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ABACABA Pattern
The ABACABA pattern is a recursive fractal pattern that shows up in many places in the real world (such as in geometry, art, music, poetry, number systems, literature and higher dimensions). Patterns often show a DABACABA type subset. ''AA'', ''ABBA'', and ''ABAABA'' type forms are also considered.Halter-Koch, Franz and Tichy, Robert F.; eds. (2000). ''Algebraic Number Theory and Diophantine Analysis'', p.478. W. de Gruyter. . Generating the pattern In order to generate the next sequence, first take the previous pattern, add the next letter from the alphabet, and then repeat the previous pattern. The first few steps are listed here. A generator can be founhere ABACABA is a "quickly growing word", often described as ''chiastic'' or "symmetrically organized around a central axis" (see: Chiastic structure and Χ). The number of members in each iteration is , the Mersenne numbers (). Gallery See also * Arch form * Farey sequence * Rondo * Sesquipower In mathematics, a s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Number Dabacaba Pattern
Binary may refer to: Science and technology Mathematics * Binary number, a representation of numbers using only two digits (0 and 1) * Binary function, a function that takes two arguments * Binary operation, a mathematical operation that takes two arguments * Binary relation, a relation involving two elements * Binary-coded decimal, a method for encoding for decimal digits in binary sequences * Finger binary, a system for counting in binary numbers on the fingers of human hands Computing * Binary code, the digital representation of text and data * Bit, or binary digit, the basic unit of information in computers * Binary file, composed of something other than human-readable text ** Executable, a type of binary file that contains machine code for the computer to execute * Binary tree, a computer tree data structure in which each node has at most two children Astronomy * Binary star, a star system with two stars in it * Binary planet, two planetary bodies of comparable ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Common Time
The time signature (also known as meter signature, metre signature, or measure signature) is a notational convention used in Western musical notation to specify how many beats (pulses) are contained in each measure (bar), and which note value is equivalent to a beat. In a music score, the time signature appears at the beginning as a time symbol or stacked numerals, such as or (read ''common time'' or ''four-four time'', respectively), immediately following the key signature (or immediately following the clef symbol if the key signature is empty). A mid-score time signature, usually immediately following a barline, indicates a change of meter. There are various types of time signatures, depending on whether the music follows regular (or symmetrical) beat patterns, including simple (e.g., and ), and compound (e.g., and ); or involves shifting beat patterns, including complex (e.g., or ), mixed (e.g., & or & ), additive (e.g., ), fractional (e.g., ), and irrational met ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Farey Sequence
In mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ..., the Farey sequence of order ''n'' is the sequence of completely reduced fractions, either between 0 and 1, or without this restriction, which when in lowest terms have denominators less than or equal to ''n'', arranged in order of increasing size. With the restricted definition, each Farey sequence starts with the value 0, denoted by the fraction , and ends with the value 1, denoted by the fraction (although some authors omit these terms). A ''Farey sequence'' is sometimes called a Farey series (mathematics), ''series'', which is not strictly correct, because the terms are not summed. Examples The Farey sequences of orders 1 to 8 are : :''F''1 = :''F''2 = :''F''3 = :''F''4 = :''F''5 = :''F''6 = :''F''7 = ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arch Form
In music, arch form is a sectional structure for a piece of music based on repetition, in reverse order, of all or most musical sections such that the overall form is symmetric, most often around a central movement. The sections need not be repeated verbatim but must at least share thematic material. It creates interest through interplay among "memory, variation, and progression". Though the form appears to be static and to deny progress, the pairs of movements create an "undirectional process" with the center, and the form "actually engenders specific expressive possibilities that would otherwise be unavailable for the work as a whole".Wilson, Paul (1992). ''The Music of Béla Bartók''. . p. 32. Béla Bartók is noted for his use of arch form, e.g., in his fourth and fifth string quartets, Concerto for Orchestra, ''Music for Strings, Percussion and Celesta'', second piano concerto, and, to a lesser extent, in his second violin concerto. Samuel Barber's ''Adagio for Strings ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Baguenaudier
Baguenaudier (; French for "time-waster"), also known as the Chinese rings, Cardan's suspension, Cardano's rings, Devil's needle or five pillars puzzle, is a disentanglement puzzle featuring a loop which must be disentangled from a sequence of rings on interlinked pillars. The loop can be either string or a rigid structure. It is thought to have been invented originally in China. The origins are obscure. The American ethnographer Stewart Culin related a tradition attributing the puzzle's invention to the 2nd/3rd century Chinese general Zhuge Liang. It was used by French peasants as a locking mechanism. Variations of this include the ''Devil's staircase'', ''Devil's Halo'' and the ''impossible staircase''. Another similar puzzle is the ''Giant's causeway'' which uses a separate pillar with an embedded ring. Mathematical solution The 19th-century French mathematician Édouard Lucas, the inventor of the Tower of Hanoi puzzle, was known to have come up with an elegant solution wh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Château De Chambord
The Château de Chambord () in Chambord, Centre-Val de Loire, France, is one of the most recognisable châteaux in the world because of its very distinctive French Renaissance architecture which blends traditional French medieval forms with classical Renaissance structures. The building, which was never completed, was constructed by the king of France, Francis I. Chambord is the largest château in the Loire Valley; it was built to serve as a hunting lodge for Francis I, who maintained his royal residences at the Château de Blois and Amboise. The original design of the Château de Chambord is attributed to Italian architect Domenico da Cortona; Leonardo da Vinci may also have been involved or influenced the design. Chambord was altered considerably during the twenty-eight years of its construction (1519–1547), during which it was overseen on-site by Pierre Neveu. With the château nearing completion, Francis showed off his enormous symbol of wealth and power by hosting hi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Double Harmonic Scale
In music, the double harmonic major scaleStetina, Troy (1999). ''The Ultimate Scale Book'', p. 59. . is a scale whose gaps may sound unfamiliar to Western listeners. This is also known as Mayamalavagowla, Bhairav Raga, Byzantine scale, Arabic (Hijaz Kar),Christiansen, Mike (2003). ''Mel Bay Complete Guitar Scale Dictionary'', p. 43. . and Gypsy major. It can be likened to a gypsy scale because of the diminished step between the 1st and 2nd degrees. ''Arabic scale'' may also refer to any Arabic mode, the simplest of which, however, to Westerners, resembles the double harmonic major scale. : Details The sequence of steps comprising the double harmonic scale is : :half, augmented second, half, whole, half, augmented second, half Or, in relation to the tonic note :minor second, major third, perfect fourth and fifth, minor sixth, major seventh, octave However, this scale is commonly represented with the first and last half step each being represented with quarter tones: : ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rotary Encoder
A rotary encoder, also called a shaft encoder, is an electro-mechanical device that converts the angular position or motion of a shaft or axle to analog or digital output signals. There are two main types of rotary encoder: absolute and incremental. The output of an absolute encoder indicates the current shaft position, making it an angle transducer. The output of an incremental encoder provides information about the ''motion'' of the shaft, which typically is processed elsewhere into information such as position, speed and distance. Rotary encoders are used in a wide range of applications that require monitoring or control, or both, of mechanical systems, including industrial controls, robotics, photographic lenses, computer input devices such as optomechanical mice and trackballs, controlled stress rheometers, and rotating radar platforms. Technologies * Mechanical: Also known as conductive encoders. A series of circumferential copper tracks etched onto a PCB is used to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gray Code
The reflected binary code (RBC), also known as reflected binary (RB) or Gray code after Frank Gray, is an ordering of the binary numeral system such that two successive values differ in only one bit (binary digit). For example, the representation of the decimal value "1" in binary would normally be "" and "2" would be "". In Gray code, these values are represented as "" and "". That way, incrementing a value from 1 to 2 requires only one bit to change, instead of two. Gray codes are widely used to prevent spurious output from electromechanical switches and to facilitate error correction in digital communications such as digital terrestrial television and some cable TV systems. Motivation and name Many devices indicate position by closing and opening switches. If that device uses natural binary codes, positions 3 and 4 are next to each other but all three bits of the binary representation differ: : The problem with natural binary codes is that physical switches are not ideal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Array Data Structure
In computer science, an array is a data structure consisting of a collection of ''elements'' (values or variables), each identified by at least one ''array index'' or ''key''. An array is stored such that the position of each element can be computed from its index tuple by a mathematical formula. The simplest type of data structure is a linear array, also called one-dimensional array. For example, an array of ten 32-bit (4-byte) integer variables, with indices 0 through 9, may be stored as ten words at memory addresses 2000, 2004, 2008, ..., 2036, (in hexadecimal: 0x7D0, 0x7D4, 0x7D8, ..., 0x7F4) so that the element with index ''i'' has the address 2000 + (''i'' × 4). The memory address of the first element of an array is called first address, foundation address, or base address. Because the mathematical concept of a matrix can be represented as a two-dimensional grid, two-dimensional arrays are also sometimes called "matrices". In some cases the term "vector" is used in comp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tower Of Hanoi
The Tower of Hanoi (also called The problem of Benares Temple or Tower of Brahma or Lucas' Tower and sometimes pluralized as Towers, or simply pyramid puzzle) is a mathematical game or puzzle consisting of three rods and a number of disks of various diameters, which can slide onto any rod. The puzzle begins with the disks stacked on one rod in order of decreasing size, the smallest at the top, thus approximating a conical shape. The objective of the puzzle is to move the entire stack to the last rod, obeying the following rules: # Only one disk may be moved at a time. # Each move consists of taking the upper disk from one of the stacks and placing it on top of another stack or on an empty rod. # No disk may be placed on top of a disk that is smaller than it. With 3 disks, the puzzle can be solved in 7 moves. The minimal number of moves required to solve a Tower of Hanoi puzzle is 2''n'' − 1, where ''n'' is the number of disks. Origins The puzzle was introduced to the West ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Box Fractal
In mathematics the Vicsek fractal, also known as Vicsek snowflake or box fractal, is a fractal arising from a construction similar to that of the Sierpinski carpet, proposed by Tamás Vicsek. It has applications including as compact fractal antenna, antennas, particularly in cellular phones. ''Box fractal'' also refers to various iterated fractals created by a square tiling, square or rectangular grid with various boxes removed or absent and, at each iteration, those present and/or those absent have the previous image scaled down and drawn within them. The Sierpinski triangle may be approximated by a box fractal with one corner removed. The Sierpinski carpet is a box fractal with the middle square removed. Construction The basic square is decomposed into nine smaller squares in the 3-by-3 grid. The four squares at the corners and the middle square are left, the other squares being removed. The process is repeated recursively for each of the five remaining subsquares. The Vics ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
