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 >>

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 >>

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 >>

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

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 >>

We say that a deck of playing cards iscompletely shuffledif 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 inmy previous postthat a perfect faro shuffle fails to completely shuffle a deck. But ariffle shuffle,一些随机性在这个过程中,可以产生complete shuffling. How many repeated riffle shuffles does that take?...read more >>

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 >>

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 >>

Use the historic cubic polynomial $x^3 - 2x - 5$ to test a few zero-finding algorithms....read more >>