- algorithm algorithms approximation arithmetic art Babylonian beauty binary binomial coefficients book review bracelets carnival Carnival of Mathematics change chess chess board combinatorics consecutive cookies counting decadic decimal derivatives diagrams divisibility divisors education expansion factorization fibonacci floor foundations fractal fractions game games GIMPS graph graphs Haskell history humor hyperbinary idempotent integers integral interactive intuition irrational irrationality Ivan Niven latex logic Mersenne metric multiplication negative notation number numbers permutations pi prime primes programming proof puzzle rectangles repunit review sequence squares triangular video visualization
### Blogroll

### Fun

### Reference

### Categories

- algebra (14)
- arithmetic (35)
- books (25)
- calculus (6)
- challenges (46)
- combinatorics (6)
- complex numbers (3)
- computation (30)
- convergence (9)
- counting (28)
- famous numbers (38)
- fibonacci (14)
- fractals (12)
- games (17)
- geometry (27)
- golden ratio (8)
- group theory (3)
- humor (6)
- induction (7)
- infinity (17)
- iteration (15)
- links (70)
- logic (6)
- meta (37)
- modular arithmetic (10)
- number theory (47)
- open problems (11)
- paradox (1)
- pascal's triangle (8)
- pattern (54)
- people (19)
- pictures (28)
- posts without words (3)
- primes (23)
- probability (3)
- programming (15)
- proof (42)
- puzzles (10)
- recursion (8)
- review (17)
- sequences (26)
- solutions (24)
- teaching (9)
- trig (3)
- Uncategorized (1)
- video (18)

### Archives

- May 2014 (1)
- December 2013 (1)
- October 2013 (1)
- July 2013 (1)
- June 2013 (1)
- May 2013 (1)
- April 2013 (3)
- March 2013 (3)
- February 2013 (2)
- January 2013 (5)
- December 2012 (3)
- November 2012 (4)
- October 2012 (5)
- September 2012 (1)
- August 2012 (4)
- July 2012 (1)
- June 2012 (6)
- May 2012 (2)
- April 2012 (3)
- March 2012 (1)
- February 2012 (4)
- January 2012 (5)
- December 2011 (1)
- November 2011 (7)
- October 2011 (4)
- September 2011 (6)
- July 2011 (2)
- June 2011 (4)
- May 2011 (5)
- April 2011 (2)
- March 2011 (4)
- February 2011 (1)
- January 2011 (1)
- December 2010 (1)
- November 2010 (4)
- October 2010 (2)
- September 2010 (1)
- August 2010 (1)
- July 2010 (1)
- June 2010 (2)
- May 2010 (3)
- April 2010 (1)
- February 2010 (6)
- January 2010 (3)
- December 2009 (8)
- November 2009 (7)
- October 2009 (3)
- September 2009 (3)
- August 2009 (1)
- June 2009 (4)
- May 2009 (5)
- April 2009 (4)
- March 2009 (2)
- February 2009 (1)
- January 2009 (7)
- December 2008 (1)
- October 2008 (2)
- September 2008 (7)
- August 2008 (1)
- July 2008 (1)
- June 2008 (1)
- April 2008 (5)
- February 2008 (4)
- January 2008 (4)
- December 2007 (3)
- November 2007 (12)
- October 2007 (2)
- September 2007 (4)
- August 2007 (3)
- July 2007 (1)
- June 2007 (3)
- May 2007 (1)
- April 2007 (4)
- March 2007 (3)
- February 2007 (7)
- January 2007 (1)
- December 2006 (2)
- October 2006 (2)
- September 2006 (6)
- July 2006 (4)
- June 2006 (2)
- May 2006 (6)
- April 2006 (3)
- March 2006 (6)

### Meta

# Monthly Archives: January 2009

## Carnival of Math #48, and Monday Math Madness #25

The 48th Carnival of Mathematics is posted at Concrete Nonsense. My favorite posts include Foxmath’s post about a strange iterated sequence involving pi and this amazing picture of a fractal cabbage. Also near and dear to my heart is Mark … Continue reading

Posted in challenges, counting, famous numbers, fractals, links
Tagged carnival, counting, fractal cabbage, monads, pi
1 Comment

## More on repetend lengths

In a previous post, I noted that the length of the repetend (repeating portion of the decimal expansion) of a fraction with prime denominator p is at most p-1, and in fact divides p-1. I also said: In fact, there’s … Continue reading

Posted in group theory, number theory, pattern, primes
Tagged decimal, expansion, fractions, length, repetend
6 Comments

## New bookshelf entry: The Annotated Turing

For my birthday I got, among other things, a copy of The Annotated Turing: A Guided Tour Through Alan Turing’s Historic Paper on Computability and the Turing Machine, by Charles Petzold. I haven’t finished reading it yet, but so far, … Continue reading

## More on decimal expansions

Today, I’d like to answer some of the questions I raised in the Decimal Expansion Zoo: Which decimal expansions terminate, and which are repeating—and how does it relate to the denominator? As we know, the decimal expansion of every rational … Continue reading

## Carnival of Mathematics and other links

The 47th Carnival of Mathematics has been put together by jd2718; go give it a read! Some of my favorite posts include factoring by puzzles, teaching binary numbers, the 2009 game, cliques of dichotomies, but there is lots of other … Continue reading

## Predicting pi: pretty graphs and convergents

Recall the challenge I posed in a previous post: given the sequence of integers , what can you learn about (assuming you didn’t know anything about it before)? The answer, as explained in another post, is that you can learn … Continue reading

Posted in convergence, famous numbers, pattern, sequences
Tagged approximation, convergents, graphs, pi
5 Comments