Definition:Triangle (Geometry)/Equilateral

Definition

An equilateral triangle is a triangle in which all three sides are the same length:

That is, a regular polygon with $3$ sides.

Thus it can be seen that an equilateral triangle can be considered to be a special case of an isosceles triangle.

Euclid's Definition

In the words of Euclid:

Of trilateral figures, an equilateral triangle is that which has its three sides equal, an isosceles triangle that which has two of its sides alone equal, and a scalene triangle that which has its three sides unequal.

(The Elements: Book $\text{I}$: Definition $20$)

Also known as

An equilateral triangle is also less commonly known as an equiangular triangle.

Also see

• Results about equilateral triangles can be found here.

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): triangle (Euclidean geometry)
• 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {A}.4$: Euclid (flourished ca. $300$ B.C.)
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): triangle
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): triangle
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): equilateral