- algorithm algorithms approximation arithmetic art Babylonian beauty binary binomial coefficients birthday book review bracelets carnival Carnival of Mathematics change chess chess board combinatorics complex 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 Mersenne number numbers permutations pi prime primes problem programming proof puzzle random rectangles repunit review sequence squares symmetry triangular video visualization
### Blogroll

### Fun

### Reference

### Categories

- algebra (14)
- arithmetic (35)
- books (25)
- calculus (6)
- challenges (47)
- combinatorics (8)
- complex numbers (5)
- computation (30)
- convergence (9)
- counting (28)
- famous numbers (38)
- fibonacci (14)
- fractals (12)
- games (17)
- geometry (29)
- golden ratio (8)
- group theory (3)
- humor (6)
- induction (7)
- infinity (17)
- iteration (15)
- links (71)
- 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 (5)
- programming (17)
- proof (42)
- puzzles (10)
- recursion (8)
- review (17)
- sequences (26)
- solutions (25)
- teaching (9)
- trig (3)
- Uncategorized (2)
- video (18)

### Archives

- August 2015 (3)
- June 2015 (2)
- April 2015 (1)
- 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

# Category Archives: arithmetic

## Factorization diagram posters!

I’ve finally gotten around to making a nice factorization diagram poster: You can buy high-quality prints from Imagekind. (If you order soon you should have them before Christmas! =) I’m really quite happy with imagekind, the print quality is fantastic … Continue reading

Posted in arithmetic, counting, geometry, number theory, pattern, pictures, primes
Tagged diagrams, factorization, posters
7 Comments

## Animated Sieve of Eratosthenes

Here’s something I made yesterday! (Note, I strongly suggest watching it fullscreen, in HD if you have the bandwidth for it.) Can you figure out what’s going on? The source code for the animation is here; I was inspired by … Continue reading

Posted in arithmetic, counting, pattern, pictures, primes, video
Tagged diagrams, Eratosthenes, primes, sieve, visualization
12 Comments

## Factorization diagram cards: help?

The other day I got a lovely email from Malke Rosenfeld thanking me for creating factorization diagrams and linking me to her blog post about “factor dominoes”: she printed out some factorization diagrams, glued them to cardstock, and used the … Continue reading

## Mersenne primes and the Lucas-Lehmer test

Mersenne numbers, named after Marin Mersenne, are numbers of the form . The first few Mersenne numbers are therefore , , , , , and so on. Mersenne numbers come up all the time in computer science (for example, is … Continue reading

Posted in arithmetic, computation, famous numbers, iteration, modular arithmetic, number theory, primes
Tagged lehmer, lucas, Mersenne, prime, test
3 Comments

## More factorization diagrams

My post on factorization diagrams from a month ago turned out to be (unexpectedly) quite popular! I got ten times as many hits as usual the day it was published, and since then quite a few other people have created … Continue reading

Posted in arithmetic, links, pictures, primes, programming, recursion
Tagged diagrams, factorization, Haskell
15 Comments

## Factorization diagrams

In an idle moment a while ago I wrote a program to generate "factorization diagrams". Here’s 700: It’s easy to see (I hope), just by looking at the arrangement of dots, that there are in total. Here’s how I did … Continue reading

Posted in arithmetic, pictures, primes, programming, recursion
Tagged diagrams, factorization, Haskell
72 Comments

## Fibonacci multiples

I haven’t written anything here in a while, but hope to write more regularly now that the semester is over—I have a series on combinatorial proofs to finish up, some books to review, and a few other things planned. But … Continue reading

Posted in arithmetic, challenges, fibonacci, number theory, pattern
Tagged divisibility, fibonacci
12 Comments