Rational Trigonometry in action! | Rational Trigonometry | N J Wildberger скачать в хорошем качестве

Rational Trigonometry in action! | Rational Trigonometry | N J Wildberger

Let's see how to apply the basic laws of Rational Trigonometry to some real-world applications coming from surveying. First we review the notions of quadrance and spread in the Euclidean 2D and 3D situation, and give an interpretation of the spread between two vectors in terms of a normalized squared area of the parallelogram formed by them. In three dimensions an analog to the Fibonacci / Diophantus identity yields again the identity that the spread is always between 0 and 1, which is essentially the Cauchy -Schwartz identity. We describe also a simple visual method of measuring the spread between two lines using Paul Miller's protractor. The important case of solving a right triangle using Rational Trig involves a pleasant complementarity between the two non-perpendicular spreads. We then apply this to solve a simple surveying problem, and show how to extend this reasoning to deal with a not so simple surveying problem also. Rational Trigonometry really is a very viable alternative to the usual trigonometry taught in schools, but it is just a lot simpler and more elegant!