# Columns of Pascal's Triangle contain Simplicial Polytopic Numbers

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## Theorem

The columns of Pascal's triangle contain the simplicial polytopic numbers:

- Column $0$: repeated instances of number $1$

and so on.

## Proof

This theorem requires a proof.In particular: Need to define the simplicial polytopic numbers and demonstrate that the $n$th simplicial polytopic number of dimension $m$ is $\dbinom m n$ or whatever the formula is.You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof.To discuss this page in more detail, feel free to use the talk page.When this work has been completed, you may remove this instance of `{{ProofWanted}}` from the code.If you would welcome a second opinion as to whether your work is correct, add a call to `{{Proofread}}` the page. |

## Sources

- 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $35$ - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $35$