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a number represented as a discrete r-dimensional regular geometric pattern of r-dimensional balls such as a polygonal number (for r = 2) or a polyhedral number (for r = 3). a member of the subset of the sets above containing only triangular numbers, pyramidal numbers , and their analogs in other dimensions.
On the patterns and the unusual properties of figurate numbers: 1974 Aug: On the fanciful history and the creative challenges of the puzzle game of tangrams: 1974 Sep: More on tangrams: Combinatorial problems and the game possibilities of snug tangrams 1974 Oct: On the paradoxical situations that arise from nontransitive relations: 1974 Nov
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 ...
Proof without words that a hexagonal number (middle column) can be rearranged as rectangular and odd-sided triangular numbers. A hexagonal number is a figurate number.The nth hexagonal number h n is the number of distinct dots in a pattern of dots consisting of the outlines of regular hexagons with sides up to n dots, when the hexagons are overlaid so that they share one vertex.
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To change this template's initial visibility, the |state= parameter may be used: {{ Figurate numbers | state = collapsed }} will show the template collapsed, i.e. hidden apart from its title bar. {{ Figurate numbers | state = expanded }} will show the template expanded, i.e. fully visible.