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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
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
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
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
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
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
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
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
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
\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
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
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
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 , ± 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
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
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
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
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
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 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 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
WYTHOFF ARRAY
WYTHOFF ARRAY
Surname or Lastname
English
English : variant of Althorp, a habitational name from Althorpe in Lincolnshire or Althorp in Northamptonshire.Possibly also an Americanized form of German Althoff ‘old farm’.Thomas Altop was transported from London to VA aboard the Thornton in 1772. This surname is recorded in the tax records of Harrison County, VA, in 1802.
Biblical
prepared; arrayed
Boy/Male
Hindu, Indian, Punjabi, Sikh, Traditional
An Array of Clouds; Garland of Clouds
Girl/Female
Gujarati, Hindu, Indian, Kannada, Marathi, Sanskrit, Sindhi, Telugu
Array of Clouds
Girl/Female
Assamese, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Oriya, Sanskrit, Sindhi, Tamil, Telugu
An Array of Clouds
Girl/Female
Tamil
Array of clouds
Girl/Female
Tamil
Kadambini | காதமà¯à®ªà®¿à®¨à¯€
An array of clouds
Kadambini | காதமà¯à®ªà®¿à®¨à¯€
Girl/Female
Hindu
Array of clouds
Girl/Female
Tamil
Meghamala | மேகமாலா
Array of clouds
Meghamala | மேகமாலா
Girl/Female
Biblical
Prepared, arrayed.
WYTHOFF ARRAY
WYTHOFF ARRAY
Boy/Male
Christian, Hindu, Indian, Tamil
Father of Christ
Boy/Male
Indian, Punjabi, Sikh
Disciple; Student; Seeker; Perpetual Learner
Boy/Male
Hebrew
Son of Benedict.
Boy/Male
American, Anglo, British, Christian, English, French
Golden Village; Spear Strength; From the Town of Gold; Golden City
Biblical
bold aspect; face of trust or protection
Boy/Male
Tamil
Hrishiraj | ஹà¯à®°à¯€à®·à¯€à®°à®¾à®œ
Pleasure
Boy/Male
Arabic
Pilgrim
Surname or Lastname
English (Yorkshire)
English (Yorkshire) : variant of Beaver.Variant of Dutch and North German Bever.
Boy/Male
Anglo, Australian
Spear
Boy/Male
Irish
Means “â€gentle childâ€â€ or “â€well born.â€â€ St. Kevin founded a great monastery at Glendalough in County Wicklow in the seventh century. Noted as a man who wasn’t always comfortable in the company of other human beings, he was very much at home with the animals. One story tells that while Kevin was praying a blackbird came and nested in his hand. He remained at prayer, motionless, until the eggs had hatched. In another story, when he dropped his psalter in a lake an otter came by and retrieved it. The name is still very popular in Ireland.
WYTHOFF ARRAY
WYTHOFF ARRAY
WYTHOFF ARRAY
WYTHOFF ARRAY
WYTHOFF ARRAY
v. t.
To put garments on; to clothe; to dress; to array; -- opposed to divest. Usually followed by with, sometimes by in; as, to invest one with a robe.
v. i.
To spread out in array.
n.
Any outer covering; array; garb.
v. t.
To array.
n.
Any body of troops or men formed in close array, or any combination of people distinguished for firmness and solidity of a union.
v. t.
TO cause to move with regular steps in the manner of a soldier; to cause to move in military array, or in a body, as troops; to cause to advance in a steady, regular, or stately manner; to cause to go by peremptory command, or by force.
a.
Not arrayed in the dress of a morris dancer.
v. t.
To invest with a robe or robes; to dress; to array; as, fields robed with green.
n.
Array; order; arrangement; dress.
p. p. & a.
Clothed; arrayed; dressed; as, he was habited like a shepherd.
p. pr. & vb. n.
of Array
a.
Not resolved; not regularly disposed and arranged; not methodical; crude; as, an indigested array of facts.
imp. & p. p.
of Array
a.
Arrayed, prepared, or furnished, unsuitably.
n.
Weapons, collectively; as, an array of weaponry.
v. t. & i.
To prepare; to make ready; to array; to dress.
n.
Order; a regular and imposing arrangement; disposition in regular lines; hence, order of battle; as, drawn up in battle array.
v. t.
To dress in armor; to equip with armor for war, as a horseman; to array.
n.
One who arrays. In some early English statutes, applied to an officer who had care of the soldiers' armor, and who saw them duly accoutered.