Figurate numbers

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(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

References in periodicals archive ?
Triangular numbers are figurate numbers because they represent counting numbers as a geometric configuration of equally spaced points.
Playing with figurate numbers can help making triangle and other geometric number-shapes.
Even without such investigations, early experience playing oware can provide both visual and tactile foundations for more formal explorations of certain mathematical ideas, including figurate numbers and their properties, iterative and self-referential processes, and cellular automata.
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
The same technique can be applied to any other sequence of figurate numbers.
If in the previous issue of AMT (page 15) you didn't try to test Fermat's declaration about figurate numbers being used to express any number, then you might be in a better position to do so now, having found a few more types of figurate numbers with which to play.
So pick any number and find it to be a figurate number itself, or the sum of two or more of them.
Its definition is linked in history to our investigation of figurate numbers.
Figurate numbers were a concern of Pythagorean geometry, (I just love these links between numbers and shapes
What might the gnomons for the next shaped figurate numbers be?
We'll use his technique to revisit figurate numbers next issue