Posts 1 - 10 of 324

The Hat, a Tridecagon Aperiordic Monotile

Two years ago, in March of 2023, an unlikely team of mathematical hobbyists announced the discovery of a remarkable 13-sided polygon that they nick-named the "Hat". Today, a Google search for the Hat's more formal name, "Aperiodic Monotile", yields dozens of links.... 更多内容 >>

Matrices at an Exposition

A look at the structure, and the eigenvalues and singular values of interesting test matrices.... 更多内容 >>

Two Flavors of SVD

MATLAB has two different ways to compute singular values. The easiest is to compute the singular values without the singular vectors. Use svd with one output argument, s1.... 更多内容 >>

LUTool, Animation of Gaussian Elimination 2

LUTool provides an interactive animation of Gaussian elimination, the most important algorithm in technical computing.... 更多内容 >>

Code for Sonic and Ten Sonic Movies 2

Two previous blog posts, Dec. 12, 2024 and Nov. 16, 2024, introduced "Sonic", my new tool for incorporating sound in videos. Today's blog post includes a link to the MATLAB source code for Sonic, as well as links to new versions of ten examples.... 更多内容 >>

Sonic Adds Sound to Logo, Recamán, Chaos

I introduced Sonic in my blog post last month. Today I will use Sonic to add sound to the graphics from three old posts, the vibrating L-shaped membrane, the Recamán sequence and the chaotic behavior of the Swinging Sticks.... 更多内容 >>

Lights, Camera, Action — and Sound 4

I am very excited to incorporate sound in animations. This blog post has five examples with links to videos enclosed in '+ + + +'.... 更多内容 >>

Möbius, Mertens and Redheffer 6

Recently, I have made a series of blog posts about Redheffer matrices and the Mertens conjecture. After each of the posts, readers and colleagues offered suggestions to speed up the calculations. Here is a summary of what I have learned.... 更多内容 >>

Experience With Chatbots Generating MATLAB 1

A friend is investigating the use of generative AI in his classes. I asked two different popular chatbots to write MATLAB programs for a mathematically nontrivial problem. Both chatbots understood my query and both wrote plausible MATLAB programs, but one of the programs was not correct. My recommendation for coursework: carefully read and test programs produced by generative AI and repair any incorrect ones.... 更多内容 >>

Redheffer and Mertens, Accelerated 4

Shortly after I published the second post about the Mertens conjecture, a reader's comment suggested a new approach to computing Redheffer determinants and the Mertens function. It is now possible to compute a half-million values of the Mertens function in about five hours.... 更多内容 >>

Posts 1 - 10 of 324

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