Definition:Regular Tetrahedron/Historical Note

Historical Note on the Regular Tetrahedron

The concept of a regular tetrahedron is not mentioned explicitly by Euclid in The Elements.

The first reference to it is in Proposition $13$ of Book $\text{XIII} $: Construction of Regular Tetrahedron within Given Sphere:

In the words of Euclid:

To construct a pyramid, to comprehend it in a given sphere, and to prove that the square on the diameter of the sphere is one and a half times the square on the side of the pyramid.

(The Elements: Book $\text{XIII}$: Proposition $13$)

According to the Pythagorean tradition, the regular tetrahedron was the symbol for the element fire.

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $4$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $4$