- algorithm Apollonian approximation art bar beauty binary binomial coefficients birthday book book review cards carnival Carnival of Mathematics Cassini chocolate combinatorics complex cookies counting decadic decimal diagrams elements expansion factorization fibonacci formula fractal game games gasket graph groups Haskell hyperbinary idempotent identity integers interactive irrational Ivan Niven Lagrange lehmer lucas MaBloWriMo making Mersenne nim number numbers objects omega order pi prime problem programming proof puzzle rectangles repunit review sequence square squares strategy subgroups tessellation test triangular units video visualization X
### Blogroll

### Fun

### Reference

### Categories

- algebra (43)
- arithmetic (58)
- books (28)
- calculus (6)
- challenges (51)
- combinatorics (8)
- complex numbers (5)
- computation (42)
- convergence (9)
- counting (31)
- famous numbers (48)
- fibonacci (18)
- fractals (12)
- games (24)
- geometry (45)
- golden ratio (8)
- group theory (26)
- humor (6)
- induction (7)
- infinity (17)
- iteration (23)
- links (73)
- logic (6)
- meta (40)
- modular arithmetic (24)
- number theory (67)
- open problems (11)
- paradox (1)
- pascal's triangle (8)
- pattern (79)
- people (20)
- pictures (51)
- posts without words (13)
- primes (33)
- probability (6)
- programming (17)
- proof (61)
- puzzles (11)
- recursion (12)
- review (19)
- sequences (28)
- solutions (28)
- teaching (13)
- trig (3)
- Uncategorized (4)
- video (19)

### Archives

- September 2016 (2)
- August 2016 (5)
- July 2016 (2)
- June 2016 (4)
- May 2016 (4)
- April 2016 (2)
- March 2016 (3)
- February 2016 (9)
- January 2016 (8)
- December 2015 (5)
- November 2015 (29)
- 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

# Monthly Archives: November 2007

## Google open-source programming contest

Are you a high school student? Are you interested in computer programming? You should participate in the Google Highly Open Participation Contest! The idea is that students compete to contribute features to various open source projects. You’re guaranteed to get … Continue reading

Posted in links

## Perfect numbers, part III

This is the last in a series of posts about perfect numbers. A quick recap of the series so far: in part I, I defined perfect numbers as positive integers n for which , where denotes the sum of the … Continue reading

Posted in algebra, number theory, open problems, primes, solutions
11 Comments

## Video: The Story of Pi

A fun video about , including a nice visual explanation of the formula for the area of a circle, and some interesting places that shows up where you might not expect it to. The video was made by Tom M. … Continue reading

Posted in famous numbers, geometry, links, video
5 Comments

## Perfect numbers, interlude (Challenge #11)

Recall that the first three perfect numbers are 6, 28, and 496. And if you tried computing as I suggested near the end of part I, you might have noticed that 8128 is perfect as well! Do you see any … Continue reading

Posted in challenges, famous numbers, number theory
4 Comments

## Video: Möbius transformations revealed

For your viewing pleasure, a fantastically beautiful video about Möbius transformations, which are functions of the form where z, a, b, c, and d are complex numbers, and . For example, is a Möbius transformation with b=2, c=1, and a=d=0. … Continue reading

Posted in complex numbers, geometry, video

## Perfect numbers, part II

In my last post I introduced the concept of perfect numbers, which are positive integers n for which , where denotes the sum of all the divisors of n. Incidentally, we could write the definition of as , that is, … Continue reading

Posted in algebra, famous numbers, number theory
8 Comments

## Perfect numbers, part I

Today I’d like to talk about perfect numbers, which touch on some clever algebra and some neat topics in number theory. At least, I’ll start talking about them, since it will probably take me three or four posts to say … Continue reading

Posted in famous numbers, number theory, sequences
3 Comments