Tags » Primes

Waring's Problem & Lagrange's Four-Square Theorem

Introduction

We are all familiar with the problem of splitting numbers into products of primes. This process is called factorisation. The problem of expressing numbers as… 759 more words

Occasional

Not going too far - just far enough

“Just how far would you like to go?” the enigmatic Frank asks in the sleeve notes to the Dylan album John Wesley Harding. “Not too far,” comes the reply. 365 more words

The Bookshelf

Duclos Lenses Acquires UniqOptics' Assets

The title pretty much says it all… But here’s the press release from Duclos Lenses, Inc.

DUCLOS LENSES ACQUIRES UNIQOPTICS’ ASSETS

September 22nd, 2014

Chatsworth, California… 197 more words

News

Crazy constructible polygons

Read on Prof Ian Stewart’s Twitter (@JoatStewart):

“Regular 618046320536701272583608037733434096317263320037227965361869850786715388113584129-gon is constructible with ruler compass & trisector

So is 756760676272923020551154471073240459834492063891235892290277703256956240171581788957704193-gon. 90-digit prime!

However, regular 11-gon is not constructible with ruler, compass, and angle-trisector.

25 more words
Fun (Maths NSFW)

The definition of a prime number

The standard definition of a prime number is an integer greater than 1 which is only divisible by itself and 1. While this definition is the simplest to state and often the easiest to work with, it’s not very… 588 more words

Mathematics

The harmonic series

The harmonic series is the expression

whose value is an infinite sum. Since the terms in the series become arbitrarily small as one goes further in (since for every positive real number and every positive integer greater than , the th term is smaller than ), one might expect the series to converge a finite value, but this is not the case—its value is actually infinite. 1,120 more words

Mathematics