Dan Drake,
KAIST

Spring

2012 April 28

A “mathlet” is a small, interactive applet used to demonstrate or experiment with mathematical ideas. They are often web-based and written in Java.

You can easily make mathlets with Sage's “@interact” feature. And the embeddable Sage cell server means you can put @interacts anywhere — including right into this presentation!

Taylor polynomials for \(\sin(x^2 + 1)\sqrt{x+2}\):

The sequence

- \(\frac{1}{4} \sqrt{2} \sin\left(1\right) x + \sqrt{2} \sin\left(1\right) + \mathcal{O}(x^2)\)
- \(-\frac{1}{32} \left(\sin\left(1\right) - 32 \cos\left(1\right)\right) \sqrt{2} x^{2} + \frac{1}{4} \sqrt{2} x \sin\left(1\right) + \sqrt{2} \sin\left(1\right) + \mathcal{O}(x^3)\)
- ...

Making a bunch of drawings is better, but
can *you* make them look good? Make them correct? Convey the idea
of a sequence of polynomials converging to the original function? If
not...

This is the “canonical” example from the Sage wiki.

- Visit the Sage cell server: aleph.sagemath.org, or log into your account on any Sage server.
- Cut and paste some code from wiki.sagemath.org/interact or these slides.
- Enjoy!

These slides online at goo.gl/Nx9U3

- Thanks to Jason Grout and his students for the Sage cell server.
- Thanks to Ira Hanson for CSS help.
- The Newton's method code is available from gist.github.com/2469090.
- Dyck/Schröder code (and my paper) is at arXiv:1006.1959.

This work is licensed under a Creative Commons
Attribution-ShareAlike 3.0 Unported License.

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