- algorithm approximation art bar beauty binary binomial coefficients birthday book review Carnival of Mathematics chocolate combinatorics complex consecutive cookies counting curve decadic decimal diagrams divisibility elements equivalence expansion factorization fibonacci finite fractal game games graph groups Haskell history hyperbinary idempotent identity integers interactive irrational Ivan Niven Lagrange lehmer lucas MaBloWriMo making Mersenne nim number numbers objects omega order permutations pi prime primes problem programming proof puzzle random rectangles repunit review sequence squares strategy subgroups symmetry test triangular video visualization X
### Blogroll

### Fun

### Reference

### Categories

- algebra (43)
- arithmetic (49)
- books (26)
- calculus (6)
- challenges (50)
- combinatorics (8)
- complex numbers (5)
- computation (38)
- convergence (9)
- counting (28)
- famous numbers (44)
- fibonacci (14)
- fractals (12)
- games (23)
- geometry (33)
- golden ratio (8)
- group theory (26)
- humor (6)
- induction (7)
- infinity (17)
- iteration (23)
- links (72)
- logic (6)
- meta (37)
- modular arithmetic (24)
- number theory (66)
- open problems (11)
- paradox (1)
- pascal's triangle (8)
- pattern (63)
- people (19)
- pictures (36)
- posts without words (6)
- primes (30)
- probability (5)
- programming (17)
- proof (56)
- puzzles (10)
- recursion (8)
- review (18)
- sequences (27)
- solutions (28)
- teaching (9)
- trig (3)
- Uncategorized (4)
- video (18)

### Archives

- February 2016 (4)
- 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

# Category Archives: group theory

## Origami stellated icosahedron!

Continuing what I started in December, I finally finished making a stellated icosahedron out of 30 Sonobe units. Each Sonobe unit corresponds to an edge of the icosahedron, and interlocks with three others to give the whole thing a remarkable … Continue reading

Posted in geometry, group theory
Tagged icosahedron, making, objects, origami, sonobe, stellated
3 Comments

## I made a Straws Thingy!

I finished my Straws Thingy! (You can see bigger versions of all the photos here.) It’s made out of 60 straws, 12 of each color. Three straws make a triangle; four triangles of each color are woven into a tetrahedron; … Continue reading

## Making stuff!

Recently I have been on a sort of kick making physical mathematical objects. First, inspired by this post on mathcraft.wonderhowto.com, I’ve learned how to fold origami Sonobe units and assemble them into various polyhedral things. So far, I’ve made a … Continue reading

## MaBloWriMo 30: Cyclic subgroups

Today, to wrap things up, we will use Lagrange’s Theorem to prove that if is an element of the group , the order of evenly divides the order of . So we have a group and an element . In … Continue reading

Posted in algebra, group theory, proof
Tagged cyclic, groups, Lagrange, MaBloWriMo, proof, subgroups
6 Comments

## MaBloWriMo 29: Equivalence classes are cosets

Today will conclude the proof of Lagrange’s Theorem! Recall that we defined subgroups and left cosets, and defined a certain equivalence relation on a group in terms of a subgroup . Today we’re going to show that the equivalence classes … Continue reading

Posted in algebra, group theory, proof
Tagged classes, cosets, equivalence, groups, Lagrange, MaBloWriMo, proof
Leave a comment

## MaBloWriMo 28: Equivalence relations are partitions

Today we’ll take a brief break from group theory to prove a fact about equivalence relations, namely, that they are the same as partitions. A partition is a pretty intuitive concept: you take a big set, and cut it up … Continue reading

Posted in algebra, group theory, proof
Tagged equivalence, groups, Lagrange, MaBloWriMo, partition, proof, relation
2 Comments

## MaBloWriMo 27: From subgroups to equivalence relations

Again, let be a group and a subgroup of . Then we can define a binary relation on elements of , called , as follows: if and only if there is some such that . That is, for any two … Continue reading

Posted in algebra, group theory, proof
Tagged equivalence, groups, Lagrange, MaBloWriMo, proof, relation, subgroups
Leave a comment