How do you find "Cool Things" to share in your own classes? In this list, we are sharing a few of our ideas, with hopefully a few pointers so you can start creating your own list:

#### Share what is interesting and exciting to you about the world and mathematics

- Tell stories! The students love to hear stories; stories about you, or your kids, etc., or stories about mathematics and mathematicians.
- Read them cool things that you have recently read, e.g. from:
- Notices AMS
- Monthly, Math. Mag., CMJ
- Scientific American
- New York Times

#### Using Ideas from our Books for "Cool Things"

- 4 dimensions and the hypercube using soap bubbles Geometry
- 0.99999... = 1, The Infinite and Patterns
- Gabriel's Wedding Cake, The Infinite
- Surreal Numbers, The Infinite
- Goldbach's Conjecture, Number Theory
- Fractals and Chaos, Geometry and Proof
- Grandi series, The Infinite
- Tangles, Knot Theory
- Polyominoes, Knot Theory
- Butterfly effect, Proof
- Bees as mathematicians, Student toolbox
- Millinillitrillion, Patterns
- Flexagons and Feynman stories, Art and Sculpture
- Perspective drawing, Geometry

#### Connections with Nature

- The 4 dimensional torus and how the universe might be finite (Jeff Weeks: The shape of Space)
- Dance of the planets Dance of the planets and how it connects to star polygons and salsa rueda ( Dance )
- Fibonacci
- Number of Trees (NPR story)

#### Connections with Society

- Arithmetic is not equal to mathematics.
- Voting and voter registration
- Share some news from the math education world (K-12 teaching, testing,...).
- Talk about the mathematics behind fingerprinting and how fingerprinting is not always correct.

#### Being a Mathematician

- What does it mean to you to be a mathematician?
- Colbert clip about Perlman and the Poincaré Conjecture.
- Dance my phd example
- Stories about how you learned mathematics and why you fell in love with it.
- Mathematical Reviews (With Stewart quote about more mathematics in the past 50 years)
- Fields Medal
- Women in mathematics
- Ask students if they know the name of a famous mathematician. They probably don't know anyone! Tell lots of stories about mathematicians, e.g.
- Alan Turing – Enigma and leopard spots
- Code Talkers
- Wiles
- Lewis Carroll was a mathematician

#### Games

- Jeff Week’s geometry games
- Straight cut origami ( Art and Sculpture ) and Erik Demaine
- The game nim ( Games and Puzzles -- play 3 piles against them and win all the time sorting piles using base 2)
- Show a maypole pattern and think about the math involved
- Math magic – Mathematical magic tricks -
- Domino Artwork and Obaminoes -
- Peg Solitaire using group theory

#### Cool student work

- Show slice forms created by students
- Show string art created by students
- Read a math poem or a poem a student wrote
- 8 graders found Rascal’s Theorem
- 13 year old invents solar tree

#### Connection with the Arts

- Play math inspired music that a student composed
- Look at math and art exhibit in the department hallway
- Show Dmitri Tymoczko's space of musical chords
- Show the space of salsa dancing – paper by Volker Ecke and Christine von Renesse

#### Other Cool Mathematics

- Milennium Prize Problems
- Minimal surfaces
- Tessellations
- Euler characteristic
- Dragon curves
- Kaleidoscopes
- Soap bubbles and paths
- M.C. Escher
- Mathematics on The Simpsons
- Fourth Dimension – Bring in the Glasses and do the animated hypercube.
- Googol the number (named by a kid) and Google the website (spelled wrong!)
- $e^{i \pi}+1=0$
- Mersenne Prime Search – GIMPS and the reward, Number Theory
- Why $\pi$? Why does it go on forever? How do we know?
- Penrose tilings and inflation and the fractal nature of the proof.
- SETI at home
- Daniel Tammet: the boy with the incredible brain