## 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.

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.

[…] 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 » […]

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