Math challenge!

Ok, you have two circles such as these: http://www.cut-the-knot.org/Outline/...gCircles.shtml

The bigger circle has the equation x^2+y^2=16. The smaller circle has a radius of 1. If we were to have the smaller circle go around the bigger one (as though the bigger one were a surface and the smaller one were a tire) and we kept track of a single point on the edge of the smaller tire and drew a dot on every point it touched on the plane, once the smaller tire had made a complete revolution around the bigger one, what would the total enclosed area be that the point on the smaller tire made?

Hey MJ, whats your IQ.

Hey MJ, whats your IQ.

Lol, that's not relevant. More importantly, I don't know. It's not that complicated of a problem. If nobody gets it in a couple of days, I'll post a hint.

It's not that complicated of a problem.

WTF. I don't even know what those small upper-type arrows are.

WTF. I don't even know what those small upper-type arrows are.

"x squared"

^ = exponent

Now that you've blessed me. Lemme give it a try.

Edit: Nevermind I came across this shit "||" and got stumped.

I quit.

Geometry hurts me.

Hint: The parametric equations of the path created by the point on circle r=1 are x(t)=5cos(t)+cos(5t), y(t)=5sin(t)+sin(5t), where 0<=t<=2*pi

Here's a better picture:



It's like the one on the right.

Ah, that makes more sense.

The question confused me somewhat:

If we were to have the smaller circle go around the bigger one (as though the bigger one were a surface and the smaller one were a tire) and we kept track of a single point on the edge of the smaller tire and drew a dot on every point it touched on the plane, once the smaller tire had made a complete revolution around the bigger one, what would the total enclosed area be that the point on the smaller tire made?

To me that meant a dot everytime it touched the other circle, and thus the area enclosed by those dots - the area of the bigger circle.

I've got a vague idea of how I might solve it, so I might get it done during my free's tomorrow. Or give it to one of my Uber Maths Genius friends and see what they make of it.

EDIT: I wonder if I can somehow make it a graph and use integration to find the area of each curve over the circle, and then add in the area of the circle...

EDIT: I wonder if I can somehow make it a graph and use integration to find the area of each curve over the circle, and then add in the area of the circle...

You're on the right track.