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Math, Music, and the Moral Imagination

Jazz saxophonist and mathematician Marcus G. Miller will share a reflection on how math and music can make us whole.

**Marcus G. Miller** is a musician and mathematician living in New York City.

Logic Puzzle

John Urschel, current MIT math PhD candidate and former NFL pro, shares his favorite logic puzzle.

**John Urschel **played professional football for the Baltimore Ravens from 2014 to 2017 before retiring to focus on his career in mathematics. He is currently a PhD candidate at MIT, where he studies spectral graph theory, numerical linear algebra, and machine learning.

Brainteaser Kahoot

Get ready to take part in a whacky and zany brainteaser Kahoot with Steve Sherman. This is a quiz that will tickle your brain-strings and challenge your thinking skills. Some of the brainteasers will be easy while others will make you think. Do you have what it takes to be our brainteaser champion?

**Materials needed:**

- Smart phone, tablet, or personal computer with internet access

**Steve Sherman** is the Chief Imagination Officer and Executive Daydreamer of Living Maths.

The Doomsday Rule

When visiting MoMath, the late, great John Horton Conway impressed people by instantly telling them the day of the week that any given date fell on or will fall on. And you can do it too! What date of the week will your birthday fall on next year? Or your anniversary? Or favorite holiday? When’s the next Friday the 13th? What day of the week were you born on? Tune in for a presentation by MoMath Puzzle Master Peter Winkler on the marvelous “Doomsday rule.” It’s easy and fun, and with a little practice you’ll be able to duplicate Conway’s feat. It’s a great trick, and it’s cleverly designed so that you can remember it and wheel it out whenever it’s needed.

**Materials needed:**

- Paper
- Pencil

**Peter Winkler** is the current MoMath Distinguished Chair for the Public Dissemination of Mathematics and Professor of Mathematics and Computer Science at Dartmouth College.

Moving in Circles

Join Karl Schaffer as we play with several surprising ways of moving our limbs in circles. Apply these actions to create movement sequences with the ultimate mathematical prop — an ordinary sheet of paper. Then, learn how it connects to the curious algebra of quaternions!

**Materials needed:**

- Several sheets of 8.5″ by 11″ printer paper
- 5′ by 5′ area in which to move (non-carpeted area preferred)

**Karl Schaffer** is a dancer, choreographer, mathematician, and math professor at De Anza College.

Conway's Rational Tangles

What can the fluidity of topology and knots have to do with the rigidity of operations on fractions? Join Alex Kontorovich to learn the fascinating connection discovered by the late mathematician John Conway.

**Materials needed:**

- 2 strings of different colors (wires or shoelaces are also okay)
- Surface to lay the strings on (e.g. floor or table is fine)
- Optional materials: paper and pencil

**Alex Kontorovich** is MoMath Dean of Academic Content and math professor at Rutgers.

Folding Fun!

Origami expert Wendy Zeichner will teach one or two origami action models that will be folded from regular printer paper. There’s math in every fold!

**Materials needed:**

- Several sheets of 8.5″ x 11″ printer paper
- Pen or pencil
- Scissors

**Wendy Zeichner** is an origami expert and president of OrigamiUSA.

Math in Motion: Build Your Own Paper Spinner

Turn two pieces of heavy paper and some tape into a spinning top, and explore the geometry behind it! Join Yana Mohanty, Ph.D., a mathematician and inventor of Geometiles®, as she guides you through this fun STEM activity. You will be provided with a printable template and shown how to transform it into your spinner. Once you master the simple construction, you may decorate your spinner with your own design.

** Materials needed** (metric equivalents in brackets)**:**

- 2 sheets of 8.5” x 11” (size A4) card stock paper, ideally in 2 different colors; manila folders cut to 8.5” x 11” will also work
- Scissors
- Tape
- Optional: This project can also be built from Geometiles® Mini Set 2, available from
*Additions*, the online shop at MoMath.

**Yana Mohanty** is a math educator, mathematician, and the creator of Geometiles®.

One Step Back, One Step Forward

If repeated flips of a coin determined which step you took, would you get anywhere? Step right in (bring your own coin) and find out!

**Materials needed:**

- 1 coin
- Paper
- Pencil

**Ralph Pantozzi** is the winner of the 2014 Rosenthal Prize and a Presidential Awardee in math teaching.

Numbers Meet Shapes in 3D Geometry

Let’s discover the magic of Euler’s Polyhedral Formula while creating structures out of toothpicks and marshmallows.

**Materials needed:**

- 1 box of traditional rounded toothpicks with points at both ends
- 1 bag of mini marshmallows
- Paper
- Pencil

**Bruce Bayly** is a math professor at the University of Arizona and bus driver for the Arizona Mathematics Road Show.

Engineering with Paper

Join us online for a math-and-paper engineering adventure! Godwyn Morris, Director of Dazzling Discoveries STEM Education Center, will demonstrate some Engineering with Paper challenges. Together we will explore proportion, ratio, and scale as Godwyn shows you how to create structures, furniture, and characters from simple supplies.

**Materials needed:**

- Printer paper
- Tape
- Scissors

**Godwyn Morris** is the Director of Dazzling Discoveries STEM Education Center.

Mathemagics!

Dr. Arthur Benjamin will amaze you with some mathematical magic, and then teach you how to do it. Bring a calculator!

**Materials needed:**

- Calculator

**Art Benjamin** is an award-winning popular entertainer, mathemagician, and math professor at Harvey Mudd College.

How to Fold Things into Thirds, Thirty-Thirds, and Three-Hundred-and-Thirty-Three-"irds"

Bring along something bendy — a tie, a shoelace, a piece of string — and let’s have fun exploring some of the curious mathematics of folding.

**Materials needed:**

- Something bendy, such as a tie, shoelace, or piece of string

**James Tanton** is a global educator, math popularizer, and mathematician.

Can Math Help You Juggle?

Educator and entertainer John Chase will show you the powerful connections between mathematics and juggling. Math modeling has given jugglers all kinds of new patterns to juggle, and we invite you to come see what mathematics can do. Bring three juggling objects so you can join the fun!

**Materials needed: **

- 3 juggling objects

**John Chase** is a mathematical juggler and math educator.

A Four-Card Mathematical Magic Trick

Manjul Bhargava will demonstrate an interactive magic trick that exhibits how one can create surprising complexity from extreme simplicity. Viewers are encouraged to participate from home!

**Materials needed:**

- 4 playing cards

**Manjul Bhargava** is the MoMath Inaugural Distinguished Visiting Professor for the Public Dissemination of Mathematics, math professor at Princeton University, and Fields Medalist.

Activities from the Julia Robinson Mathematics Festival

Come and enjoy some non-competitive explorations in mathematics.

**Mark Saul** is the Senior Scientist at the Julia Robinson Mathematics Festival.

Let the Math Fun Begin!

Cindy Lawrence, MoMath Executive Director, and Tim Nissen, MoMath Associate Director, welcome all to the fifth annual NYC Math Festival, featuring hours of mathematical fun and entertainment. Join presenters from all over the world to share an afternoon of lively, engaging activities.

James Tanton, Chair of MoMath’s Advisory Council, kicks the Festival off by sharing the highly intriguing “International Math Salute.” Can you figure out how it works?

NYC Math Festival Pre-Show

The Festival site opens at 1:30 pm EDT (New York). Enter at any time between 1:30 pm and 2:00 pm to view some favorite MoMath pix from years gone by. Activities begin promptly at 2:00 pm EDT (New York).

See our selection of Geometiles® and browse for books by Festival presenters Peter Winkler and Art Benjamin.

A MoMath retail specialist will be on hand to answer questions and offer expert shopping advice for all your mathematical gift needs.

Stop by to view a selection of Rubik’s Cubes, browse for Christopher Danielson’s delightful books, *Which One Doesn’t Belong? *and *How Many?*, and learn more about the film *The Man Who Knew Infinity*, for which Manjul Bhargava served as technical advisor to ensure the accuracy of the math featured in the film.

A MoMath retail specialist will be on hand to answer questions and offer expert shopping advice for all your mathematical gift needs.

Check out MoMath’s selection of colorful origami paper, Karl Schaffer’s book *Math Dance*, and other great items from *Additions, *the online shop at MoMath.

A MoMath retail specialist will be on hand to answer questions and offer expert shopping advice for all your mathematical gift needs.

Math Meets Art: Rubik's Cube Mosaics

Watch as Lauren Rose builds a Rubik’s Cube mosaic, and try to figure out what the picture will be. Math meets art in this creative application of the popular Rubik’s Cube.

**Lauren Rose **is a mathematician and math professor at Bard College.

Rubik's Cube With Feet

Daniel Rose-Levine will demonstrate how he solves the Rubik’s Cube with his feet in under 20 seconds.

**Daniel Rose-Levine** is the former Rubik’s-Cube-with-feet world record holder.

Mime-matics

How can the invisible world of mime explore mathematical ideas? Join Tim Chartier as he uses mime to investigate weight, magnitude of force, and projective motion with the art of mime. You’ll also learn how to make an infinite chocolate bar. (The candy bar is a real prop but eating is pantomimed so enjoyment is calorie-free.)

** Tim Chartier** is a mathematical mime performer and math professor at Davidson College. He has performed throughout the world and has been trained in several mime schools, including master classes with the legendary Marcel Marceau.

Finding and Creating Symmetry

Symmetry is all around us. We see symmetry in our bodies, car wheels, fences, fabric patterns, the MoMath logo, and many other objects! We will learn about different types of symmetry and have fun creating symmetric art using common objects.

**David Reimann** is an Albion College math and computer science professor and artist who uses symmetry in his work.

Fun with Mathematical Definitions

Is an elevator a vehicle? Is a hot dog a sandwich? Is a heart a shape? Is an emoji a word? The answers to these questions depend on your definitions of vehicle, sandwich, shape, and word. Precise definitions are essential tools of mathematics, but few definitions start out as precise as they’ll need to be later on. Come play with the boundary between precision and ambiguity in this fast-paced participatory session.

**Christopher Danielson** is an award-winning author and math educator.

Math Raps and the Math Behind Them

Join Mr. A. as he shares one of his many Math Raps, discusses how he got started rapping about math, and takes you through some of the mathematical ideas and references in the rap.

**Mike Andrejkovics** is a high school math teacher from Long Island, NY who creates and performs raps about mathematics based on popular hip-hop tracks.

Christopher Danielson is an award-winning author and math educator.

Cindy Lawrence is the Executive Director and CEO of the National Museum of Mathematics.

Tim Nissen is the Associate Director of the National Museum of Mathematics.

Steve Sherman is the Chief Imagination Officer and Executive Daydreamer, Living Maths.

Karl Schaffer is a dancer, choreographer, mathematician, and math professor at De Anza College.

Alex Kontorovich is MoMath Dean of Academic Content and math professor at Rutgers.

Bruce Bayly is a singer, violinist, and math professor at the University of Arizona.

Daniel Rose-Levine is the former Rubik’s-cube-with-feet world record holder.

Godwyn Morris is the Director of Dazzling Discoveries STEM Education Center.

James Tanton is a global educator, math popularizer, and research mathematician.

John Chase is a mathematical juggler and math educator.

Lauren Rose is a dancer, choreographer, mathematician, and math professor at De Anza College.

Mark Saul is the Executive Director of the Julia Robinson Mathematics Festival.

Origami expert Wendy Zeichner is the Executive Director of Origami USA.

Ralph Pantozzi is the winner of the 2014 Rosenthal Prize and a math educator.

Yana Mohanty is a math educator, mathematician, and the creator of Geometiles®.

Carolyn Figuereo is the retail manager of the National Museum of Mathematics.

Tim Chartier is a mathematical mime performer, math professor at Davidson College.

International Math Salute

Details TK

Rohan Jha

“The purpose of Math Musings, the magazine I started in high school,” wrote Rohan Jha, “was to show that math is everywhere, yet many times we are not aware of it. It is behind some of the music we play, or how nature uses it for its own optimal benefit, or it could be behind a fancy card trick, or math could help us reduce the ubiquitously observed annoyance of traffic jams during peak hours.” The magazine tries to humanize and enliven math in various ways: by telling anecdotes about famous mathematicians; by challenging fellow students with fun puzzles; or by leading them some deeper ideas, such as a lily pad puzzle that leads to the notion of backward recursion in finance. With clear illustrations and step-by-step instructions for magic tricks and other activities, Rohan attempts to make math fun for everyone… and succeeds admirably.

Kyna Airriess

The project submitted by Kyna Airriess is a “zine” based on a quote from *A Mathematician’s Lament*, a polemical essay by high school teacher Paul Lockhart. “There is nothing as dreamy and poetic, as radical, subversive, and psychedelic, as mathematics,” wrote Lockhart. Reading Lockhart’s essay, says Kyna, “contributed to my own conversion from ardent math-hater to aspiring mathematician; I’d never heard someone describe math, the subject of unfeeling calculations, with words like ‘poetic’ and ‘radical.’ It was a long time before I began to see these traits for myself, but today I self-identify as a math nerd, and I want to study math in college.”

In the zine, each of Lockhart’s memorable adjectives—dreamy, poetic, subversive, and psychedelic—is illustrated and connected to math ideas, using symbols, history, color, and imagery. The judges were impressed by the passionate energy conveyed by the zine’s words and design. The overall effect achieves what Kyna intended: to embody “what those of us who love math want the world to understand. It isn’t about cold calculations at all— it’s a field full of creativity and beauty, and it is just as infused with humanity as any other.”

Sarah Thau

“Limericks and poetry are not a typical way to convey information about math,” admits Sarah Thau, “but I think it makes it more palatable than learning functions by rote. Who doesn’t love a limerick?” So Sarah created a series of short rhyming poems to list some basic properties of linear, quadratic, trigonometric, polynomial, rational, and other types of functions encountered in algebra and precalculus, and illustrated the pages with examples.

The judges were tickled by the playfulness of this entry. Limericks are a lighthearted form of poetry in which creativity comes from working within constraints and overcoming them delightfully—and much the same can be said of math! Indeed, as Sarah wrote, “I love math and am always trying to solve problems but this was a new type of problem to tackle. One that didn’t need any algebra or modeling. Each poem became a problem to solve as I tried to figure out words to make each function type’s properties rhyme neatly.” The poems illuminate the distinctive properties of the various kinds of functions, and draw readers in through a unique, creative, and memorable way of communicating mathematical ideas.

Jonah Yoshida

Jonah Yoshida’s project is a pencil-and-paper infographic on graph theory. He says “I conceived of the idea when reading about how Arthur Cayley used trees to represent structures of hydrocarbons with n carbon atoms and 2n+2 hydrogen atoms. The entire structure imitates one of these hydrocarbons, ethane (n=2), and a unique application of graph theory is included inside each atom. I divided the page into two sections so that the hydrogens bonded to the left carbon contain puzzles and fun applications of graph theory, while the ones bonded to the right hydrogen focus more on direct applications, much like our brains’ left and right hemispheres.” For example, the Four Color Theorem (a fun application of graph theory to coloring maps and an longstanding research question) appears on the left, while the right side includes applications of graphs to computer science (neural networks and spanning trees) and electrical engineering (circuit diagrams).

The judges appreciated the ingenious design concept of this graphic, which underscores the universality and interdisciplinary spirit of graph theory. The words and imagery combine history, math, chemistry, and psychology, and the questions in the small text boxes invite the reader to do some research of their own.

Yvonne Hong

“My math communication project, *Infinity Universe*,” wrote Yvonne Hong, “is an illustrative yet mathematical depiction of the world in which we live. Every inanimate object illustrated represents a simple, yet ubiquitous concept in math: upon closer inspection, the monochromatic tree is a fractal Pythagoras tree, the galaxy in the background is constructed using the Fibonacci sequence, and the planet and comet are both different variations of the Apollonian gasket. *Infinity Universe* promotes the universality of math communication through an abstraction of objects and phenomena that people all around our world are familiar with.”

Carefully executed with great attention to detail, the painting submitted by Yvonne drew the judges in with its vibrant colors and hypnotic patterns. Moreover, the theme of infinity pervades the painting, just as it does in all of mathematics. But here, the suggestion of the infinite is magical and otherworldly rather than scientific and literal, and so may appeal to audiences not normally attracted to math.

Zoe Markman

Zoe Markman created a visual proof of the “sum of squares formula” by cleverly using three wooden 3-D pyramids that fit together. Each pyramid consisted of a total of 1^{2 }+ 2^{2 }+ … + n^{2} identical wooden cubes; thus, its volume visually represented the sum of the squares of all the whole numbers from 1 to n. To find a formula for this sum of squares, **Zoe** manipulated and rearranged the three pyramids to form a rectangular prism, whose volume could then be easily calculated to obtain the desired formula for the sum of squares.

The judges agreed with **Zoe **that this sort of visual, hands-on manipulative “provides a deeper understanding of math than that provided by a written project. Since you can observe, hold, and manipulate the pyramids (even more so in person), the audience is able to understand why the formula works rather than just taking it at face value and accepting that it was true arbitrarily. Second, the presentation could be understood even by people without a significant knowledge of math. It put what looks like an intimidating problem in terms that are easily digestible.” Zoe even tested the presentation on friends who said they didn’t like math. That’s a good practice in any form of communication. Overall, this project is modest but extremely well done and produces a very pleasurable “Aha!” moment for many viewers; indeed, it led one of the judges to understand the “sum of squares formula” in a whole new way!

Katarina Cheng

To express the universality of math, Katarina Cheng translated it into another universal language: dance. “Just as dance exists as a part of many cultures around the globe to express abstract ideas and emotions through movement, mathematics defies cultural lines to express abstract ideas through structures and forms on the page,” she wrote in her project description. Her video “Dancing the Dihedral Group” sought, through dance, “to represent the visual symmetries, primarily those of a square,” and, through words, “how they translated into algebra, primarily the group D8 .”

The judges commend Katarina for the elegance of her communication in the video. Especially notable was the esthetic of minimalism — in how the video is shot, and the choice of clothing, background, and colors — all of which mesh perfectly with the minimal esthetic of group theory. The integration of the math graphics with the dance moves was also carried out gracefully. Although others in the past have recognized the similarities between math and dance, few have conveyed that analogy with such finesse in the execution. The dancing and music were artfully minimal too. The overall effect is to reinforce the central idea of beauty in simplicity.

Hamza E. Alsamraee

Hamza Alsamraee loves Instagram – and he also loves math. But when he noticed that very few math pages existed on Instagram, he sought to change that by starting @daily_math, a page dedicated to intriguing problems and ideas about algebra, geometry, calculus, number theory, and other parts of math. “With high-quality educational posts,” he says, “I hoped to build an Instagram community centered around a shared passion for math.”

The judges were impressed with the creativity of Hamza’s entry, expressed through its skillful use of visuals, history, and puzzles, all presented in attractive ways. His explanations of mathematical concepts are clear and insightful, and he is very interactive with his followers, even inviting them to post. The judges also commend him on his growth as a creator and communicator. His Instagram page has evolved from a focus on tricky integrals in the early days to doing more accessible problems now, and the visual presentation has evolved in tandem. With his engaging design choices, which foster clear communication, he is making increasingly good use of the strengths of the Instagram medium.