Definition of Figurate numbers. Meaning of Figurate numbers. Synonyms of Figurate numbers

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Definition of Figurate numbers

Figurate numbers
Figurate Fig"ur*ate, a. [L. figuratus, p. p. of figurare. See Figure.] 1. Of a definite form or figure. Plants are all figurate and determinate, which inanimate bodies are not. --Bacon. 2. Figurative; metaphorical. [Obs.] --Bale. 3. (Mus.) Florid; figurative; involving passing discords by the freer melodic movement of one or more parts or voices in the harmony; as, figurate counterpoint or descant. Figurate counterpoint or descant (Mus.), that which is not simple, or in which the parts do not move together tone for tone, but in which freer movement of one or more parts mingles passing discords with the harmony; -- called also figural, figurative, and figured counterpoint or descant (although the term figured is more commonly applied to a bass with numerals written above or below to indicate the other notes of the harmony). Figurate numbers (Math.), numbers, or series of numbers, formed from any arithmetical progression in which the first term is a unit, and the difference a whole number, by taking the first term, and the sums of the first two, first three, first four, etc., as the successive terms of a new series, from which another may be formed in the same manner, and so on, the numbers in the resulting series being such that points representing them are capable of symmetrical arrangement in different geometrical figures, as triangles, squares, pentagons, etc. Note: In the following example, the two lower lines are composed of figurate numbers, those in the second line being triangular, and represented thus: -- . 1, 2, 3, 4, etc. . . . 1, 3, 6, 10, etc. . . . . . . . etc. 1, 4, 10, 20, etc . . . . . . . . . . . .

Meaning of Figurate numbers from wikipedia

- The term figurate number is used by different writers for members of different sets of numbers, generalizing from triangular numbers to different shapes...
- in an infinite sequence of numbers in decimal whose digits start with 1 and have trailing 9's, that form triangular numbers containing trailing zeroes...
- with the sum between the smallest number that is the sum of two abundant numbers, and the largest that is not (24, 46). 70 is the tenth Erdős–Woods number...
- notable numbers and articles about notable numbers. The list does not contain all numbers in existence as most of the number sets are infinite. Numbers may...
- study of these numbers goes back to Archimedes and Fibonacci. They are part of a broader topic of figurate numbers representing the numbers of points forming...
- of the two elements that precede it. Numbers that are part of the Fibonacci sequence are known as Fibonacci numbers, commonly denoted Fn . Many writers...
- natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite...
- Partition numbers Pn 1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, ... The partition numbers, number of additive breakdowns of n. A000041 Fibonacci numbers F(n) 0...
- centered hexagonal numbers: Centered hexagonal numbers should not be confused with cornered hexagonal numbers, which are figurate numbers in which the ****ociated...
- Michel-marie; Deza, Elena (2012). Figurate Numbers. World Scientific. p. 436. ISBN 978-981-4458-53-5. Other sources on its figurate numbers can be found in the following:...