My recent obsession with cubes in this blog has led me back to Rubik's cube, perhaps the greatest mathematical puzzle of all time.... 続きを読む >>

A few months ago, I had never heard of Karl Menger or the cube-like fractal that he invented. Now I have this long blog post about the sponge, and an extension that I am calling its "associate".... 続きを読む >>

A cube is the familiar three-dimensional solid with eight vertices, six faces and twelve edges. I have been working with cubes recently in posts about both the Menger sponge fractal and the 4-by-4 matrix from computer graphics.... 続きを読む >>

The complement of an evolving Menger sponge is all of the material that has been removed so far.... 続きを読む >>

Season's Greetings 2021 __________________________________________________________Marc Lätzel (2021). XMas Tree (https://www.mathworks.com/matlabcentral/fileexchange/9337-xmas-tree),MATLAB... 続きを読む >>

Matrices in action.... 続きを読む >>

See Cube and Teapot.... 続きを読む >>

Use a cube instead of the Utah Teapot in my previous post. I was pleasantly suprised by the final screen shot.... 続きを読む >>

Matrices like the ones shown in the following screen shots are at the heart of computer graphics. They describe objects moving in three-dimensional space. MATLAB's Handle Graphics uses them. So does MathWork's new RoadRunner editor. And so do all popular video games and CAD packages.... 続きを読む >>

Quaternions are generalizations of the complex numbers that have found applications in computer graphics and many other fields.... 続きを読む >>