The proof resolves a nearly 80-year-old problem known as the Duffin-Schaeffer conjecture. In doing so, it provides a final answer to a question that has preoccupied mathematicians since ancient times: ...

rational approximations of π (pi) using Python. Learn how fractions can closely approximate irrational numbers and discover why famous ratios like 22/7 and 355/113 work so well. We’ll use Python to ...

Time-domain simulation has become an indispensable tool in electrical engineering, enabling the detailed analysis of transient phenomena across complex systems. By numerically solving the differential ...

When my students grow too dependent on their calculators, I ask them to find a number that, when multiplied by itself, gives them 2. Students quickly see that since 1² = 1 and 2² = 4, the answer has ...

The ancient Greeks wondered when “irrational” numbers can be approximated by fractions. By proving the longstanding Duffin-Schaeffer conjecture, two mathematicians have provided a complete answer. The ...

Matrix functions, such as the exponential, square root and cosine, play an indispensable role in various fields including quantum mechanics, control theory and numerical solution of differential ...

This article was published in Scientific American’s former blog network and reflects the views of the author, not necessarily those of Scientific American The more I learn about continued fractions, ...