- algorithm algorithms approximation arithmetic art Babylonian beauty binary binomial coefficients 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 logic Mersenne metric number numbers permutations pi prime primes 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 (46)
- combinatorics (6)
- 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 (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 (17)
- proof (42)
- puzzles (10)
- recursion (8)
- review (17)
- sequences (26)
- solutions (24)
- teaching (9)
- trig (3)
- Uncategorized (2)
- video (18)

### Archives

- 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

# Tag Archives: triangular

## Triangular number equations via pictures: solutions

Here are some solutions to my previous post. However, they are almost certainly not the only solutions! If you have other cool ways to visualize any of these (or any other triangular number equations) feel free to post in the … Continue reading

Posted in arithmetic, pattern, pictures, proof, solutions
Tagged number, pictures, proof without words, triangular
10 Comments

## Triangular number equations via pictures

The other day I was fiddling around a bit with triangular numbers. By only drawing pictures I was able to come up with the following triangular number equations, where denotes the th triangular number (that is, the number of dots … Continue reading

## Triangunit divisors and quadratic reciprocity

Recall that the triangunit numbers are defined as the numbers you get by appending the digit 1 to the end of triangular numbers. Put another way, where denotes the th triangular number, and the th triangunit number. The challenge, posed … Continue reading

Posted in arithmetic, modular arithmetic, number theory, primes, proof
Tagged OEIS, quadratic, reciprocity, triangular, triangunit
5 Comments

## Triangunit divisors

Here’s a neat problem from Patrick Vennebush of Math Jokes 4 Mathy Folks: Append the digit 1 to the end of every triangular number. For instance, from 3 you’d get 31, and from 666 you’d get 6,661. Now take a … Continue reading

Posted in number theory, pattern, puzzles
Tagged divisors, numbers, triangular, triangunit, unit
9 Comments

## Math Teachers at Play #21

Math Teachers at Play #21 is up at Math Mama Writes…, and it includes this cute puzzle, which Sue apparently made up herself: The Numberland News runs personal ads. 21 was looking for a new friend and put an ad … Continue reading

Posted in fibonacci, links, number theory, puzzles
Tagged binary, fibonacci, MTaP, palindrome, puzzle, semi-prime, triangular
13 Comments