In this video, at 5:13, I need to know where -theta came from? Why theta?

Jul 2013
476
40
United Kingdom
In this video I got lost at 5:13. How did the guy come up with -theta?? Why didn't he say -x or something? How did -theta fit into the equation at 5:13 so smoothly?

Totally baffled at the moment. Help would be appreciated.

 

romsek

Math Team
Sep 2015
2,961
1,674
USA
I didn't watch the whole vid but he's got $\theta$ labled as the angular distance the inner circle travels during some period of time.
He's essentially using $\theta$ as a time variable.

Why $\theta$? Well it measures angular distance and $\theta$ is usually associated with an angle of some sort.

Why not $\theta$? You have some problem with $\theta$ ?
 
Jul 2013
476
40
United Kingdom
Well you have to watch the video carefully to understand what I mean. He doesn't explain how he got -theta. Any variable could have been used, why that though? Theta had already been used at the start of the video. If he used it again, he should have explained why. You can't just use theta for two different sized angles. He must explain how the second theta got there.
 
Jul 2013
476
40
United Kingdom
He found a relationship and didn't care to mention how he found it. It's a piece that's missing from the jigsaw puzzle.
 
Jul 2013
476
40
United Kingdom
I didn't watch the whole vid but he's got $\theta$ labled as the angular distance the inner circle travels during some period of time.
He's essentially using $\theta$ as a time variable.

Why $\theta$? Well it measures angular distance and $\theta$ is usually associated with an angle of some sort.

Why not $\theta$? You have some problem with $\theta$ ?
You can close the discussion. He has to be right not necessarily because theta is a time variable but because of a standard geometrical rule. No matter where the inner circle is, if you strike a line going through the starting point (on its edge) and its radius, which will inevitably intersect one of the lines which forms the angle theta on the large circle, the angle theta will be produced. What you essentially get is two parallel lines intersecting another line going through the radius of the large circle and the radius of the smaller circle. This is what the tutor didn't explain. I knew it had to be the reason why, but it only became obvious after using a pair of compasses to construct the proof.

I have to think of two points on the smaller circle. The starting point which never moves, and the new point which can change.
 
Last edited:

skipjack

Forum Staff
Dec 2006
21,481
2,470
What do you mean by "going through the radius"?