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Figurate numbers were a concern of the Pythagorean worldview. It was well understood that some numbers could have many figurations, e.g. 36 is a both a square and a triangle and also various rectangles. The modern study of figurate numbers goes back to Pierre de Fermat, specifically the Fermat polygonal number theorem.
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In mathematics, a polygonal number is a number that counts dots arranged in the shape of a regular polygon [1]: 2-3 . These are one type of 2-dimensional figurate numbers . Polygonal numbers were first studied during the 6th century BC by the Ancient Greeks, who investigated and discussed properties of oblong , triangular , and square numbers ...
How to be a psychic, even if you are a horse or some other animal 1979 Jun: Chess problems on a higher plane, including mirror images, rotations and the superqueen 1979 Jul: Douglas R. Hofstadter's "Gödel, Escher, Bach" 1979 Aug: The imaginableness of the imaginary numbers: 1979 Sep: In some patterns of numbers or words there may be less than ...
The parity of centered pentagonal numbers follows the pattern odd-even-even-odd, and in base 10 the units follow the pattern 1-6-6-1. Centered pentagonal numbers follow the following recurrence relations: = +, = = +, =, =, = Centered pentagonal numbers can be expressed using triangular numbers:
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