In this video lecture, Prof. N.J. Wildberger gives proofs of the two triangle spread rules, which tell us how to choose the third spread of a triangle given two spreads. The arguments are somewhat complicated, involving some rather magical identities.
This video is part of the WildTrig series, which introduces Rational Trigonometry and applies it to many different aspects of geometry.
In this course, Prof. N.J. Wildberger gives 72 video lectures on Rational Trigonometry.
This video series on Rational Trigonometry (RT) and related geometry presents a much needed alternative to the traditional tedious and painful subject of trigonometry, which alienates millions of students each year from mathematics. By dispensing with transcendental notions, circular functions and square roots, this new theory gives simpler, faster and more accurate ways to solve a wide variety of engineering, surveying, physics and geometry problems, essentially only with high school algebra (that's right, calculators or trig tables are not required). RT is also a much more satisfying and logical way to introduce young people to the beauty and elegance of geometry, and teaches them that mathematics should, first and foremost, always make sense. Prepare to depart on a modern adventure, in the spirit of the ancient Greeks! Assoc Prof N J Wildberger is the author of the first book on this subject, 'Divine Proportions: Rational Trigonometry to Universal Geometry'. He is also and innovative and highly regarded teacher in the School of Mathematics and Statistics at UNSW.