Centered figurate number that represents a triangle with a dot in the center
This article includes a list of references, related reading, or external links, but its sources remain unclear because it lacks inline citations. Please help improve this article by introducing more precise citations.(June 2014) (Learn how and when to remove this message)
A centered (or centred) triangular number is a centered figurate number that represents an equilateral triangle with a dot in the center and all its other dots surrounding the center in successive equilateral triangular layers.
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 new dots (in blue).
The first eight centered triangular numbers on a hex grid
and 10 Related for: Centered triangular number information
A centered (or centred) triangularnumber is a centered figurate number that represents an equilateral triangle with a dot in the center and all its other...
A triangularnumber or triangle number counts objects arranged in an equilateral triangle. Triangular numbers are a type of figurate number, other examples...
A tetrahedral number, or triangular pyramidal number, is a figurate number that represents a pyramid with a triangular base and three sides, called a tetrahedron...
centered k-gonal number contains k more dots than the previous layer. Each centered k-gonal number in the series is k times the previous triangular number...
decagonal and centered decagonal numbers. On the other hand, 10 is the first non-trivial centeredtriangularnumber and tetrahedral number. While 55 is...
is the first prime centered pentagonal number, and the fifth centeredtriangularnumber. The fifth pentagonal and tetrahedral number is 35, which is equal...
In number theory, the sum of the first n cubes is the square of the nth triangularnumber. That is, 1 3 + 2 3 + 3 3 + ⋯ + n 3 = ( 1 + 2 + 3 + ⋯ + n ) 2...
to triangular numbers: every third triangularnumber (the 1st, 4th, 7th, etc.) is also a centered nonagonal number. Thus, the first few centered nonagonal...
A square number is also the sum of two consecutive triangular numbers. The sum of two consecutive square numbers is a centered square number. Every odd...
combinatorics, a centered hexagonal number, or hex number, is a centered figurate number that represents a hexagon with a dot in the center and all other...
Global Information
