The numbers that are both square and triangular are beautifully related to the best approximations to √2:
|
Number |
Square Root |
Factors of root |
| 1 | 1 | 1 |
| 36 | 6 | 2 * 3 |
| 1225 | 35 | 5 * 7 |
| 41616 | 204 | 12 * 17 |
and so on.
In each case the factors of the root are the numerator and denominator of the next approximation to √2. — David Wells, The Penguin Dictionary of Curious and Interesting Mathematics (1986), entry for “36”.
Elsewhere other-accessible
• A001110 — Square triangular numbers: numbers that are both triangular and square
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