Editing Square pyramidal number (section)

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{{Short description|Number of stacked spheres in a pyramid}}
[[File:Square pyramidal number.svg|thumb|upright=1.35|Geometric representation of the square pyramidal number {{nowrap|1=1 + 4 + 9 + 16 = 30.}}]]
In mathematics, a '''pyramid number''', or '''square pyramidal number''', is a [[natural number]] that counts the stacked spheres in a [[pyramid (geometry)|pyramid]] with a square base. The study of these numbers goes back to [[Archimedes]] and [[Fibonacci]]. They are part of a broader topic of [[figurate number]]s representing the numbers of points forming regular patterns within different shapes.

As well as counting spheres in a pyramid, these numbers can be described algebraically as a sum of the first <math>n</math> positive [[square number]]s, or as the values of a [[cubic polynomial]]. They can be used to solve several other counting problems, including counting squares in a square grid and counting [[acute triangle]]s formed from the vertices of an odd [[regular polygon]]. They equal the sums of consecutive [[tetrahedral number]]s, and are one-fourth of a larger tetrahedral number. The sum of two consecutive square pyramidal numbers is an [[octahedral number]].