User:GFauxPas/Sandbox

Welcome to my sandbox, you are free to play here as long as you don't track sand onto the main wiki. --GFauxPas 09:28, 7 November 2011 (CST)

Thoughts on the picture, anyone? --GFauxPas 14:37, 9 November 2011 (CST)


 * Looks okay to me. I was going to get round to doing something similar myself at one point.


 * Mind, if you're planning on using it to illustrate sine and cosine, you might want to add the actual distances as lines. Oh, and purists may wince when they see x and y used to define the axes and the point on it, but I wouldn't be too fussed. --prime mover 14:47, 9 November 2011 (CST)

Try 2. I see I lost too many colors by saving it as a .gif, try 3 will be a .png or something.

File:Unitcirclev2.gif

Let $P = (x,y)$ be a point on the unit circle centered at the origin.

Let $\theta$ be the angle formed by the arc $(1,0)$, $(x,y)$ subtending the origin, measured counterclockwise.

The unit circle definition of the trigonometric functions are

$\cos \theta := x$

$\sin \theta := y$

That is, the directed distance between $P$ and the $x$-axis is the cosine, and the directed distance between $P$ and the $y$-axis is the sine.

Sources: khan academy "tau versus pi", wolfram mathworld "trigonometry"

After this is set up I can do a proof of the consistency between the right triangle definition and the circle definition. --GFauxPas 07:22, 17 November 2011 (CST)

Cylinder
Aaah, I'm having such a hard time proving the volume of a cylinder. Everywhere I look takes it for granted. I have so far http://tinyurl.com/7j2597f which I can't find a proof for ("But surely it's obvious, GFauxPas?") and I don't know what it means to stack so many 2D disks on top of each other that it makes a 3D stack, that doesn't make sense! Euclid defined a cylinder as a rotational solid of a rectangle, and I don't know how to integrate that without knowing it already. Can someone give me a clue, please? Where do I look? I'll keep thinking and looking. --GFauxPas 18:22, 21 November 2011 (CST)


 * If you can't prove something, move on. I understand your desire to use ProofWiki as your training exercise, but for this sort of fundamental stuff it's a bad idea to try and cut something out of whole cloth, so to speak. Leave it and wait till you find a book on the subject. Or wait till someone else posts it up. --prime mover 00:30, 22 November 2011 (CST)