Pyramidal numbers

(redirected from Pyramidal number)
Also found in: Encyclopedia, Wikipedia.
(Math.) certain series of figurate numbers expressing the number of balls or points that may be arranged in the form of pyramids. Thus 1, 4, 10, 20, 35, etc., are triangular pyramidal numbers; and 1, 5, 14, 30, 55, etc., are square pyramidal numbers.

See also: Pyramidal

References in periodicals archive ?
[PP.sub.n] = Pentagonal Pyramidal number of rank n = [n.sup.2](n + 1)/2
[TP.sub.n] = Triangular Pyramidal number of rank n = n(n + 1)(n + 2)/6
[SP.sub.n] = Square Pyramidal number of rank n = n(n + 1)(2n + 1)/6
The nth Pyramidal number [t.sub.n], n [member of] N is defined by:
In this paper we have defined and investigated the s-consecutive, s-reversed, s-mirror and s-symmetric sequences of Pyramidal numbers (Triangular numbers of dimension 3.) using Maple 6.
Nichomachus also considered the connections between numbers and three-dimensional geometrical patterns, such as the cubic numbers and the pyramidal numbers. The latter had practical use in the 18th and 19th centuries in counting the number of cannonballs in a pyramidal stack.
The activities on ziggurats and pyramidal numbers also fit in nicely with this syllabus in the components of Measurement: M2 (applications of area and volume) and Algebraic Modelling: AM4 (modelling linear and non-linear relationships).
The difference here is the pentagonal pyramidal numbers [6], so