1. The problem involves determining if it is possible to create a two-colored equilateral triangle using given triangular jigsaw pieces without moving the pieces already placed. 2. The pieces are of types T1 and T2 with specific side lengths and angles, and the problem uses trigonometric relations such as the law of cosines: $$a_2 = l^2 + l^2 - 2(l)(l) \cos 120^\circ$$ and sine values like $$\sin 60^\circ = \frac{\sqrt{3}}{2}$$. 3. The question explores combining these pieces to form larger equilateral triangles and examines area ratios and side length relations, for example, expressions like $$L = \sqrt{3} A + B$$ and ratios involving $$\frac{\sqrt{3}(A + \sqrt{3} B)}{2}$$. 4. The problem also involves geometric dissection and coloring, which relates to tiling, tessellation, and geometric constructions. 5. To search for more questions like this, you can look up topics such as "geometric dissections," "equilateral triangle tiling," "triangle tessellations," "jigsaw puzzle geometry," "polygon dissection problems," or "colored tiling problems in geometry." These terms cover the study of subdividing shapes into smaller parts and reassembling them, often with color constraints. Final answer: These types of questions are generally called **geometric dissections** or **triangle tessellation problems** in mathematics.