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In combinatorics, the twelvefold way is a systematic classification of 12 related enumerative problems concerning two finite sets, which include the classical problems of counting permutations, combinations, multisets, and partitions either of a set or of a number. The idea of the classification is credited to Gian-Carlo Rota, and the name was ...
In particle physics, the quark model is a classification scheme for hadrons in terms of their valence quarks —the quarks and antiquarks that give rise to the quantum numbers of the hadrons. The quark model underlies "flavor SU (3)", or the Eightfold Way, the successful classification scheme organizing the large number of lighter hadrons that ...
Eightfold way (physics) The pseudoscalar meson octet. Particles along the same horizontal line share the same strangeness, s, while those on the same left-leaning diagonals share the same charge, q (given as multiples of the elementary charge ). In physics, the eightfold way is an organizational scheme for a class of subatomic particles known ...
Kawasaki's theorem. In this example, the alternating sum of angles (clockwise from the bottom) is 90° − 45° + 22.5° − 22.5° + 45° − 90° + 22.5° − 22.5° = 0°. Since it adds to zero, the crease pattern may be flat-folded. Kawasaki's theorem or Kawasaki–Justin theorem is a theorem in the mathematics of paper folding that ...
An aperiodic tiling using a single shape and its reflection, discovered by David Smith. An aperiodic tiling is a non-periodic tiling with the additional property that it does not contain arbitrarily large periodic regions or patches. A set of tile-types (or prototiles) is aperiodic if copies of these tiles can form only non- periodic tilings.
Rotational symmetry of order n, also called n-fold rotational symmetry, or discrete rotational symmetry of the nth order, with respect to a particular point (in 2D) or axis (in 3D) means that rotation by an angle of (180°, 120°, 90°, 72°, 60°, 51 ⁄7 °, etc.) does not change the object. A "1-fold" symmetry is no symmetry (all ...
A ring torus with aspect ratio 3, the ratio between the diameters of the larger (magenta) circle and the smaller (red) circle. In geometry, a torus ( pl.: tori or toruses) is a surface of revolution generated by revolving a circle in three-dimensional space one full revolution about an axis that is coplanar with the circle.
Quasicrystal. Potential energy surface for silver depositing on an aluminium – palladium – manganese (Al–Pd–Mn) quasicrystal surface. Similar to Fig. 6 in Ref. [1] A quasiperiodic crystal, or quasicrystal, is a structure that is ordered but not periodic. A quasicrystalline pattern can continuously fill all available space, but it lacks ...