Exploring Pascal 
Student Center 
Teachers' Place
A tetrahedral number is a figurate number: a number that can be represented by a regular geometric arrangement of equally spaced points. Tetrahedral numbers correspond to placing discrete points in the configuration of a tetrahedron (triangular base pyramid).Tetrahedral numbers are the sum of consecutive triangular numbers. The formula is 1/6n(n+1)(n+2). The first few tetrahedral numbers are 1, 4, 10, 20, 35, 56, 84, 120, ...
The tetrahedral numbers are found in the fourth 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
 Eric's Treasure Trove of Mathematics: Tetrahedral Number
 Eric's Treasure Trove of Mathematics: Figurate Number
[Pascal Web Unit]
[Web Links] [Lessons] [Standards]
[Teacher Reference] [Number Patterns]
[Privacy Policy] [Terms of Use]
Home  The Math Library  Quick Reference  Search  Help