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In mathematics, a polygonal number is a number that counts dots arranged in the shape of a regular polygon. These are one type of 2-dimensional figurate numbers . Definition and examples
The term figurate number is used by different writers for members of different sets of numbers, generalizing from triangular numbers to different shapes (polygonal numbers) and different dimensions (polyhedral numbers). The term can mean. polygonal number. a number represented as a discrete r -dimensional regular geometric pattern of r ...
The centered polygonal numbers are a class of series of figurate numbers, each formed by a central dot, surrounded by polygonal layers of dots with a constant number of sides. Each side of a polygonal layer contains one more dot than each side in the previous layer; so starting from the second polygonal layer, each layer of a centered k-gonal ...
Fermat polygonal number theorem. In additive number theory, the Fermat polygonal number theorem states that every positive integer is a sum of at most n n -gonal numbers. That is, every positive integer can be written as the sum of three or fewer triangular numbers, and as the sum of four or fewer square numbers, and as the sum of five or fewer ...
In geometry, a polygon (/ ˈ p ɒ l ɪ ɡ ɒ n /) is a plane figure made up of line segments connected to form a closed polygonal chain. The segments of a closed polygonal chain are called its edges or sides. The points where two edges meet are the polygon's vertices or corners. An n-gon is a polygon with n sides; for example, a triangle is a 3 ...
Centered square number. In elementary number theory, a centered square number is a centered figurate number that gives the number of dots in a square with a dot in the center and all other dots surrounding the center dot in successive square layers. That is, each centered square number equals the number of dots within a given city block ...
Ternary: The base-three numeral system with 0, 1, and 2 as digits. Quaternary: The base-four numeral system with 0, 1, 2, and 3 as digits. Hexadecimal: Base 16, widely used by computer system designers and programmers, as it provides a more human-friendly representation of binary-coded values.
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