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
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.