Information that is declared to be forever inaccessible is sometimes revealed within a short period. Until recently, it seemed impossible that we would ever know the value of the quintillionth decimal digit of pi. But a remarkable formula has been found that allows the computation of binary digits starting from an arbitrary position without the need to compute earlier digits. This is known as the BBP formula.

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## Posts Tagged 'Number Theory'

### The remarkable BBP Formula

Published August 8, 2013 Occasional Leave a CommentTags: Archimedes, Computer Science, History, Number Theory, Pi

### The Ups and Downs of Hailstone Numbers

Published July 11, 2013 Occasional 1 CommentTags: Algorithms, Arithmetic, Number Theory

Hailstones, in the process of formation, make repeated excursions up and down within a cumulonimbus cloud until finally they fall to the ground. We look at sequences of numbers that oscillate in a similarly erratic manner until they finally reach the value 1. They are called** hailstone numbers**.

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### Amazing Normal Numbers

Published June 21, 2013 Occasional Leave a CommentTags: Number Theory, Recreational Maths

For any randomly chosen decimal number, we might expect that all the digits, 0, 1 , … , 9, occur with equal frequency. Likewise, digit pairs such as 21 or 59 or 83 should all be equally likely to crop up. Similarly for triplets of digits. Indeed, the probability of finding any finite string of digits should depend only on its length. And, sooner or later, we should find any string. That’s “normal”!

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### Prime Secrets Revealed

Published June 5, 2013 Irish Times Leave a CommentTags: Number Theory, Primes

This week, *That’s Maths* in the *Irish Times* ( TM022 ) reports on two exciting recent breakthroughs in prime number theory.

The mathematics we study at school gives the impression that all the big questions have been answered: most of what we learn has been known for centuries, and new developments are nowhere in evidence. In fact, research in maths has never been more intensive and advances are made on a regular basis.

### Dis, Dat, Dix & Douze

Published April 18, 2013 Occasional Leave a CommentTags: Arithmetic, Number Theory

How many fingers has Mickey Mouse? A glance at the figure shows that he has three fingers and a thumb on each hand, so eight in all. Thus, we may expect Mickey to reckon in octal numbers, with base eight. We use decimals, with ten symbols from 0 to 9 for the smallest numbers and larger numbers denoted by several digits, whose position is significant. Thus, 47 means four tens plus seven units.

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### Happy Pi Day 2013

Published March 14, 2013 Occasional Leave a CommentTags: Archimedes, Number Theory, Pi

Today, 14th March, is Pi Day. In the month/day format it is 3/14, corresponding to 3.14, the first three digits of π. So, have a Happy Pi Day. Larry Shaw of San Francisco’s Exploratorium came up with the Pi Day idea in 1988. About ten years later, the U.S. House of Representatives passed a resolution recognizing March 14 as National Pi Day.

Today is also the birthday anniversary of Albert Einstein, giving us another reason to celebrate. He was born on 14 March 1879, just 134 years ago today.

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### Chess Harmony

Published January 30, 2013 Occasional Leave a CommentTags: Games, Number Theory, Puzzles, Recreational Maths

Long ago in the Gupta Empire, a great-but-greedy mathematician, Grababundel, presented to the Maharaja a new game that he had devised, called Chaturanga.

Thirty-two of the Maharaja’s subjects, sixteen dressed in white and sixteen in black, were assembled on a field divided into 64 squares. There were rajas and ranis, mahouts and magi, fortiers and foot-soldiers. Continue reading ‘Chess Harmony’

### Ramanujan’s Lost Notebook

Published December 6, 2012 Irish Times 2 CommentsTags: Number Theory, Ramanujan

In the *Irish Times* column this week ( TM010 ), we tell how a collection of papers of Srinivasa Ramanujan turned up in the Wren Library in Cambridge and set the mathematical world ablaze. Continue reading ‘Ramanujan’s Lost Notebook’

### The Root of Infinity: It’s Surreal!

Published November 22, 2012 Occasional 1 CommentTags: Analysis, Number Theory

Can we make any sense of quantities like “the square root of infinity”? Using the framework of *surreal numbers*, we can.

- In Part 1, we develop the background for constructing the surreals.
- In Part 2, the surreals are assembled and their amazing properties described.

### A Mersennery Quest

Published November 1, 2012 Irish Times Leave a CommentTags: History, Number Theory, Primes

**The theme of That’s Maths (TM008) this week is prime numbers. Almost all the largest primes found in recent years are of a particular form **

*M*(

*n*)

*=*2

^{n}

*−*1

**. They are called Mersenne primes. The**Continue reading ‘A Mersennery Quest’

*Great Internet Mersenne Prime Search*(GIMPS) is aimed at finding ever more prime numbers of this form.### The Beautiful Game

Published September 14, 2012 Occasional Leave a CommentTags: Games, Number Theory

What is the most beautiful rectangular shape? What is the ratio of width to height that is most aesthetically pleasing? This question has been considered by art-lovers for centuries and one value appears consistently, called the golden ratio or Divine proportion. Continue reading ‘The Beautiful Game’