Animated Fundamental Theorem of Algebra

April 23, 2010

This is what The Fundamental Theorem of Algebra looks like. Click on the above to get it to animate. The polynomial is given by f(z) = z³ – 4z² + 25z – 3000. Fix r>0, and plug in all values of z=x+iy into f such that x²+y²=r². This will give you a single snapshot of the above animation, which shows what happens as r increases. It looks as if there should be some value of r for which the curve crosses through 0, doesn’t it?

The animated .gif is so useful toward the explanation I have in mind that I may decide to write this next essay in .html form instead of as a .pdf. I’ve never tried to put LaTeX into html files before, so I don’t know exactly how well this is going to go. I’m also a bit annoyed that I can’t seem to get the animated .gif to autoplay, and I have to open a new window just for the image. Maybe it’s an annoying WordPress setting.

Advertisements

3 Responses to “Animated Fundamental Theorem of Algebra”

  1. rezniko2 said

    The animation is very good but to fast at the end: the interesting picture when the curve goes through 0 immediately dissapears.
    You can also try to draw it in Flash. It should be not so easy though.

    As far as I know, wordpress works with LaTeX pretty good, but if you want to put formulas in your .html file then it would be a pain. The best way that I know is to make each formula as a .gif and include it as a picture. However, it´ll be not very nice.

  2. […] Euler’s Formula and the Fundamental Theorem of Algebra (work just barely begun) – At the moment, there is only an animation of what happens when you plug in a circle of z-values into a polynomial as you increase the radius. This is one version of the proof, but the reason the animation looks the way it does is Euler’s Formula. I will someday say more. At the moment, I am not sure whether this article should be a .pdf (with no animation) or take the form of a web page. This and some subtleties in how to present the ideas have delayed work on further drafts for now. Possibly related posts: (automatically generated)Humanities HW 4/27Branding papers and articles…O levels so far Posted by Matthew Bond Filed in Uncategorized Leave a Comment » […]

  3. betrudy said

    Perhaps it would be best to just state more then drifting away from the original thought

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: