Editing Centered polygonal number (section)

{{Short description|Class of series of figurate numbers, each having a central dot}}
{{Use American English|date=March 2021}}
{{Use mdy dates|date=March 2021}}
[[File:visual_proof_centered_polygonal_numbers.svg|thumb|upright|[[Proof without words|Proof]] that each centered ''k''-gonal number is ''k'' times the previous triangular number, plus 1]]
In [[mathematics]], the '''centered polygonal numbers''' are a class of series of [[figurate number]]s, 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 number contains ''k'' more dots than the previous layer.