Thread: visualizing nth degree equations

Hi there, are there any good methods for visualizing quadratic and cubic equations?

Thanks!

Well, if you find the roots you would know where it has zeros. So for example if you find the roots of a quadratic and they're both real numbers, you know the graph crosses the x-axis at those values of x. If the only zero is at zero then you have a parabola. If the roots are imaginary it'll be strictly above or below the x-axis and not have any zeros. This can tell you a bit about what the graph of a given polynomial is like, if that's the kind of thing you're after.

Thanks for the reply Chemboy, but that's not really what I had in mind... I had a more "geometric" idea... I've been reading up about the Italian mathematicians who discovered solutions to the cubic (i.e. Gerolamo Cardano), but they were limited by their method of looking at the math, they had a geometric point of view, but not algebraic...

I'm interested in how they visualized this in terms of geometry, and by visualization, I mean how did they visualize both the quadratic and cubic equations?

Hope you know what I mean, thanks!

Originally Posted by rgba

Thanks for the reply Chemboy, but that's not really what I had in mind... I had a more "geometric" idea... I've been reading up about the Italian mathematicians who discovered solutions to the cubic (i.e. Gerolamo Cardano), but they were limited by their method of looking at the math, they had a geometric point of view, but not algebraic...

I'm interested in how they visualized this in terms of geometry, and by visualization, I mean how did they visualize both the quadratic and cubic equations?

Hope you know what I mean, thanks!

http://en.wikipedia.org/wiki/Algebraic_geometry

Good luck, Algebraic geometry requires a lot background in pure mathematics.

Hi DrRocket, thanks, yeah I had come to an understanding that was called algebraic geometry, had a look at it, saw what it looked like and said to myself, "bugger that, not now!" - surely there must be some sequence of geometrical constructs somewhere on the net that shows what the quadratic and cubics look like?

Hopefully at some point I'll be able to understand algebraic geometry...

Hopefully!