4 ms·
> If you allow negative side lengths, as you should [...] I mean, the blog post was about a pedagogically better suited construction of trig functions. If we a
by Tainnor 3y ago
> If you allow negative side lengths, as you should [...]
I mean, the blog post was about a pedagogically better suited construction of trig functions. If we allow negative side lengths, it's not really going to be intuitive anymore. At this point, you might just as well use the power series definition (or the one based on the complex exp function) since it makes things easy to prove.
- lupire 3y agoImaginary lengths may be unintuitive but negative is pretty simple. The idea of negative measurements (meaning "opposite direction along a line") as is well understood before children study geometry. Kindergarteners learn "left" vs "right" and "forward" vs "backward". I agree with other poster about the value of showing negative and positive lengths visually in the same diagram.
- Tainnor 3y agoMagnitudes are intuitionally directionless (hence why norms and measures are nonnegative reals). Of course, you can extend notions suitably and make it work, but I really don't think that this is terribly intuitive. (Of course, different people will find different things intuitive.)