Explore the extension of Paul Miller's protractor for measuring projective quadrance between projective points using the core circle in this 49-minute mathematics lecture. Delve into the application of these concepts in the red relativistic setting, examining the analogous core circle with equation x^2-y^2=x. Investigate the Parallel chords theorem and gain geometrical interpretations of rotations and Lorentz boosts, highlighting the symmetry between different types of geometry. Discover how abandoning angles, transcendental functions, and traditional notions of real numbers leads to powerful algebraic insights, offering a more general and comprehensive understanding of geometric principles.