Square Pyramidal Numbers
Calculates the square pyramidal number: the total number of balls stacked in the shape of a square pyramid.
| Total number of balls: Tn | |
| Stacking height hn | |
| (Assume the diameter of the ball is 1.) |
| \(\normalsize Square\ pyramidal\ number\\ (1)\ total\ balls\\ \hspace{40px} T_n={\large\displaystyle \sum_{\small k=1}^{\small n}} k^2={\large\frac{n(n+1)(2n+1)}{6}}\\ (2)\ height\ to\ accumulate\\ \hspace{40px} h_n={\large\frac{n-1}{\sqrt{2}}}+1\\ \) |
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