2023 Joint Mathematics Meetings
Dan Bach
Artists
Dan Bach
3d math artist / book designer
dansmathshop
oakland, california, usa
http://sketchfab.com/dansmath/models
Statement
After a 36-year teaching career, I am now a 3D math artist and interactive book author, trying to bring the joy and beauty of mathematics to an unsuspecting audience. Students convinced me long ago that my nice-looking calculus graphs could qualify on their own as art. Math is still perceived by many as separate from art, but as creators and viewers of math art, we enjoy using both halves of our brains!
Artworks
The colored cylinders have length log(p) for various primes, starting with p = 2: red, 3: green, etc. Each number n, from 2 to 42, has a prime factorization n = p1 * p2 * … * pk, so that log(n) = log(p1) + … + log(pk). This makes the prime logs stack up just right! See if you can read off the factorizations of various n’s from the picture. The sun is made up of cyclotomic integers: linear combinations of fifth roots of unity in the complex plane. (Drawn in Mathematica and imported into Pixelmator.)
Based on the Prime Logs which have length log(p), each integer n is the product of its prime factors, so log(n) is the sum of all its log(p), shown as color-coordinated cylinders. These are arranged here in spirals and helices of various spacings and orientations. But in all six images the 2 is always red, 3 is green, 5 is purple, and you can see the rest. (Drawn with Mathematica and Pixelmator.)