Continued Fraction

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Continued fractions are better than mediants.

Math provokes dread in so many people—yet we are all born with a sense for numbers.

Recently I was invited to give a 1-hour tutorial at the Computing in Topological Structures workshop (CTS 2022) held partially by zoom and in person in Sochi, Russia. Here are the slides plus some …

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Sketch of The Analytical Engine

After I wrote recently about Ramanujan's approximation \(\pi^4\approx 2143/22\), writing "why do powers of \(\pi\) seem to have unusually good rational appro...

This book, originally published in 1765, is a gentle introduction to algebra by one of history's greatest mathematicians, Leonhard Euler. Starting with basic...

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The division of the chromatic scale in $7$ natural notes (white keys in a piano) and $5$ accidental ones (black) seems a bit arbitrary to me. Apparently, adjacent notes in a piano (including white...

This is going to a longish question, so the short version first: Is there a way to sanity-check which solution to the 3-term recurrence relation an application of Miller's algorithm has converged ...

Suppose you have a number x between 0 and 1. You want to find a rational approximation for x, but you only want to consider fractions with denominators below a given limit. For example, suppose x = 1/e = 0.367879… Rational approximations with powers of 10 in the denominator are trivial to find: 3/10, 36/100,

Computable Archive of Mathematics project's progress in representing abstract concepts of function spaces, topological spaces, general topology in the Wolfram Language.

Are there mathematical ways to prove that pi is an irrational number that has no end?

Math research gives meaning to years spent in prison

#4 in a series on dreams

Born poor in colonial India and dead at 32, Ramanujan had fantastical, out-of-nowhere visions that continue to shape the field today.

Article URL: https://www.galoisrepresentations.com/2023/03/23/deciphering-quanta/ Comments URL: https://news.ycombinator.com/item?id=35291663 Points: 1 # Comments: 0

In honor of Pi Day, we bring you a brief history of everyone's favorite irrational constant.

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