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: ...

New Proof Settles How to Approximate Numbers Like Pi | RealClearScienceThe proof resolves a nearly 80-year-old problem known as the Duffin-Schaeffer conjecture. In doing so, it provides a final answer ...

Why do irrational numbers exist? originally appeared on Quora: the place to gain and share knowledge, empowering people to learn from others and better understand the world. Answer by Alon Amit, PhD ...

Most people rarely deal with irrational numbers—it would be, well, irrational, as they run on forever, and representing them accurately requires an infinite amount of space. But irrational constants ...

This article is adapted from Shape: The Hidden Geometry of Information, Biology, Strategy, Democracy, and Everything Else by Jordan Ellenberg. © Penguin Press 2021 ...