Explore the fundamentals of rational spherical/elliptic trigonometry in this 34-minute lecture, part of the Universal Hyperbolic Geometry series. Delve into a cleaner, more logical approach to classical spherical trigonometry and its close connection to hyperbolic geometry. Examine the basic laws through an in-depth analysis of a specific spherical triangle, formed by three vectors positioned at the origin in three-dimensional space. Gain valuable insights into the geometry of three-dimensional space, laying a strong foundation for further exploration of this fascinating subject.