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Invited Paper Session Abstracts - Mathematics and Magic

Friday, August 5, 1:00 p.m. - 3:55 p.m., Fairfield

Speakers will demonstrate and explain magic tricks based on interesting mathematical principles.

Organizer:
Arthur Benjamin, Harvey Mudd College

Tricks You Can Count On

1:00 p.m. - 1:15 p.m.
Irl BivensDavidson College

In Spring 2016 I taught a course at Davidson College entitled "Math, Magic, and Mystery". The course satisfied a graduation requirement in "Mathematical and Quantitative Thought" and the students in the class were bright and enthusiastic, but had limited technical facility in mathematics. The first component of the course consisted of tricks built upon counting cards or coins in unusual ways. Such tricks provide a natural pathway into important mathematical concepts such as one-to-one correspondence, the pigeonhole principle, and inclusion-exclusion. In this talk I will focus upon the use of a one-to-one correspondence to help students understand a brilliant self-working card trick that Martin Gardner referred to simply as "Henry Christ's Improvement".

Shuffling Cards and Binary Numbers

1:20 p.m. - 1:35 p.m. 
Steve ButlerIowa State University

Magicians (and more recently mathematicians) have worked to master the art of shuffling to manipulate cards in the deck. We will focus on one particular type of shuffling, the perfect shuffle, and look at how this can be used together with binary numbers to manipulate the location of a card in the deck.

More Card Effects from the Perfect Shuffle

1:40 p.m. - 1:55 p.m.
Doug Ensley, Shippensburg University

In this presentation we will explore variations on the inverse perfect shuffle that preserve some of the properties that make perfect shuffleeffects so interesting mathematically. The corresponding small packet effects rely on invariant properties well known for perfect shuffle tricks, while allowing the flexibility of having a spectator mix the cards.

Dunninger Meets DeBruijn

2:00 p.m. - 2:15 p.m.
Ron Graham, University of California, San Diego

Joseph Dunninger was one of the most famous mentalists of all time. N. G. de Bruijn was a well-known mathematician with notable contributions in analysis, number theory, and combinatorics. What links them together? Come to the talk and find out!

Telepathy or Tele-mathy-y?

2:20 p.m. - 2:35 p.m.
John Harris, Furman University

“Is your number 1089?” “Are you thinking of a gray elephant from Denmark?” These are the punchlines from some classic (but simple) mathematical mind-reading tricks. In this talk, we will have a look at a fun mind-reading effect that relies on a more sophisticated concept relating to Fibonacci and the lucky number 7.

Tricks with SET \(^®\)

2:40 p.m. - 2:55 p.m.
Liz McMahon and Hannah Gordon, Lafayette College

The card game SET gives rise to tricks that look quite magical. The tricks can shed light on the geometry, and modular arithmetic, that underlies the game. These tricks show how using mathematics increases the enjoyment of an already enjoyable game.

Fitch Cheney's 5 Card Trick for Values of 5 Less Than 5

3:00 p.m. - 3:15 p.m.
Colm Mulcahy, Spelman College

Fitch Cheney's classic five card trick sees two mathematicians, Aodh and Bee hand out a deck of card for mixing. Five random cards are given to Aodh, while Bee looks away. Aodh displays four of the cards in a row on the table, following which Bee inspects them. Soon Bee identifies the fifth card. It's entirely based on mathematics. This can be generalized to work if just four cards are selected at the outset and given to Aodh, three of which are then shown to Bee. It even works if we start with three cards, and amazingly, if we start with two cards. In all cases, Bee can identify one card whose face is not seen.

This is Knot a Trick!

3:20 p.m. - 3:25 p.m.
Heather Russell, University of Richmond

A knot is a flexible embedding of a circle in three-dimensional space. Knot theory seeks to understand properties of knots and is particularly interested in distinguishing between different knots. In this demonstration, we will explore the concept of unknotting a knotas well as obstructions to doing so. This talk is inspired by Louis H. Kauffman’s excellent repertoire of knot tricks.

Stretching Your Mind with Topological Mime

3:40 p.m. - 3:55 p.m
Tim and Tanya Chartier, Davidson College

Tim and Tanya Chartier have performed their mime show throughout the United States and in such countries as Holland, Japan and South Korea. The presentation introduces mathematical ideas to audiences using the illusionary world of mime to visualize the often invisible world of mathematics. This talk will demonstrate mime pieces that introduce topology, from tying a tie to a human-sized Slinky. Come see how topological ideas can come alive through the silent world of mime.

 

Year: 
2016