The northern section of El Paso County known as the Tri-Lakes region appears to be an epicenter of a significant housing boom. Shannon Bingham, owner of Western Demographics, estimates that 2,350 new homes will be built in the area by 2024, with the majority being completed in the coming four years.
We use these relationships to derive the general formula for polygonal numbers. In finding the number of dots in a polygon, two quantities vary. The first varying quantity is the number of sides of the polygon which we have denoted above as n. The second quantity is the size of the polygon which we denote as k.
A figurate number, also (but mostly in texts from the 1500 and 1600s) known as a figural number (Simpson and Weiner 1992, p. 587), is a number that can be represented by a regular geometrical arrangement of equally spaced points. If the arrangement forms a regular polygon, the number is called a polygonal number. The polygonal numbers illustrated above are called triangular, square, pentagonal, and hexagonal numbers, respectively. Figurate numbers can also form other shapes such as centered polygons, L-shapes, three-dimensional solids, etc.