Further Twists of the Moebius Strip

Posted by Cleve Moler,

The equations generating a surf plot of the Moebius strip can be parameterized and the parameters allowed to take on expanded values. The results are a family of surfaces that I have been displaying for as long as I have had computer graphics available.... read more >>

The Eigenwalker Model of the Human Gait

Posted by Cleve Moler,

A model of the human gait, developed by Nikolaus Troje, is a five-term Fourier series with vector-valued coefficients that are the principal components for data obtained in motion capture experiments involving subjects walking on a treadmill.... read more >>

Dark Energy Gravitational Waves

Posted by Cleve Moler,

Recent theoretical, observational and computational results establish the possibility that gravitational waves produced by the dark energy created at the dawn of the universe affect the clock rate of silicon digital processors operating at very low temperatures.... read more >>

Piet Hein, Super Ellipses and Soma Cubes3

Posted by Cleve Moler,

An extraordinarily creative Danish mathematician, inventor, and poet who often wrote under the Old Norse pseudonym "Kumbel" meaning "tombstone." A direct descendant of the Dutch naval hero of the 16th century who had the same name, Piet Hein was born in Copenhagen and studied at the Institute for Theoretical Physics of the University of Copenhagen (later the Niels Bohr Institute) and the Technical University of Denmark. ... read more >>

Investigating the Classic Crossed Ladders Puzzle

Posted by Cleve Moler,

Today's blog post is a complete working MATLAB program investigating the crossed ladders problem. Download a copy of the program via the link at the end. Publish it again with the publish command or the publish editor tab.... read more >>

Posted by Cleve Moler,

Here is a classic puzzle. A pair of ladders leaning against the sides of an alley form a lopsided cross. Each ladder is propped against the base of one wall and leans against the opposite wall. If one ladder is 30 feet long, the other 20 feet long, and the point where they cross 10 feet above the ground, how wide is the alley?... read more >>

How Many Times Should You Shuffle the Cards?

Posted by Cleve Moler,

We say that a deck of playing cards is completely shuffled if it is impossible to predict which card is coming next when they are dealt one at a time. So a completely shuffled deck is like a good random number generator. We saw in my previous post that a perfect faro shuffle fails to completely shuffle a deck. But a riffle shuffle, with some randomness in the process, can produce complete shuffling. How many repeated riffle shuffles does that take?... read more >>

Perfect Shuffles of Playing Cards

Posted by Cleve Moler,

When a deck of playing cards is shuffled perfectly, the result is not random. A perfect shuffle places the cards in a mathematically precise order. As a result, when the most common version of a perfect shuffle is repeated eight times, the deck returns to its original state.... read more >>

Fractal Global Behavior of Newton’s Method

Posted by Cleve Moler,

When the starting point of Newton's method is not close to a zero of the function, the global behavior can appear to be unpredictable. Contour plots of iteration counts to convergence from a region of starting points in the complex plane generate thought-provoking fractal images. Our examples employ the subject of two recent posts, the historic cubic $x^3-2x-5$.... read more >>

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