Exploring Pascal ||
Student Center ||
Teachers' Place
Exploring Pascal ||
Student Center ||
Teachers' Place
Hexagonal numbers are figurate numbers (numbers that can be represented by a regular geometric arrangement of equally spaced points), and 6-polygonal numbers of the form n(2n-1). The first few are 1, 6, 15, 28, 45, ... . Every hexagonal number is also a triangular number.Like the triangular numbers, the hexagonal 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
- Eric's Treasure Trove of Mathematics: Figurate Number, Hexagonal 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 Drexel University School of Education.