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Download as PDF; Printable version; In other projects ... Figurate numbers (1 C, 51 P) Pages in category "Dot patterns"
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.
Print/export Download as PDF; Printable version; In other projects ... This category includes not only articles about certain types of figurate 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.
Triangular numbers are a type of figurate number, other examples being square numbers and cube numbers. The n th triangular number is the number of dots in the triangular arrangement with n dots on each side, and is equal to the sum of the n natural numbers from 1 to n. The sequence of triangular numbers, starting with the 0th triangular number, is
This is also the number of points of a hexagonal lattice with nearest-neighbor coupling whose distance from a given point is less than or equal to . The following image shows the building of the centered triangular numbers by using the associated figures: at each step, the previous triangle (shown in red) is surrounded by a triangular layer of ...