# Fourier Trainer, TaylorTrainer

An intuitive interface for playing with coefficients of the first five Fourier terms (sin and cos) and respectively, the first five terms of the Taylor expansion, and see what happens to their sum, compared to the original function. Also, get an intuitive idea of minimizing distance in the sense of the infinite-dimensional metric. Fully usable before knowing advanced math.

# A Topological Picturebook

George Francis, 2006, A Topological Picturebook. If you need an excuse to buy, you may see there the tobacco pouch sphere eversion. But you don’t really need an excuse to buy. This is how visual textbooks should be.

# Outside In

This is a piece of mathematical animation history, and was made on the glorious PDP (for the kids out there, that’s a 16-bit machine. Yep, in our days these usually work as washing machine embedded controllers….) By Nelson Max, published in 1976. It is no exhaggeration to say that generations of mathematicians learned to visualize a possible sphere eversion thanks to this video.

Unfortunately the video is out of print and worse, the masters were lost. The original Topology Film series had four films: the sphere eversion, planar homotopies of curves 1 and 2, and the Sierpinski curve.

In the early 2000, the director worked on a remake of “Outside In”, published in 2004 by A K Peters. That videotape is, as well, very hard to find. Please feel free to contact me in private if you have a copy.

# Pendulums

We promised this week we’d post a multiple pendulums app. Sorry, I’m not sure we can keep our promise. We have many more. A quick search on one of our iDevices listed the following. Enjoy! Feel free to use the comments to suggest more.

Double Pendulum

DoublePendulum

Pendulums

ChaosPend

MechanicalPendulums

ChaosSwitchView2

TriplePendulum

SextuplePendulum

# Number-crunching

We all have heard about how important is qualitative analysis of, e.g., differential equations, lest the numerical solution leads us astray. But have we heard any lecture on situations which defy calculus, and yet can be tackled by a modern computer? Of course, the Monte Carlo method. Anything else? If you can’t come up with anything else, read the book by Paul Nahin for a lot more.