
Lattices and Fermat “Near Misses”
Nearly 400 years ago, the mathematician Pierre de Fermat famously claimed that there are no integer solutions to the equation: \[x^n + y^n = z^n\] when and . [And, after centuries, this extremely difficult theorem was completely proved in 1994.] Yet, even if there are no exact solutions to this equation, there are some striking…

Finding Anagrams with Sledgehammers
An anagram is a word (or phrase) that you get by rearranging the letters of another word (or phrase), for example: LISTEN SILENT ELEVEN PLUS TWO TWELVE PLUS ONE Traditionally, an anagrammist (i.e., someone looking to create anagrams) might start with a name and then look for interesting/humorous/clever anagrams, but there are plenty of other…

Tilings and Integer Programming
This is the story behind sequence A355477 from the Online Encyclopedia of Integer Sequences. Let’s say you have an unlimited supply of “zigzag” Tetris pieces: How many can you pack into an n x n square? For example, if you’re trying to fill a 4×4 square, then you can fit three such pieces: but, try…

Circular Reasoning in Ancient Egypt
In grade school, we all learned how to calculate the area of a circle: $$A = \pi r^2.$$ This formula dates back to Archimedes and the mathematics of ancient Greece, but the Greeks were not the only ancient civilization to tackle such problems. Other ancient cultures – including the ancient Babylonians, Egyptians, Indians, Chinese, etc.…