PROGRAM
"The Card Game SET and Affine Geometry" by John Lind, California State University, Chico.
In the popular card game SET, players seek triples of cards where each property (color, number, shape, and shading) is either the same or all different. Put another way, if two are the same and one is different, then it’s not a SET. In this talk, we see that SET players are actually affine geometers — who use the field F3 with three elements. Generalizations to other finite fields and questions in algebraic combinatorics arise from this perspective. Bring a deck of SET cards if you have one!
"Four Squares, Many Ideas" by Matt Krauel, California State University, Sacramento.
This talk explores Jacobi's Four Square Theorem and illustrate how many different mathematical ideas can be combined to answer a seemingly simple question. Along the way, we encounter a variety of mathematical areas, some quite advanced, and sketch a broad framework that can be applied to not only prove the theorem, but to related theorems as well.
Discussion Under the Oaks. "64 = 65: Recreational Mathematics and Puzzles from Lewis Carroll and Martin Gardner" by Stuart Moskowitz, California State Polytechnic University, Humboldt.
We begin by cutting an 8 by 8 square into four pieces. We then rearrange these four pieces into a rectangle with an area of 65 square units. How is it possible to gain a unit of area? Tucked behind his lecture notes for a course on Geometry, Charles Dodgson (Oxford University Mathematics Lecturer), aka Lewis Carroll (Alice in Wonderland), scribbled several pages of notes explaining this geometrical paradox. It’s a puzzle that can be explained using concepts from nearly all levels of the math curriculum. In case you’ve already seen this puzzle, I promise I have many others just as (and even more) baffling.
Geometric paradox puzzles are just one of many types of mechanical and mathematical puzzles. During this workshop, we also explore (hands-on) puzzles to put together, puzzles to take apart, puzzles to untangle, and others.
I also bring a few puzzles from Martin Gardner. Gardner was one of Lewis Carroll’s biggest fans. Besides being a co-founder of the Lewis Carroll Society of North America, from 1957 to 1986 Gardner wrote the Mathematical Games column in Scientific American, showing and convincing both lovers and non-lovers of math that there really is such a thing as recreational mathematics. A goal for this workshop is for you to want to attend the 17th Gathering for Gardner (G4G17) in San Francisco in February 2028.
This workshop is based on a paper co-authored with Dr. Phyllis Chinn, Cal Poly Humboldt Mathematics Department Professor Emeritus.
Social Gathering and annual five minute business meeting.
Organizers: Elaine Newman, Thomas Mattman.