Neusis construction

Neusis construction is a classical geometric method used to create a specific angle or construct certain shapes using only a straightedge and compass. It involves drawing a line segment and then adjusting it to meet certain conditions, like intersecting with a circle at a specific angle. Unlike traditional compass-and-straightedge methods, which only allow for precise constructions, neusis allows for "imprecise" adjustments to achieve a desired geometric outcome. This method originates from ancient Greek geometry and serves as a bridge between pure theoretical constructions and practical applications in geometry.