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  2. Möbius function - Wikipedia

    en.wikipedia.org/wiki/Möbius_function

    The Möbius function () is a multiplicative function in number theory introduced by the German mathematician August Ferdinand Möbius (also transliterated Moebius) in 1832. [i] [ii] [2] It is ubiquitous in elementary and analytic number theory and most often appears as part of its namesake the Möbius inversion formula.

  3. Möbius inversion formula - Wikipedia

    en.wikipedia.org/wiki/Möbius_inversion_formula

    The classical arithmetic Mobius function is the special case of the poset P of positive integers ordered by divisibility: that is, for positive integers s, t, we define the partial order to mean that s is a divisor of t.

  4. Möbius strip - Wikipedia

    en.wikipedia.org/wiki/Möbius_strip

    Examples of this trope include Martin Gardner ' s "No-Sided Professor" (1946), Armin Joseph Deutsch ' s "A Subway Named Mobius" (1950) and the film Moebius (1996) based on it. An entire world shaped like a Möbius strip is the setting of Arthur C. Clarke 's "The Wall of Darkness" (1946), while conventional Möbius strips are used as clever ...

  5. Möbius transformation - Wikipedia

    en.wikipedia.org/wiki/Möbius_transformation

    Möbius transformations are defined on the extended complex plane ^ = {} (i.e., the complex plane augmented by the point at infinity).. Stereographic projection identifies ^ with a sphere, which is then called the Riemann sphere; alternatively, ^ can be thought of as the complex projective line.

  6. Linear fractional transformation - Wikipedia

    en.wikipedia.org/wiki/Linear_fractional...

    Each model has a group of isometries that is a subgroup of the Mobius group: the isometry group for the disk model is SU(1, 1) where the linear fractional transformations are "special unitary", and for the upper half-plane the isometry group is PSL(2, R), a projective linear group of linear fractional transformations with real entries and ...

  7. Homogeneous coordinates - Wikipedia

    en.wikipedia.org/wiki/Homogeneous_coordinates

    Rational Bézier curve – polynomial curve defined in homogeneous coordinates (blue) and its projection on plane – rational curve (red) In mathematics, homogeneous coordinates or projective coordinates, introduced by August Ferdinand Möbius in his 1827 work Der barycentrische Calcul, [1] [2] [3] are a system of coordinates used in projective geometry, just as Cartesian coordinates are used ...

  8. Möbius ladder - Wikipedia

    en.wikipedia.org/wiki/Möbius_ladder

    In graph theory, the Möbius ladder M n, for even numbers n, is formed from an n-cycle by adding edges (called "rungs") connecting opposite pairs of vertices in the cycle. It is a cubic, circulant graph, so-named because (with the exception of M 6 (the utility graph K 3,3), M n has exactly n/2 four-cycles [1] which link together by their shared edges to form a topological Möbius strip.

  9. Cyclotomic polynomial - Wikipedia

    en.wikipedia.org/wiki/Cyclotomic_polynomial

    In mathematics, the nth cyclotomic polynomial, for any positive integer n, is the unique irreducible polynomial with integer coefficients that is a divisor of and is not a divisor of for any k < n.