California Mathematics Council Community Colleges    
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CMC3 Recreational Math Conference
Lake Tahoe
April 22 and 23, 2016
At the MontBleu Hotel and Spa

PDF for student speaker Nick Saal's talk on Divergent Series

PDF for Corey Shanbrom's talk on Kepler's Third Law

PowerPoint presentation and the Superman Punch document from Tityik Wong's talk on Math and Martial Arts

PowerPoint presentation for Cliff Nelson's talk on Government, Liberty and Prosperity

PDF for Stephan Garcia's talk on Gaussian Periods

PDF for Nathan Carlson's talk on the Infinitude of Primes

For Hotel room reservations at MontBleu you can call 800-648-3353 or go online at and let them know of the group code:  STMTH16 to get the $109 room rates.

Register for the Conference:
You can register for the conference by clicking on the registration form link below, filling it out and sending it to Kevin Brewer, our membership chair:
Tahoe Conference Registration Form:  Word     pdf

Download the Conference Program:  Word    pdf

Friday Keynote: 

Friday Evening:  7:30 to 9:00 pm:  Bruce Armbrust, Lake Tahoe Community College
Worlds Beyond Our Own

Throughout history, humanity has explored the world around them. With the advent of the telescope, that exploration shifted towards the stars. Today the search continues for worlds that lie beyond our solar system. This talk will share the history of planetary discovery as well as the various methods of exoplanet detection used today.

Saturday Keynote:

Saturday 1:00 to 2:15:  Paul Zorn, St. Olaf College
Extreme Calculus

There is more to elementary calculus than may first meet the eye, especially to those of us who teach it again and again. Well-worn calculus techniques and topics---polynomials, optimization, root-finding, methods of integration, and more---often point to deeper, more general, more interesting, and sometimes surprising mathematical ideas and techniques. I'll illustrate my thesis with figures, examples, and calculation, and give references to MAA publications and resources that can support taking elementary calculus to its extremes.

Born and raised in India, Paul Zorn is a professor of mathematics at St. Olaf College.  His professional interests include complex analysis, mathematical exposition, textbook writing, and the role of mathematics among the liberal arts.   His 1986 paper "The Bieberbach Conjecture" was awarded the 1987 Carl B. Allendoerfer Award for mathematical exposition.  He has co-authored several calclulus textbooks with his St. Olaf colleague, Arnold Ostebee.  His most recent book is Understanding Real Analysis (AK Peters, 2010).   From 1996 to 2000, he was editor of Mathematics Magazine, and also served a hitch (2011-12) as President of the Mathematical Association of America.

Tahoe Student Speaker:
Saturday 5:15 to 5:45 pm
Nick Saal, Santa Rosa Junior College

Summation Methods on Divergent Series

In this talk, I will discuss summation methods that can be applied to certain divergent series in order to get a “convergent” value. I will show some surprising results that these methods lend themselves to, and while counter-intuitive these results are indeed of value in areas of applied mathematics.

Nick Saal is a dedicated and enthusiastic math major at Santa Rosa Junior College. He hopes to transfer to UC Berkeley in the fall to major in pure mathematics, and then attend graduate school to obtain his PhD. When he is not busy with school he is an avid musician.

Session Talks:

   Session 1
9:00 - 10:00
Session 2
10:30 - 11:30
Session 3
2:30 - 3:30
Session 4
4:00 - 5:00
Aspen A Pat McKeague
A Spiritual Side of Mathematics
Rick Luttmann
The Eternal Triangle Part I
 Rick Luttmann
The Eternal Triangle Part II

Cheryl Ooten
Number Sense and the Chinese Abacus
Aspen B Nathan Carlson
A Connection Between Furstenberg’s and Euclid’s Proofs of the Infinitude of Primes
Cliff Nelson
Government, Liberty and Prosperity
No Session No Session
Aspen C Lori Maloney
Math and Statistics with Social Justice
Tityik Wong & James Lee
The Mathematics of Martial Arts
Stephan Garcia
Gauss' Hidden Menagerie:  the Graphic Nature of Gaussian Periods 
Corey Shanbrom
Where does Kepler's Third Law Hold?

Pat McKeague, XYZ Textbooks,

A Spiritual Side to Mathematics?

Can the patterns and connections in mathematics strengthen our spiritual perspective?  You will judge for yourself.  We start with a simple sequence of numbers and end with fractals and chaos.  Along the way we meet philosophers and mathematicians from Pythagoras and Fibonacci, to Pascal and Stephen Hawking.  If you like mathematics, this talk is for you.  If you dislike mathematics, this talk is especially for you.

Nathan Carlson, California Lutheran University,

A Connection Between Furstenberg’s and Euclid’s Proofs of the Infinitude of Primes

In 1955, Furstenberg gave a surprising topological proof that there are an infinite number of primes. At first glance, the proof seems unusual and unlike other proofs of this famous result. Cass and Wildenberg (2003) and Mercer (2009) unraveled the topology in Furstenberg’s proof to uncover the essential number theory. Yet on the surface none of these proofs seem to bear much resemblance to Euclid’s original proof. In this interactive talk we give a modification of the Furstenberg/Mercer proof that in fact looks much like that classical proof.  This demonstrates that while Furstenberg’s proof seems unusual, at its core it is in fact quite similar to the first and most well-known.

Lori Maloney, Sacramento City College,

Math and Statistics with Social Justice

Often times mathematics instructors use real-world applications in the classroom in an effort to present mathematics as meaningful and useful to students. Mathematics and statistics problems that stem from social justice concerns can be a way to motivate and engage students while using authentic applications of math to their lives.

Tityik Wong and James Lee, (both) College of Southern Nevada,  and

The Mathematics of Martial Arts

Mathematics and martial arts are two of the greatest human creations. In this talk, a brief survey of some current studies and the authors’ own research results will be presented. No martial arts background is necessary to enjoy the talk. The audience will have opportunities to participate and experiment.

Rick Luttmann, Sonoma State University (retired),

The Eternal Triangle, Part 1

One of the simplest non-trivial entities in all of mathematics is the triangle -- it takes just three locations anywhere in the universe to get started.  But there is an incredibly rich lore to triangles, and many surprises.  There are coincidences that are almost mystical.
The four most well-known “special” points of a triangle: circumcenter, incenter, orthocenter (plus orthocentric sets, and a theorem on concyclicity), and centroid (plus triangle of medians, the Van Lamoen circle of circumcenters); isogonal conjugates and the symmedian point; the Euler line and Meyer’s Theorem; Feuerbach’s Theorem; the circle of Bellot-Rosada and Sachelarie’s Theorem; Ceva’s Theorem; the Gergonne Point; excircles; the harmonic relationship of the radii; the Nagel point; the Merck point

Cliff Nelson, College of Marin,

Government, Liberty, and Prosperity

How would you define government and what is the appropriate scope of governmental powers? This interesting and controversial question will be addressed in this talk from mathematical, economical, and philosophical perspectives. Come and enjoy a thought provoking discussion!

Stephan Ramon Garcia, Pomona College,

Gauss' Hidden Menagerie: the Graphic Nature of Gaussian Periods

At the age of eighteen, Gauss established the constructibility of the 17-gon, a result that had eluded mathematicians for two millennia. At the heart of his argument was a keen study of certain sums of complex exponentials, known now as Gaussian periods. It turns out that these classical objects, when viewed appropriately, exhibit dazzling array of visual patterns of great complexity and remarkable subtlety. (Joint work with Bill Duke, Trevor Hyde, and Bob Lutz).

Rick Luttmann, Sonoma State University (retired),

The Eternal Triangle, Part 2

Part I of this talk is a highly-recommended prerequisite to Part II, which will include:  Torricelli’s Problem, Fermat’s Theorem, two Fermat points, and Dao’s Theorem on Fermat Circumcircles; Napoleon’s Theorem; Morley’s Theorem; Van Lamoen’s Theorem and point; Steiner’s Theorem; Wallace’s Theorem; the Erdös-Mordell inequality; inscribed ellipses; the Theorems and Corollaries of de Guzman, Romero-Marquez, Chakerian, and Luttmann (the “Spanish-American” Theorem) including Pascal’s Magic Hexagon Theorem and Desargues’s Theorem on projectivities (as time permits).

Cheryl Ooten, Santa Ana College (retired),

Number Sense and the Chinese Abacus

Be introduced to fascinating Chinese mathematical symbols and systems. Through world history of abacus development, learn how and why the Chinese used the abacus. Practice basic operations (addition, subtraction, and multiplication) on a Chinese abacus to discover its advantages and use for developing student number sense.

Corey Shanbrom
, CSU Sacramento,

Where Does Kepler's Third Law Hold?

The only homogeneous Riemannian geometries admitting dilations are Euclidean spaces. We explain the surprising relationship between this theorem and Kepler's third law of planetary motion. Kepler's first two laws are known to hold in spherical and hyperbolic geometries, while the third law fails. We then investigate this problem on the Heisenberg group.

You can view the past Tahoe conferences by going to the past conference link.

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