Fuzzy

triangular numbers A: (a, m, P) and the mean are computed by the following formula:

Some important results dealing with the mathematical concept of

triangular numbers will be proved.

In this paper we consider a figurate sequence of

Triangular numbers of dimension 3, also called as Pyramidal numbers.

If 1 is subtracted from the number of regions, the pattern is 1, 3, 6, 10, 15, 21, which are the

triangular numbers again.

uk *We received no correct entries, but the answer to the Dr Math's puzzle from October 30, to find four different ways of making 49 with

triangular numbers, are; 1+3+45, 3+10+36, 6+15+28, and 21+28.

Key Words: Prime Numbers, Perfect numbers, and

Triangular numbers.

He covers Ramanujan's work in congruences for p(n) and r(n), sums of squares and sums of

triangular numbers, Eisenstein series, the connection between hypergeometric functions and theta functions and the applications of the primary theorem, and the Rogers-Ramanujan continued fraction.

For example, the

triangular numbers 1, 3, 6, and 10 are illustrated in Figure 1.

Therefore the next two

triangular numbers are 15 (10 + 5) and 21 (15 + 6) On July 10,1796, when he was 19-years-old, the mathematician Carl Friedrich Gauss wrote in his diary: "I have just proved this wonderful result that any natural number is the sum of three or fewer

triangular numbers".

Gupta regarding the Smarandache consecutive and the reversed Smarandache sequence of

triangular numbers [Smarandache Notions Journal, Vol.

These are the

triangular numbers, and for the fourth row the tetrahedral numbers.

The trivial

triangular numbers SRPS(1) = 1 and SRPS(2) = 3 were found.