### Here are some links to fun (or thought-provoking) math sites:

#### TRICKS AND MIND TEASERS

Telephone Number Trick

Chocolate Math

Comic Book Math

#### GAMES AND PUZZLES

Towers of Hanoi Puzzle

Planarity

Set Daily Puzzle

Math Game and Puzzle Site

Nets of Cubes

#### VIDEO CLIPS

Fractal Zoom Animation

Hypercube Animation You can also find this on Wikipedia and see a version that rotates endlessly, and, yes, it is rotating, not turning inside out!

The Pi Song  - to the tune of American Pie -lyrics and performance by Dr. Arthur Benjamin - world-famous mathemagician.

Best Function EVER! YouTube music video of OK GO's "This to Shall Pass."  A mathematical function is a machine to provide outputs for given inputs.  OK GO has created the most amazing machine I've ever seen for achieveing an output from an input!  You've got to see it to believe it!

0.9 Repeating = 1 (by Vi Hart)

Animation of the Hilbert Hotel an exploration of one sort of infinity

Kentucky Math Ma and Pa Kettle do math.

Sarah's Certain Death Riddle (Logic from Labyrinth)

Julia Sets Relative to the Mandelbrot Set For this video you really need to understand the topic before the video will be meaningful to you, as there isn't background explanation with it, but if you know about the M-Set and Julia Sets I think you'll enjoy this animation about the relationship.  Of course you can watch it just for the pretty pictures too.

Fibonacci Numbers in Nature - just beautiful - sit back and enjoy.

Fascinating Fibonaccis This is a six and a half minute video, a TED talk given by Arthur Benjamin.  It includes some neat properties of the Fibonacci Numbers that are not usually seen in classes.  He also addresses how and why we learn math.  I wish this talk were more than 6 minutes long - both because there is so much more cool stuff to see about Fibonacci Numbers and because there's so much more he could have said, given time, about what math is and why we learn it.

Short Mandelbrot Autobiography In this clip Beniot Mandelbrot, the Father of Fractal Geometry, gives a brief history of his family and his early education.

Math and Animated Movie Characters At about 16 minutes, this video from Numberphile is a bit more than a "clip," but it is a cool explanation of part of what is behind how Pixar creates animated movie characters.

Animated New Math Song - Everything old is new again!! Tom Lehrer's classic song decrying the "New Math" could be just as well applied (for good or ill) to today's Common Core!  This is a full version of the song with illustrations throughout.

#### FULL LENGTH VIDEOS

The Story of 1 The story of the number one is the story of Western civilization. Terry Jones ("Monty Python's Flying Circus") goes on a humor-filled journey to recount the amazing tale behind the world's simplest number. Using computer graphics, "One" is brought to life, in all his various guises, in STORY OF 1

Fractals: Hunting the Hidden Dimension  NOVA presentation of the dynamic new branch of mathematics known as fractal geometry.

Fractals: The Colors of Infinity  This is a somewhat older presentation about fractal geometry put out by Films for the Humanities and Sciences.  It is narrated by Arthur C. Clarke

Fermat's Last Theorem  BBC Horizon program. Simon Singh's moving documentary of Andrew Wiles' extraordinary search for the most elusive proof in number theory.

The Fourth Dimension This is the best introduction to the fourth dimension I have ever seen.  It is presented by Dr. Edward Burger of Williams College.  It is very accessible and is actually a talk given to a general audience (not just to mathematicians).  It gives a good idea of what it would be like to be able to use the fourth dimension - the possibilities that would give us and why - very entertaining as well.  HINT: Before you watch it, make sure you have a free hour because you can't pause or rewind this one.

The Golden Ratio An hour-and-a-half presentation by Keith Devlin (NPR's "Math Guy"), in which he explores the Golden Ratio and also corrects common misconceptions about this number.

RAMANUJAN: Letters from an Indian Clerk The extraordinary story of how in 1914 the self-taught math genius Srinivasa Ramanuhan was brought from Madras to Trinity College, Cambridge, by the great English pure mathematician GH Hardy, who called their relationship 'the one truly romantic episode of my life'. A 1987 documentary for the Channel 4 'Equinox' science series. Uploaded to YouTube from an old VHS tape.

Breaking the Code: Biography of Alan Turing This 90-minute BBC documentary movie stars Derek Jacobi as tragic and amazing code-breaking mathematician Alan Turing, whose mathematical work at Bletchley Part, England during WWII is said to have shortened the length of the war by two to three years.

Fermat's Last Theorem This is a BBC/Horizon documentary about the history of the centuries-long search for a proof for one of the most famous problems in mathematics Fermat's Last Theorem.  It focuses a great deal on the life and work of mathematician Andrew Wiles who is the mathematician who finally discovered a proof.

Mathemagic! This is a TED video of Mathematician Arthur Benjamin doing amazing feats of mathematical magic.  This video is only about 15 minutes long but packed with fun, cool stuff!

Monster Primes This is a TED video of Adam Spencer an Australian talk show host who is also passionate about math.  He shared how and why he fell in love with numbers and how large the current largest prime is (Feb. 2013).  The talk is only about 15 minutes long, and the punch line is really a good explanation of how big the current largest prime is.

Spring 2012 MAPS Presentation - "Infinite Possibility: The Importance of Mathematical Play" This is an hour-long presentation I gave at Modesto Junior College for Modesto Area Partners in Science.  Within a framework of play, topics include graph theory, knot theory, and tessellations.

Fall 2016 MJC Science Colloquium Presentation - "Overcoming Obstacles: 19th Century Women of Mathematics" This is an hour-long presentation I gave at Modesto Junior College for Science Colloquium.  It was based on my Spring 2016 sabbatical - traveling in northern Europe and exploring the history of mathematics from the Renaissance to the present.  In this talk I focus on the obstacles women had to overcome in order to study mathematics prior to the 20th century and also the inspirations that led them to be interested in math and to persevere despite obstacles.  It is a talk about the triumph of the human spirit.

Fall 2016 MAPS Presentation - "Mathematics: A Human Endeavor" or "Beyond Infinity: The Life and Work of Georg Cantor" This presentation includes a brief introduction of my sabbatical focused on the history of mathematics from the Renaissance to the present in northern Europe, with a focus on the life and work of Georg Cantor of Halle, Germany, and his controversial study of the infinite as a completed set.

Spring 2018 Science Colloquium Presentation - "Math and Poetry Connections" This hour-long presentation is something I put together to help my students who are stronger in English and literature classes than in mathematics.  It is my attempt to build a bridge between the topics, hoping it might help those people find mathematics more approachable.  I give five points of connection, along with many bite-sized samples of mathematics and poetry - a wide variety of topics coming quickly and lightly.

Numberphile These YouTube videos from Brady Haran cover a wide variety of interesting math topics from infinity to primes to pi to how the NSA can hack our emails!

3Blue1Brown Yet another amazing mathematical YouTube Channel!

Vi Hart I've linked to some of her videos elsewhere on this page.  She has a fun, random assortment of music, art, dance, food and math.  She covers fractals, Fibonacci numbers, spirals, knots, etc.  I especially like her math doodling.

MinutePhysics Yep - the focus here is physics, not math, but there's a lot of overlap, and he covers some very interesting ideas, so I thought I'd link it.  Some of his math videos have to do with "adding past infinity" or what dimensions are, and there's even one on the "Hairy Ball Theorem" (yes, really).

#### EXPLORATIONS

Factor Conga This is an amazing visual dance involving factoring whole numbers.  It runs from 1 to 10,000.  It's rather hypnotic to watch but also instructive to look for patterns.

Fractal Metamorphs Go to this site to slide the cursor over fractals and change the parameters that create them in order to see different images.

Menger Sponge Fractal Slices This one has a very surprising result!

Foucault Pendulum Check out this site to see how it is that a Foucault Pendulum, such as the one at the base of MJC's observatory, demonstrates the fact that the earth rotates.

GIFS Illustrating Mathematical Properties and Ideas The Pythagorean Theorem "proof" and the creation of the parabola are my favorites.

Desmos Graphing Calculator This calculator allows you to see what happens when you change components of equations.  For a trial run you might want to put in either y=mx+b or just mx+b (you don't need the whole equation).  Then click on "all," so that you get a "slider" for m and b.  The sliders allow you to change values of m and b so that you can see how larger or smaller numbers, positive or negative numbers in those spots affect the graph.  Next try sin (ax + b), click on "all" so that you have sliders for a and b; see what happens.  Explore whatever graphs you'd like; this is a great tool for getting a feel for how each component of an equation affects the graph of that equation.

Completing the Square Like a Babylonian - Ancient cultures did not have the notation that we have, nor the algebraic techniques that we have, yet ancient Babylonians could solve problems like x^2+6x=16.  They couldn't use the Quadratic Formula - didn't have it.  They couldn't subtract 16 from both sides and factor, because they didn't have the notation to see it was we do.  They would have written this as something like, "A number times itself increased by six times itself is equal to sixteen.  What is the number?"  Instead of using algebra (a rather modern invention!), they used geometry.  Check out this link to see how they did it!

#### ARTICLES

The Birthday Problem An entertaining article about the classic birthday problem - includes real-life applications of the principle, an explanation of how it works, and a funny story about Johnny Carson and his audience really misunderstanding the problem.

The Hilbert Hotel A New York Times article by mathematician Steven Strogatz, in which he explores some paradoxes of the infinite.

#### MISCELLANEOUS

Optical Illusions  Many optical illusions, particularly those M.C. Escher used in his artwork, are based on mathematical concepts.

Inversions Inversions are created through a combination of art and mathematics.  If you've seen the movie "Angels and Demons" you've seen an inversion called an ambigram.  This link takes you to famous inversion creator Scott Kim's site.

Achirality of Four-Crossing Knot - A knot with four crossings can be turned into its own mirror image.

Mandelbrot Set Generation This link contains a nice image showing the oribits of two c-values that are very close but differ in their behavior.  It also shows the "control radius."

0.9 repeating = 1 This is a blog post containing multiple arguments for the truth of this equality and responses to arguments against it.  If you haven't already, for a more dynamic and fun approach to this check out the Vi Hart video clip linked further up on this page.

Teaching and Learning This is a short talk given by one of the best teachers and most interesting mathematicians in the country, Ed Burger.  I find it very inspirational both as a teacher and as a student.  It has to do with what you are really taking classes for (any classes) and how they can and should positively impact your life if you let them.  It's actually more aimed at teachers than at students, but he has a lot of good things to say that can help you as a student alter your vision a bit in a way that is positive and helpful to you.

Metric System From NPR's "Here and Now" (6/9/15) in response to presidential candidate Lincoln Chafee proposing the US officially adopt the metric system.  This clip includes some interesting history of the English system and the metric system.

Partitions This site will allow you to find the number of partitions (and the number of digits in the number of partititions) of any number from 1 to 10,000.