Hi there,

I have a problem with math, if I can't visualize it I have problems understanding it...

Taking the standard equation (also called implicit?) for a circle:

I totally understand what this equation is saying. It's saying that the squared radius of the circle is equal to the length of the point at coordinates

by Pythorean theorem. (assuming origin is

)

The general equation of the circle is:

whenever

I understand how the general form results from the expansion of the standard form.

But my question is, would one attempt to visualize the general equation? Or simplify and attempt to visualize the standard form (which is easy to visualize).

I used the above for an example. There is quite a bit of stuff I've come across in math that I can't even visualize. What are your thoughts on that?

Thanks!

EDIT: On another note, looking at the fundamental theorem of algebra, I can see how it arises from the properties of numbers, but how the hell would you visualize it? Or would one not attemp that? Hence it being called abstract algebra (please correct me if I'm wrong)?