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.... 続きを読む >>

A look at the structure, and the eigenvalues and singular values of interesting test matrices.... 続きを読む >>

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.... 続きを読む >>

LUTool provides an interactive animation of Gaussian elimination, the most important algorithm in technical computing.... 続きを読む >>

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.... 続きを読む >>

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.... 続きを読む >>

I am very excited to incorporate sound in animations. This blog post has five examples with links to videos enclosed in '+ + + +'.... 続きを読む >>

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.... 続きを読む >>

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.... 続きを読む >>

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.... 続きを読む >>