Explore the concept of parallels and the double triangle in Universal Hyperbolic Geometry through this informative video lecture. Delve into Euclid's parallel postulate and its historical impact on hyperbolic geometry. Learn about the unique approach of defining parallels to a line through a point, rather than parallel lines themselves. Discover the construction of the double triangle and its associated perspective centers, including the x, y, and z points. Examine the ortho-axis and its relationship to these points. Gain insights into various perspective theorems and the zbhs harmonic range theorem. Follow along with algebraic constructions and geometric explanations to deepen your understanding of these advanced mathematical concepts.