Darius Bacon

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Trying to comment on this post: https://plus.google.com/+johncbaez999/posts/81M1B5TCmhb I keep getting back "Something isn't right. Can't share right now." Here's that comment as a post of its own, to see if that goes through. The original post sketches an idea for a toy to explore a certain polynomial. So:

I wrote a program last year that lets you drag the coefficient around and watch

If you want to try it, though, the idea is to do complex arithmetic by direct manipulation. You start by clicking or tapping on the canvas, which creates a point named 'a' (which you can rename to 'x' via the little form below the canvas). Click on this point to select it, then drag from the red multiplication sign that appears where '1' was, to your point -- you're stretching and turning the plane to make x^2, assuming you stop at x. Do this again to make x^3, x^4, x^5. Click somewhere else and rename to make 't'. Multiply t by x^3, then drag from the plus sign at the origin, to add to x^5 -- the plane slides along. Finally, add 1 by dragging from the origin to where 1 is, the same way. Now you have your polynomial, hurray -- how do you make it zero? You grab that point and drag it to the origin: notice when it's close to another point, the 'Merge points' button at the bottom becomes enabled. If you click that with the polynomial's value at the origin, it gets nailed down there -- now when you drag t around, the polynomial doesn't move, but x does! OK! Well, I really need to add some feature for sharing so that I could build this model and just link to it from here.

It should also be possible to construct the polynomial from its roots, and constrain that to equal the form we just built, but this comment has enough of how-to-use-this-GUI already.

I wrote a program last year that lets you drag the coefficient around and watch

**one**of the roots move. If you keep dragging you can visit the other roots, because the equation-solving is by gradient descent. It's at http://wry.me/math-toys/ and I'm afraid it's almost completely undocumented.If you want to try it, though, the idea is to do complex arithmetic by direct manipulation. You start by clicking or tapping on the canvas, which creates a point named 'a' (which you can rename to 'x' via the little form below the canvas). Click on this point to select it, then drag from the red multiplication sign that appears where '1' was, to your point -- you're stretching and turning the plane to make x^2, assuming you stop at x. Do this again to make x^3, x^4, x^5. Click somewhere else and rename to make 't'. Multiply t by x^3, then drag from the plus sign at the origin, to add to x^5 -- the plane slides along. Finally, add 1 by dragging from the origin to where 1 is, the same way. Now you have your polynomial, hurray -- how do you make it zero? You grab that point and drag it to the origin: notice when it's close to another point, the 'Merge points' button at the bottom becomes enabled. If you click that with the polynomial's value at the origin, it gets nailed down there -- now when you drag t around, the polynomial doesn't move, but x does! OK! Well, I really need to add some feature for sharing so that I could build this model and just link to it from here.

It should also be possible to construct the polynomial from its roots, and constrain that to equal the form we just built, but this comment has enough of how-to-use-this-GUI already.

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On Google+'s names policy: it's against the community standards of my preferred community, so I don't plan to post here any more.

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