The Mathematical Beauty of Triangular Numbers

  • Destiney Bonwell
  • Mulatu Lemma
Keywords: Triangular numbers, Perfect square, Pascal Triangles, perfect numbers


The triangular numbers are formed by partial sum of the series 1+2+3+4+5+6+7….+n [2].  In other words, triangular numbers are those counting numbers that can be written as  = 1+2+3+…+ n.   So,

T1= 1

T2= 1+2=3

T3= 1+2+3=6

T4= 1+2+3+4=10

T5= 1+2+3+4+5=15

T6= 1+2+3+4+5+6= 21

T7= 1+2+3+4+5+6+7= 28

T8= 1+2+3+4+5+6+7+8= 36


T10 =1+2+3+4+5+6+7+8+9+10=55

 In this paper, we investigate some important properties of triangular numbers. Some important results dealing with the mathematical concept of triangular numbers will be proved.  We try our best to give short and readable proofs.  Most of the results are supplemented with examples.  


Download data is not yet available.

Author Biographies

Destiney Bonwell

Department of Mathematics, Savannah State University, USA.

Mulatu Lemma

Department of Mathematics, Savannah State University, USA.


1. Jones K, Parker S, and Lemma M: The Mathematical Magic of Perfect Numbers: GaJSci 66(3): 97-106, 2008
2. Gupta S: “Fascinating Triangular Numbers” : p3, 2002
3. Hamburg C: “Triangular Numbers Are Everywhere!”: Illinois, Mathematics and Science Academy: p5, 1992.
How to Cite
Bonwell, D., & Lemma, M. (2021). The Mathematical Beauty of Triangular Numbers. GPH - International Journal of Mathematics, 4(06), 23-32. Retrieved from