A New Method of Approximate Angle Trisection Using only Compass and Unmarked Straightedge with Error Analysis

Exact trisection of an arbitrary angle using only an unmarked straightedge and compass is impossible, as proven by Wantzel (1837). Nevertheless, many approximate constructions have been proposed throughout history. In this work, we are are doing approximate angle trisection and then prove using trigonometry. The method makes no error at θ = 90⁰ and 54⁰. We also attached an .xlsx file of error in degrees and percentage. A continuous error function is constructed and graphically analysed for angles from 0⁰ to 90⁰. The results show that the error is not uniform and increases significantly as the angle decreases, revealing a systematic limitation of this approximation method. This approach provides a simple and visual framework for comparing approximate trisection formulas and understanding their accuracy behaviour.