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Infinite matrix of integers derived from the Fibonacci sequence
In mathematics, the Wythoff array is an infinite matrix of positive integers derived from the Fibonacci sequence and named after Dutch mathematician Willem
Wythoff_array
Two-player mathematical subtraction game
Subtract a square Wythoff array Wythoff's game at Cut-the-knot, quoting Martin Gardner's book Penrose Tiles to Trapdoor Ciphers Wythoff, W. A. (1907), "A
Wythoff's_game
Dutch mathematician
Wythoff array, a two-dimensional array of numbers related to this game and to the Fibonacci sequence, is also named after him. In geometry, Wythoff is
Willem_Abraham_Wythoff
Numbers obtained by adding the two previous ones
Randomized mathematical sequence based upon the Fibonacci sequence Wythoff array – Infinite matrix of integers derived from the Fibonacci sequence International
Fibonacci_sequence
Integers formed by rounding down the integer multiples of a positive irrational number
sequences define the optimal strategy for Wythoff's game, and are used in the definition of the Wythoff array. As another example, for the square root
Beatty_sequence
Infinite integer series where the next number is the sum of the two preceding it
Fibonacci-like integer sequences appear in shifted form as a row of the Wythoff array; the Fibonacci sequence itself is the first row and the Lucas sequence
Lucas_number
Mathematical sequences
a shift by a finite number of positions) as one of the rows of the Wythoff array. The Fibonacci sequence itself is the first row, and a shift of the
Generalizations of Fibonacci numbers
Generalizations_of_Fibonacci_numbers
Sequence that contains itself as a subsequence
sequence A003603 (Fractal sequence obtained from Fibonacci numbers (or Wythoff array)) OEIS sequence A112382 (Self-descriptive fractal sequence: the sequence
Fractal_sequence
Type of radio antenna
the $500.00 Prize Contest: Who Will Save the Radio Amateur? (1923)", in Wythoff, Grant (ed.), The Perversity of Things, Hugo Gernsback on Media, Tinkering
Cage_aerial
Regular 5-polytope
the row's element. The diagonal f-vector numbers are derived through the Wythoff construction, dividing the full group order of a subgroup order by removing
5-demicube
Covering by shapes without overlaps or gaps
honeycombs in three dimensions. Uniform honeycombs can be constructed using the Wythoff construction. The Schmitt-Conway biprism is a convex polyhedron with the
Tessellation
Polyhedron with 32 faces
± φ , ± 1 φ , ± 2 φ ) ( ± 1 φ 2 , ± 1 φ , ± 2 ) {\displaystyle {\begin{array}{crclc}{\Bigl (}&0,&\pm \,\varphi ,&\pm {\bigl [}2-{\frac {1}{\varphi }}{\bigr
Great stellated truncated dodecahedron
Great_stellated_truncated_dodecahedron
\left\{{\begin{array}{l}3\\4,3\end{array}}\right\}} rr{3,3,4}= r { 3 3 , 4 } {\displaystyle r\left\{{\begin{array}{l}3\\3,4\end{array}}\right\}} r{31
Rectified_24-cell
Uniform polychoron
elements are shown. The diagonal f-vector numbers are derived through the Wythoff construction, dividing the full group order of a subgroup order by removing
Rectified_5-cell
Uniform 6-polytope
the row's element. The diagonal f-vector numbers are derived through the Wythoff construction, dividing the full group order of a subgroup order by removing
6-demicube
Polyhedron with 62 faces
1 , ± 1 φ 3 , ± 1 ) ( ± 1 φ , ± 1 φ 2 , ± 2 φ ) {\displaystyle {\begin{array}{ccclc}{\Bigl (}&\pm \,{\frac {1}{\varphi ^{2}}},&0,&\pm {\bigl [}2-{\frac
Nonconvex great rhombicosidodecahedron
Nonconvex_great_rhombicosidodecahedron
elements are shown. The diagonal f-vector numbers are derived through the Wythoff construction, dividing the full group order of a subgroup order by removing
Truncated_24-cells
Class of 4-dimensional polytopes
constructed in one or more reflective point group in 4 dimensions by a Wythoff construction, represented by rings around permutations of nodes in a Coxeter
Uniform_4-polytope
Geometric operation applied to a polyhedron
Essays, Dover Publications, 1999, ISBN 978-0-486-40919-1 (Chapter 3: Wythoff's Construction for Uniform Polytopes) Norman Johnson Uniform Polytopes,
Snub_(geometry)
Polyhedron with 32 faces
φ , ± 1 φ 3 ) ( ± [ 1 + 1 φ 2 ] , ± 1 , ± 2 φ ) {\displaystyle {\begin{array}{crccc}{\Bigl (}&\pm \,1,&0,&\pm \,{\frac {3}{\varphi }}&{\Bigr )}\\{\Bigl
Truncated_great_icosahedron
Uniform 7-polytope
the row's element. The diagonal f-vector numbers are derived through the Wythoff construction, dividing the full group order of a subgroup order by removing
7-demicube
shell neighbors or the central sphere is √2. There are five different Wythoff constructions of this tessellation as a uniform polytope. They are geometrically
24-cell_honeycomb
Plane figure bounded by line segments
Spherical polygons play an important role in cartography (map making) and in Wythoff's construction of the uniform polyhedra. A skew polygon does not lie in
Polygon
the row's element. The diagonal f-vector numbers are derived through the Wythoff construction, dividing the full group order of a subgroup order by removing
Rectified_5-simplexes
Polyhedron with 62 faces
± 5 , ± 2 , ± 5 φ ) , ( ± 1 φ , ± 3 , ± 2 φ ) , {\displaystyle {\begin{array}{ccclc}{\Bigl (}&\pm \,\varphi ,&\pm \,\varphi ,&\pm {\bigl [}3-{\frac {1}{\varphi
Great truncated icosidodecahedron
Great_truncated_icosidodecahedron
Polyhedron with 44 faces
2 , ± φ 2 ) , ( ± φ 2 , ± 1 , ± [ 3 φ − 2 ] ) , {\displaystyle {\begin{array}{crrlc}{\Bigl (}&\pm {\bigl [}2-{\frac {1}{\varphi }}{\bigr ]},&\pm \,1
Icositruncated dodecadodecahedron
Icositruncated_dodecadodecahedron
elements are shown. The diagonal f-vector numbers are derived through the Wythoff construction, dividing the full group order of a subgroup order by removing
Truncated_5-cell
Polyhedron with 54 faces
, φ 2 ) , ( φ 2 , 1 φ 2 , 2 ) , ( 5 , 1 , 5 ) . {\displaystyle {\begin{array}{lcr}{\Bigl (}1,&1,&3{\Bigr )},\\{\Bigl (}{\frac {1}{\varphi }},&{\frac
Truncated_dodecadodecahedron
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