé special quartic; Lame's Special Quartic
Klein quartic
![The tiling of the quartic by reflection domains is a quotient of the [[3-7 kisrhombille]].](https://commons.wikimedia.org/wiki/Special:FilePath/3-7 kisrhombille.svg?width=200 "The tiling of the quartic by reflection domains is a quotient of the [[3-7 kisrhombille]].")
![Dually, the Klein quartic is a quotient of the dual tiling, the [[order-3 heptagonal tiling]].](https://commons.wikimedia.org/wiki/Special:FilePath/Heptagonal tiling.svg?width=200 "Dually, the Klein quartic is a quotient of the dual tiling, the [[order-3 heptagonal tiling]].")
![An animation by [[Greg Egan]] showing an embedding of Klein’s Quartic Curve in three dimensions, starting in a form that has the symmetries of a tetrahedron, and turning inside out to demonstrate a further symmetry.](https://commons.wikimedia.org/wiki/Special:FilePath/KleinDualInsideOutDivided.gif?width=200 "An animation by [[Greg Egan]] showing an embedding of Klein’s Quartic Curve in three dimensions, starting in a form that has the symmetries of a tetrahedron, and turning inside out to demonstrate a further symmetry.")
![The eight functions corresponding to the first positive eigenvalue of the Klein quartic. The functions are zero along the light blue lines. These plots were produced in [[FreeFEM++]].](https://commons.wikimedia.org/wiki/Special:FilePath/Kleineigenspace.png?width=200 "The eight functions corresponding to the first positive eigenvalue of the Klein quartic. The functions are zero along the light blue lines. These plots were produced in [[FreeFEM++]].")
![The [[small cubicuboctahedron]] is a polyhedral immersion of the tiling of the Klein quartic with octahedral symmetry.](https://commons.wikimedia.org/wiki/Special:FilePath/Small cubicuboctahedron.png?width=200 "The [[small cubicuboctahedron]] is a polyhedral immersion of the tiling of the Klein quartic with octahedral symmetry.")
![''The Eightfold Way'' – sculpture by [[Helaman Ferguson]] and accompanying book.](https://commons.wikimedia.org/wiki/Special:FilePath/The Eightfold Way - Silvio Levy - cover.jpg?width=200 "''The Eightfold Way'' – sculpture by [[Helaman Ferguson]] and accompanying book.")
COMPACT RIEMANN SURFACE OF GENUS 3
Klein Quartic; Klein's quartic curve; Klein curve
In hyperbolic geometry, the Klein quartic, named after Felix Klein, is a compact Riemann surface of genus with the highest possible order automorphism group for this genus, namely order orientation-preserving automorphisms, and automorphisms if orientation may be reversed. As such, the Klein quartic is the Hurwitz surface of lowest possible genus; see Hurwitz's automorphisms theorem.
Igusa quartic
In algebraic geometry, the Igusa quartic (also called the Castelnuovo–Richmond quartic CR4 or the Castelnuovo–Richmond–Igusa quartic) is a quartic hypersurface in 4-dimensional projective space, studied by .
Quartic reciprocity
COLLECTION OF THEOREMS IN ELEMENTARY AND ALGEBRAIC NUMBER THEORY THAT STATE CONDITIONS UNDER WHICH THE CONGRUENCE X⁴ ≡ P (MOD Q) IS SOLVABLE
Biquadratic reciprocity; Biquadratic Reciprocity Theorem
Quartic or biquadratic reciprocity is a collection of theorems in elementary and algebraic number theory that state conditions under which the congruence x4 ≡ p (mod q) is solvable; the word "reciprocity" comes from the form of some of these theorems, in that they relate the solvability of the congruence x4 ≡ p (mod q) to that of x4 ≡ q (mod p).
Wikipedia
Lamé's special quartic
Lamé's special quartic, named after Gabriel Lamé, is the graph of the equation
where . It looks like a rounded square with "sides" of length and centered on the origin. This curve is a squircle centered on the origin, and it is a special case of a superellipse.
Because of Pierre de Fermat's only surviving proof, that of the n = 4 case of Fermat's Last Theorem, if r is rational there is no non-trivial rational point (x, y) on this curve (that is, no point for which both x and y are non-zero rational numbers).
