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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] |
