Basic facts: triangles are three-sided, two-dimensional flat shapes. Triangles were first described in euclid's elements, books 1–4 , c. 300 bc. They are classified according to the lengths of their sides, and have three main variations. This painting is based on the first one:
-an equilateral triangle, which is a regular polygon with three equal length sides and all angles measuring 60°.
The other two main types of triangles are:
-an isosceles triangle has two equal-sided lengths, and two (opposite) equal-measured angles; this fact is the content of the isosceles triangle theorem known by euclid.
-a scalene triangle has all sides of different lengths. equivalently, it has all angles of different measurements.