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?... 更多内容 >>

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.... 更多内容 >>

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 $x^3-2x-5$. ... 更多内容 >>

"New Directions in Numerical Computation" was a conference in celebration of Nick Trefethen's 60th birthday held August 25-28 in the new Andrew Wiles building, which houses the Mathematical Institute of the University of Oxford.... 更多内容 >>

A rectangular box, such as a book or a cell phone, thrown in the air can tumble stably about its longest axis, or about its shortest axis, but not about its middle axis.... 更多内容 >>

An interactive graphical experiment lets you discover the value of one of the most important numerical quantities in mathematics. ... 更多内容 >>

My experience with the forthcoming MATLAB watch exceeds my most optimistic expectations. The watch has not yet been announced officially, but a few of us have been testing prototypes for the past several weeks.... 更多内容 >>

I came across this "ornamental geometric inequality" in a tribute to Lothar Collatz.... 更多内容 >>

If $n$ is odd, replace $n$ by $3n+1$, if not, replace $n$ by $n/2$. Repeat. A famous conjecture made by Lothar Collatz is that no matter what value of $n$ is chosen to start, the process eventually terminates at $n=1$. Do not expect a proof, or a counterexample, in this blog. ... 更多内容 >>

The prime spiral was discovered by Stanislaw Ulam in 1963, and featured on the cover of Scientific American in March, 1964. ... 更多内容 >>