Pyramidal number
Encyclopedia
A pyramidal number is a figurate number
that represents a pyramid
with a base and a given number of sides. The term is most often used to refer to square pyramidal number
s, which have four sides, but it can also refer to:
The formula for a r-gonal pyramid number is:
Figurate number
The term figurate number is used by different writers for members of different sets of numbers, generalizing from triangular numbers to different shapes and different dimensions...
that represents a pyramid
Pyramid
A pyramid is a structure whose outer surfaces are triangular and converge at a single point. The base of a pyramid can be trilateral, quadrilateral, or any polygon shape, meaning that a pyramid has at least three triangular surfaces...
with a base and a given number of sides. The term is most often used to refer to square pyramidal number
Square pyramidal number
In mathematics, a pyramid number, or square pyramidal number, is a figurate number that represents the number of stacked spheres in a pyramid with a square base...
s, which have four sides, but it can also refer to:
- Triangular pyramidal numberTetrahedral numberA tetrahedral number, or triangular pyramidal number, is a figurate number that represents a pyramid with a triangular base and three sides, called a tetrahedron...
(three sides) - Square pyramidal numberSquare pyramidal numberIn mathematics, a pyramid number, or square pyramidal number, is a figurate number that represents the number of stacked spheres in a pyramid with a square base...
(4 sides) - Pentagonal pyramidal numberPentagonal pyramidal numberA pentagonal pyramidal number is a figurate number that represents the number of objects in a pyramid with a pentagonal base. The nth pentagonal pyramidal number is equal to the sum of the first n pentagonal numbers....
(five sides) - Hexagonal pyramidal number (six sides)
- Heptagonal pyramidal numberHeptagonal pyramidal numberA heptagonal pyramidal number is the sum of the first few heptagonal numbers. The heptagonal number for n can be calculated by adding up the heptagonal numbers for 1 to n, or by using the formula n/6....
(seven sides)
The formula for a r-gonal pyramid number is: