5040/Historical Note

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: $738$, $741$, $747$, $771$, $878$

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. $\text {580}$ – $\text {500}$ B.C.): Footnote $5$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $5040$