### Meta

### Categories

- algebra (47)
- arithmetic (85)
- books (34)
- calculus (7)
- challenges (57)
- combinatorics (29)
- complex numbers (6)
- computation (82)
- convergence (9)
- counting (38)
- famous numbers (48)
- fibonacci (18)
- fractals (13)
- games (34)
- geometry (72)
- golden ratio (8)
- group theory (28)
- humor (8)
- induction (8)
- infinity (19)
- iteration (24)
- links (76)
- logic (9)
- meta (43)
- modular arithmetic (30)
- number theory (108)
- open problems (11)
- paradox (1)
- pascal's triangle (8)
- pattern (105)
- people (23)
- pictures (74)
- posts without words (38)
- primes (57)
- probability (9)
- programming (20)
- proof (91)
- puzzles (18)
- recursion (16)
- review (24)
- sequences (28)
- solutions (31)
- teaching (15)
- trig (3)
- Uncategorized (6)
- video (19)

### Archives

- January 2020 (3)
- December 2019 (4)
- November 2019 (2)
- October 2019 (5)
- September 2019 (7)
- August 2019 (3)
- July 2019 (5)
- May 2019 (4)
- April 2019 (2)
- March 2019 (3)
- February 2019 (3)
- January 2019 (4)
- November 2018 (3)
- October 2018 (4)
- September 2018 (4)
- August 2018 (6)
- July 2018 (2)
- June 2018 (5)
- May 2018 (3)
- April 2018 (5)
- March 2018 (4)
- February 2018 (3)
- January 2018 (4)
- December 2017 (3)
- November 2017 (3)
- October 2017 (1)
- September 2017 (1)
- July 2017 (4)
- June 2017 (4)
- May 2017 (9)
- April 2017 (7)
- March 2017 (5)
- February 2017 (4)
- January 2017 (3)
- December 2016 (4)
- November 2016 (6)
- October 2016 (6)
- 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)

# Monthly Archives: September 2008

## Decimal expansion zoo

In a comment on a previous post about rational numbers and decimal expansions, Steve Gilberg noted: I’ve been fascinated at how any multiple of 1/7 thatâ€™s not an integer repeats the same digits in decimal expression, only starting at different … Continue reading

## Two Very Large primes

As promised, I can now reveal the identity of the two newly discovered Mersenne primes. The smaller of the two, discovered on September 6 by Hans-Michael Elvenich in Langenfeld, Germany, is an 11,185,272-digit number which you can download here. The … Continue reading

## New Mersenne primes!

The Great Internet Mersenne Prime Search just announced not one, but two new Mersenne primes! You might also recall the last time they announced a new prime, in September 2006, so these new primes were found almost exactly two years … Continue reading

Posted in computation, famous numbers, links, primes
Tagged announcement, discovery, GIMPS, Mersenne, prime
1 Comment

## Rational numbers and decimal expansions

As you may remember from school, rational numbers have a terminating or eventually repeating (periodic) decimal expansion, whereas irrational numbers don’t. So, for example, 0.123123123123…, with 123 repeating forever, is rational (in fact, it is equal to 41/333), whereas something … Continue reading

## Mandelbrot Maps

Run, don’t walk, to play with the Mandelbrot Maps applet, which lets you play around with the Mandelbrot set while seeing the associated Julia sets updated in real time. This fantastic applet was created by Iain Parris, an MSc student … Continue reading

Posted in fractals, links
Tagged applet, fractal, interactive, julia, mandelbrot, real-time