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A triangular number is a figurate number: a number that can be represented by a regular geometric arrangement of equally spaced points.Triangular numbers can be thought of as the numbers of dots you need to make a triangle:
The triangular numbers are found in the third diagonal of Pascal's triangle:







1 








Row 0  






1 

1 







Row 1  





1 

2 

1 






Row 2  




1 
3 
3 

1 





Row 3  



1 

4 

6 

4 

1 




Row 4  


1 

5 

10 

10 

5 

1 



Row 5  

1 

6 

15 

20 

15 

6 

1 


Row 6  
1 

7 

21 

35 

35 

21 

7 

1 

Row 7  
1 

8 

28 

56 

70 

56 

28 

8 

1 
Row 8 
References
 Ask Dr. Math Archives: What is a triangular number? Why is 1 a triangular number?
 Ask Dr. Math FAQ: Pascal's Triangle
 Eric's Treasure Trove of Mathematics: Triangular Number
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