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Square pyramidal number - Wikipedia

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In mathematics, a pyramid number, or square pyramidal number, is a natural number that counts the number of stacked spheres in a 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 numbers 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 𝑛 positive square numbers, 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 triangles formed from the vertices of an odd regular polygon. They equal the sums of consecutive tetrahedral numbers, and are one-fourth of a larger tetrahedral number. The sum of two consecutive square pyramidal numbers is an octahedral number. The pyramidal numbers were one of the few types of three-dimensional figurate numbers studie

Square pyramidal number - Wikipedia Jump to content From Wikipedia, the free encyclopedia Number of stacked spheres in a pyramid Geometric representation of the square pyramidal number 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 with a square base. The study of these numbers goes back to Archimedes and Fibonacci . They are part of a broader topic of figurate numbers representing the numbers of points forming regular patterns within different shapes. As well as counting spheres in a pyramid

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