The discussion centers on the concept of external division in geometry, specifically how mathematicians conceptualized a point dividing a line externally. The inquiry suggests that this idea likely originated from Greek geometry, particularly through compass and straightedge constructions. The notion of constructible numbers is relevant, as it relates to these geometric methods. Additionally, the invariance of ratios under affine mappings, such as parallel projections, plays a crucial role in understanding this concept.
PREREQUISITESMathematicians, geometry enthusiasts, educators, and students seeking to deepen their understanding of geometric concepts and their historical development.
I assume because of the invariance of the ratios under affine mappings, e.g. parallel projections. These mappings are essential to the constructions @jedishrfu mentioned.prashant singh said:Why they discovered it.