1+ hour, 57+ min ago  (208+ words) The'n queens problem is to place on an'n "n chessboard'n queens so that none attacks any other. This means there is only one queen on every horizontal, vertical, and diagonal line. When'n is a prime number " 5, it is sufficient to…...

4+ day, 11+ hour ago  (391+ words) I've been testing Claude's ability to generate Lean 4 code to prove theorems. I've written about a couple experiments that verified calculations. I did not write about my failed attempt to get Claude to formalize a proof of the pqr theorem…...

5+ day, 15+ hour ago  (139+ words) You can't prove a theorem by just checking a few examples. Except sometimes you can. A few weeks ago I wrote Pentagonal numbers are truncated triangular numbers. In a nutshell, if the pentagonal numbers are defined by and the triangular…...

6+ day, 6+ hour ago  (174+ words) I got an email message this afternoon reporting a typo in a blog post from about a year ago on converting between quaternions and rotation matrices [1]. The email said exactly where the typo was, but I decided to see whether…...

1+ week, 4+ day ago  (204+ words) I ran an experiment today to see whether Claude could generate Lean code to prove a calculation at the bottom of this post, six lines of calculus. I started with this prompt This page contains a mathematical proof that a…...

2+ week, 9+ hour ago  (256+ words) I ran across a cranky formula for " based on physical constants here and decided to play around with it. The source describes " as "wavelength (chosen in the microwave region)" and I thought perhaps you could chose a value of " to…...

2+ week, 2+ day ago  (399+ words) Yesterday I wrote a post showing that the trapezoid rule evaluates the integral very efficiently. But how do we know what the exact integral is for comparison? If you ask Mathematica, it will tell you the integral equals "2" J1(1) where J1 is…...

2+ week, 3+ day ago  (180+ words) Several posts lately have looked at the function f(x) = cos(sin(x) +x). This post will look at the function from a different angle. It's a smooth function with period 2, and it's very flat at odd multiples of, i. e. the first five derivatives…...

3+ week, 12+ hour ago  (115+ words) gives a fair approximation to the Gaussian density You can make the approximation much better by raising it to a power. The function gives a good lower bound and gives a good upper bound. More on that here. There are…...

3+ week, 1+ day ago  (303+ words) If a polynomial identity holds at a few random points, it's very like true. We'll make this statement more precise, but first let's look at some applications. You may want to test an identity that naturally presents itself as a…...