njwildberger (August 16, 2008 at 12:12 am)

You are quite correct. So this will help you in connecting rational trig to ordinary trig. However the notion of spread is more elementary than both the notions of angle or sin x.

ukbraintrainer (August 15, 2008 at 10:55 pm)

Looks to me like spread A = (sin^2 A). Am I wrong? Am I missing something important?

IcyNami (July 20, 2008 at 7:58 am)

you went pretty fast in the last one.

Bloodsaberxy (June 9, 2008 at 1:53 pm)

you shouldve been my teacher

opinionhead444 (June 8, 2008 at 10:15 am)

Thank you very much for answering my question, Mr. Wildberger.

njwildberger (June 8, 2008 at 9:58 am)

It will be a while before rational trig replaces classical trig, but I believe it will happen. The circular trig functions are indeed important for integration---but that is a more advanced subject than the geometry of triangles. In a future video I'll show how many calculus problems that involve circular trig functions can also be solved with quadrances and spreads.

opinionhead444 (June 8, 2008 at 3:48 am)

I like the videos so far. I teach secondary mathematics here in the States. How likely is it for all the math communities (secondary on up) to accept rational trigonometry over the standard trigonometry we love and use today?Furthermore, how would this relate to calculus? To integrate certain radical expression, one needs to use the circular trig functions. How do you approach that problem?

njwildberger (May 1, 2008 at 6:27 pm)

Angles are needed primarily in mechanics: studying uniform circular motion. They are also important in harmonic analysis, and some other more advanced areas. My point is that they are not needed for most elementary geometry. An angle is a sophisticated concept!

sikory (April 30, 2008 at 11:27 am)

but having a second thought about it, the problem I see isn't trigonometry, but the way I see it, it can't replace the classical concepts everywhere

sikory (April 30, 2008 at 11:21 am)

this is a great concept, however the spread simply can't be useful in a lot of fields of science where it is needed to indicate angles(mostly rotations ) of more than 2/π since every spread(except 0 and 1) has, over the range of 2π, 4 values that have the same spread and but a different angle. But I appreciate it a lot that people like you try to question the fundamentals of today's mathematics and really come up with something useful, since I do think(not having read your book) that it's useful