Definition:Plato's Geometrical Number

Definition

The actual value of what is generally known as Plato's geometrical number is uncertain.

The passage in question from Plato's Republic is obscure and difficult to interpret:

But the number of a human creature is the first number in which root and square increases, having received three distances and four limits, of elements that make both like and unlike wax and wane, render all things conversable and rational with one another.

There are two numbers which it is generally believed it could be:

$216$

$12 \, 960, \, 000$

It is believed that the expression:

three distances and four limits

refers to cubing.

It is further believed that the reference is to the area of the $3-4-5$ triangle, which is $6$.

The passage is also deduced to contain a reference to $2 \times 3$.

It is also interpreted by other commentators as being $12 \, 960 \, 000$, which is $60^4$.

Also known as

Some sources refer to this just as Plato's number.

Also see

• 216
• 12,960,000

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $216$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $216$