Explore a comprehensive approach to organizing metrical geometry in this 39-minute video lecture. Learn how to systematically categorize various mathematical geometries using a pizza-making analogy. Discover different types of geometries, basic orientations for description, and the importance of choosing a base number system. Delve into affine and projective geometry, and examine a hierarchy of interconnected geometries. Investigate specific examples such as the Euclidean plane, Lorentz (relativistic) plane, and elliptic geometry. Gain valuable insights into the structure and organization of geometric systems, enhancing your understanding of this fundamental mathematical field.