# 3/Historical Note

## Historical Note on $3$ (**three**)

The number **$3$** was considered by the ancient Greeks to be the first odd number, as they did not consider $1$ (one) a number, as such.

They associated the number **$3$** with the triangle, with its **$3$** vertices and **$3$** sides.

To the Pythagoreans, odd and even numbers were considered to be either male or female, but sources differ on which was which.

Some suggest that $3$ was considered to be the first male number, being composed of unity ($1$) and $2$, the principle of **diversity**.

Such sources state that in contrast, the even numbers were considered to be female.

However, other sources suggest that it was the odd numbers which were female, while the even numbers were male.

In addition to that, in the eyes of the Pythagoreans, **$3$** was in fact the first number, as in addition they considered that $2$ was not a number either, as it had a beginning and an end, but no middle.

Proclus similarly considered **$3$** to be the first number, but his reason was that it was the first number to be increased more by multiplication than by addition: $3 \times 3$ is greater than $3 + 3$.

**$3$** is a common number into which to divide a body into parts.

For example:

- The
**positive**,**comparative**and**superlative**of natural language.

- The world is divided into $3$ parts:
**the Underworld**,**the Earth**(or**Middle-Earth**), and**the Heavens**.

- In the English language, the sequence (beloved of fairy tales)
**once**,**twice**,**thrice**ends there -- there is no single word for "$n$ times" for any higher number.

In many cultures in history, **$3$** is particularly significant.

In Greek mythology, there were:

- $3$ Fates
- $3$ Furies
- $3$ Graces
- $3 \times 3$ Muses
- Paris had to choose between $3$ goddesses

Oaths are repeated $3$ times.

Saint Peter denied Christ $3$ times.

The Bellman states, in *The Hunting of the Snark*, that:

*What I tell you three times is true.*

## Sources

- 1980: David M. Burton:
*Elementary Number Theory*(revised ed.) ... (previous) ... (next): Chapter $1$: Some Preliminary Considerations: $1.3$ Early Number Theory - 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $3$ - 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {A}.2$: Pythagoras (ca. $580$ – $500$ B.C.) - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $3$ - 2008: Ian Stewart:
*Taming the Infinite*... (previous) ... (next): Chapter $2$: The Logic of Shape: Pythagoras