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...
- the sixth power of four, 46. In figurate numbers, 5 is a pentagonal number, with the sequence of pentagonal numbers starting: 1, 5, 12, 22, 35, ... 5...
- twenty steps, like eighteen. Less than ten thousand, only thirty-one other numbers require nineteen steps to return back to one: {56, 58, 60, 61, 352, 360...
- 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...
- equilateral triangle. Triangular numbers are a type of figurate number, other examples being square numbers and cube numbers. The nth triangular number is...
- function for p = 2 {\displaystyle p=2} . The origin of happy numbers is not clear. Happy numbers were brought to the attention of Reg Allenby (a British author...
- 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...
- the sum of the two preceding ones. Numbers that are part of the Fibonacci sequence are known as Fibonacci numbers, commonly denoted Fn . The sequence...
- thought of as alphas (units). These are one type of 2-dimensional figurate numbers. The number 10 for example, can be arranged as a triangle (see triangular...
- following sections. The pronic numbers were studied as figurate numbers alongside the triangular numbers and square numbers in Aristotle's Metaphysics, and...