[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