Compass-and-straightedge problems

Compass-and-straightedge problems are classical geometric construction challenges that involve creating precise shapes or points using only a compass (to draw circles or arcs) and a straightedge (a ruler without measurements). These problems date back to ancient Greece and include famous tasks like bisecting an angle, constructing perpendicular lines, or doubling the cube. The key limitation is that no measuring devices or calculators are allowed—only these two tools. Some constructions are impossible, such as squaring the circle or trisecting certain angles, illustrating fundamental limits within pure geometric methods.