Tag: Approximation
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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…
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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.…