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.
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.
In this paper we consider a figurate sequence of Triangular numbers of dimension 3, also called as Pyramidal numbers.
We can obtain the first k terms of Pyramidal numbers in Maple as; > t := n->(1/6)*n*(n+1)*(n+2): > first :+ k -> seq (t(n), n=1 ...
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).