Patricia Shanahan wrote: > Andrew Bettilyon wrote: >> I'm curious what everybody has to say about Norman Wildberge's book >> "Divine Proportions" which poses an alternate approach to trigonometry >> with respect to his critique of modern mathematics, saying that much of >> modern mathematics is too convoluted and inaccessable to >> non-specialists, due to it's inefficient organization. > > For those of us who don't have the book, could you post a summary of its > approach to trigonometry? > > In particular, I'm interested in which operations it makes harder, and > which it makes easier, and in what ways.
It seems to be VERY concerned with the problems of doing trigonometry with arbitrary angles without a scientific calculator.
When I was first learning trig, in the 1960's, getting a usable approximation to the sine of an arbitrary angle was an elaborate process involving using the most significant digits to select a page in a table, then using more digits to select a row and column. Finally, interpolation could squeeze out a little more precision. There was a real problem that might have been solved by alternative approaches.
Now, it is a few button clicks on a calculator.
Similarly, he is concerned about the difficulties of remembering the relationships between the trig functions. There is no need to remember them, they are plastered all over the Internet, and appear in high school mathematics texts whenever they are relevant.
His paper http://web.maths.unsw.edu.au/~norman/papers/Survivor.pdf "Survivor: the Trigonometry Challenge" uses a desert island scenario to set up a situation in which people would attempt trigonometry without access to calculators or tables.
If his approach is really superior, he should be able to demonstrate its superiority in the real world, in which people doing trig have calculators, reference books, computers, and the Internet.
