However, we do not yet have the square. We have the base and the potential for height, but we lack the specific corners of the square. The standard player impulse is to draw lines to connect these intersections or to draw perpendiculars—moves that would push the count beyond 3E.

To understand the brilliance of the 3E solution, one must first understand the constraints. In Euclidea, an "E" (Elementary) move is defined as the use of a specific tool: a point, a line, a circle, or the goniometer (angle tool). The level provides a given segment, let's call it AB, and asks the player to construct a square using AB as one of its sides.