CENTERED NONAGONAL NUMBER Meaning and
Definition
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A centered nonagonal number refers to a specific type of polygonal number that is derived from a nonagon, which is a polygon with nine sides. The term "centered" in the context of polygonal numbers indicates that the dots forming the polygon are arranged in a symmetrical pattern with a dot in the center and additional dots surrounding it. The concept of a nonagonal number involves the calculation of the number of dots required to form a nonagon.
To elaborate further, a centered nonagonal number is the outcome of arranging nonagon-shaped dots in successive layers, where each subsequent layer is added around the previously formed layers in a concentric manner. These dots are arranged systematically to create a nonagon with a central dot that serves as the starting point for the pattern. As more layers of dots are appended, the centered nonagonal number increases accordingly.
Mathematically, a centered nonagonal number can be obtained by multiplying 7 by the nonagon's index number, then adding 2. Symbolically, it can be represented by the formula 7n + 2, where "n" represents the index variable. This formula enables the calculation of the specific centered nonagonal number corresponding to a given index value. For instance, when "n" is 1, the resulting centered nonagonal number is 9; for n = 2, it is 16; for n = 3, it is 23; and so on.
In summary, a centered nonagonal number is a polygonal number that represents the quantity of dots needed to form a symmetrical nonagon by adding successive concentric layers of dots around a central dot.
