Exploring Pascal ||
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Exploring Pascal ||
Student Center ||
Teachers' Place
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:
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1 |
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Row 0 | |
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1 |
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1 |
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Row 1 | |
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1 |
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2 |
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1 |
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Row 2 | |
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1 |
3 |
3 |
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1 |
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Row 3 | |||
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1 |
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4 |
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6 |
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4 |
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1 |
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Row 4 | |
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1 |
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5 |
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10 |
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10 |
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5 |
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1 |
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Row 5 | |
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1 |
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6 |
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15 |
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20 |
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15 |
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6 |
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1 |
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Row 6 | |
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1 |
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7 |
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21 |
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35 |
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35 |
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21 |
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7 |
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1 |
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Row 7 | |
| 1 |
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8 |
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28 |
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56 |
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70 |
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56 |
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28 |
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8 |
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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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