Tag: Approximation

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…

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.…