scholarly journals Triangle of Triangular Numbers

2021 ◽  
Vol 09 (10) ◽  
Author(s):  
Dr. R. Sivaraman ◽  
Keyword(s):  
Whole Numbers ◽  
Pythagorean Triples ◽  
Pascal’S Triangle ◽  
Mathematical Properties ◽  
Triangular Numbers ◽  
Pascal's Triangle

Among several interesting number triangles that exist in mathematics, Pascal’s triangle is one of the best triangle possessing rich mathematical properties. In this paper, I will introduce a number triangle containing triangular numbers arranged in particular fashion. Using this number triangle, I had proved five interesting theorems which help us to generate Pythagorean triples as well as establish bijection between whole numbers and set of all integers.

scholarly journals PASCAL TRIANGLE AND PYTHAGOREAN TRIPLES

2021 ◽  
Vol 8 (8) ◽  
pp. 75-80
Author(s):  
R. Sivaraman
Keyword(s):  
Pythagorean Triples ◽  
Pascal’S Triangle ◽  
Pascal Triangle ◽  
Pascal's Triangle

The concept of Pascal’s triangle has fascinated mathematicians for several centuries. Similarly, the idea of Pythagorean triples prevailing for more than two millennia continue to surprise even today with its abundant properties and generalizations. In this paper, I have demonstrated ways through four theorems to determine Pythagorean triples using entries from Pascal’s triangle.

Pascal's Prism

2012 ◽  
Vol 96 (536) ◽  
pp. 213-220
Author(s):  
Harlan J. Brothers
Keyword(s):  
Probability Theory ◽  
Fractal Geometry ◽  
Euclidean Geometry ◽  
Fibonacci Series ◽  
Pascal’S Triangle ◽  
Number Sequences ◽  
Definition Of ◽  
Image Position ◽  
Pascal's Triangle

Pascal's triangle is well known for its numerous connections to probability theory [1], combinatorics, Euclidean geometry, fractal geometry, and many number sequences including the Fibonacci series [2,3,4]. It also has a deep connection to the base of natural logarithms, e [5]. This link to e can be used as a springboard for generating a family of related triangles that together create a rich combinatoric object.2. From Pascal to LeibnizIn Brothers [5], the author shows that the growth of Pascal's triangle is related to the limit definition of e.Specifically, we define the sequence sn; as follows [6]:

3057. A Note on Pascal's Triangle

1963 ◽  
Vol 47 (359) ◽  
pp. 57
Author(s):  
Robert Croasdale
Keyword(s):  
Pascal’S Triangle ◽  
Pascal's Triangle

scholarly journals The Fibonacci p-numbers and Pascal’s triangle

2016 ◽  
Vol 3 (1) ◽  
pp. 1264176 ◽  
Author(s):  
Kantaphon Kuhapatanakul ◽  
Lishan Liu
Keyword(s):  
Pascal’S Triangle ◽  
Pascal's Triangle

scholarly journals Arithmetic Triangle

2017 ◽  
Vol 9 (2) ◽  
pp. 100
Author(s):  
Luis Dias Ferreira
Keyword(s):  
Arithmetic Progression ◽  
Modus Operandi ◽  
Interesting Point ◽  
Pascal’S Triangle ◽  
Initial Term ◽  
The Common ◽  
Pascal's Triangle

The product of the first $n$ terms of an arithmetic progression may be developed in a polynomial of $n$ terms. Each one of them presents a coefficient $C_{nk}$ that is independent from the initial term and the common difference of the progression. The most interesting point is that one may construct an "Arithmetic Triangle'', displaying these coefficients, in a similar way one does with Pascal's Triangle. Moreover, some remarkable properties, mainly concerning factorials, characterize the Triangle. Other related `triangles' -- eventually treated as matrices -- also display curious facts, in their linear \emph{modus operandi}, such as successive "descendances''.

Sign in / Sign up

Export Citation Format

Share Document