- 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

# Category Archives: fibonacci

## Wythoff’s game at Three-Cornered Things

I’ve really been enjoying Zachary Abel’s series of posts on Wythoff’s game [Wythoff’s Game: Red or Blue?; A Golden Observation; The “Fibonacci”est String; Wythoff’s Formula], over on his blog Three-Cornered Things. The Fibonacci numbers show up in the strangest places! … Continue reading

## Fibonacci multiples, solution 1

In a previous post, I challenged you to prove If evenly divides , then evenly divides , where denotes the th Fibonacci number (). Here’s one fairly elementary proof (though it certainly has a few twists!). Pick some arbitrary and … Continue reading

Posted in fibonacci, modular arithmetic, number theory, pattern, pictures, proof, sequences
Tagged divisibility, fibonacci, proof, remainders
5 Comments

## Nature by Numbers

This has been making the rounds of the math blogosphere (blathosphere?), but in case you haven’t seen it yet, check out Cristóbal Vila’s awesome short video, Nature by Numbers. Especially appropriate given that I have been writing about Fibonacci numbers … Continue reading

## 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

## Cassini’s identity

My previous post asked you to take any Fibonacci number, square it, and also multiply the two adjacent Fibonacci numbers, and see if a pattern emerged. Here’s a table I made for the first 6 Fibonacci numbers: (Hmm, the numbers … Continue reading

## A Fibonacci pattern

Recall the Fibonacci numbers, , the sequence of numbers beginning with where each subsequent number is the sum of the previous two: Try this: pick any Fibonacci number. Square it. Now, look at the two Fibonacci numbers on either side … Continue reading

Posted in algebra, arithmetic, challenges, fibonacci, pattern, sequences
Tagged fibonacci, number, pattern
4 Comments