The Missing Square That Explains the Quadratic Formula

Every triangle hides an equilateral triangle, even when the original triangle is completely irregular. Take any triangle. Divide each of its three angles into three equal parts. Now consider the intersections of the adjacent internal angle trisectors. The three intersection points always form an equilateral triangle. No condition is required: The original triangle may be acute, obtuse, scalene or isosceles. Its sides may have any lengths. Its angles may be completely different. Yet the hidden triangle always has three equal sides and three 60° angles. This is Morley’s trisector theorem. Local divisions of three unrelated angles produce perfect global symmetry.