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Figurate numbers

   Also found in: Wikipedia 0.01 sec.
(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.

See also: Figurate



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This is exemplified in the student notes booklet of the "Euler Enrichment Stage" in a section that deals with figurate numbers.
We pick up from there and use another neat way of adding lists of numbers to find a way of getting general formulae for figurate numbers and use Gauss's method to check it
Figurate numbers A figurate number is a number that can be represented as a regular and discrete geometric pattern (e.
 
 
 
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