In this video lecture, Prof. N.J. Wildberger talks about why trigonometry is hard.
The usual trigonometry is overly complicated, inaccurate and logically dubious. This is the first of a series that shows you a better way---rational trigonometry. Rational trigonometry replaces distance and angle with more algebraic notions called quadrance and spread. All of those complicated formulas become much simpler, you don't need a calculator any more, and the theory extends Euclidean geometry to arbitrary fields. What mathematics teacher or student could ask for more?
Assoc. Prof. N J Wildberger from UNSW is also the creator of the MathFoundations series, the WildLinAlg series, and a more advanced video series on Algebraic Topology.
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.