The New Trig

Some math professor in Sydney has developed rational trigonometry. Same great trig, no annoying sines.

His argument is that classical plane trigonometry is hard and that a more holistic approach is easier to understand.

Instead of "sides", there are "quadrances". Instead of "angles", there are "spreads". This is a fascinating approach to an old field of study, and I'm thinking of going out and buying the book.

Maybe.

Update #1: Maybe not. Found an error on page 16 of Chapter 1 (courtesy of the PDF on the website).

r = (1/2) ± (3/8)sqrt{7}

not

r = (1/2) ± (3/16)sqrt{7}

Man. If you're going to reinvent a major school of mathematics, get a damned proofreader. Pun intended.

Update #2: Now I'm confused. I rechecked my math with a calculator (after cleaning up the battery acid, that is) and I discovered that I was wrong, and the equation really should be what is listed in the book: r = (1/2) ± (3/16)sqrt{7}.

But then I just stumbled over another problem on the exact same page.

1400 - 525 sqrt{7} = 10.98056

1400 + 525 sqrt{7} = 2789.0194

So far, so good. Only Professor Wildberger states that sqrt{10.98056} = 3.3137 and sqrt{2789.0194} = 264.056.

My math tells me that sqrt{2789.0194} = 52.81117.

So in conclusion: yeah, this is one crazy-ass math book all right.