# 5040/Historical Note

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## Historical Note on $5040$

The philosopher Plato decided that the exact number of citizens suitable for his ideal city was $5040$.

His reasons included:

- $5040$ has $59$ divisors excluding itself
- Can be divided by all numbers from $1$ to $10$ and so can be assembled for various wartime or peacetime collective activities into so many equal teams
- Subtracting two hearths (that is, people) from the total, you get $5038$, which is divisible by $11$ as well.

- -- Plato's
*Laws*: $738$, $741$, $747$, $771$, $878$

- -- Plato's

In the science of campanology, a complete sequence of Stedman triples contains $5040$ changes, and takes between $3$ and $4$ hours to accomplish.

## Sources

- 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $5040$ - 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {A}.2$: Pythagoras (ca. $580$ – $500$ B.C.): Footnote $5$ - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $5040$