Exploring Pascal ||
Student Center ||
Teachers' Place
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
The Math Forum is a research and educational enterprise of the Goodwin College of Professional Studies.