Fuzzy triangular numbers
A: (a, m, P) and the mean are computed by the following formula:
A triangular fuzzy number A or simply triangular number
with membership function _A(x) is defined on R by
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.
There is a substantial starter course on the origins of numbers, before the reader is invited to gorge on the main courses that include how calculations were devised, big numbers (like googol), symmetry in nature, phi, triangular numbers
, logic, probability, art, magic and fractals.
Used procedure with the application of fuzzy triangular numbers
is described in the following steps (Van Laarhoven & Pedrycz, 1983; Zadeh, 1965; Kwong & Bai, 2002).
2] Triangular numbers
[ILLUSTRATION OMITTED] 1 1 3 1 + 2 6 1 + 2 + 3 10 1 + 2 + 3 + 4 15 1 + 2 + 3 + 4 + 5 .
In this paper, the sequences that are deemed to be 'interesting' enough for further discussion include the counting numbers, squares, cubes, triangular numbers
, tetrahedral numbers and Fibonacci numbers, among others.
As an alternative to looking solely at linear functions, a three-lesson learning progression developed for Year 6 students that incorporates triangular numbers
to develop children's algebraic thinking is described and evaluated.
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.