Matrix Magic

Thursday, November 16, 2023

Michael kicked off the event by showing us some examples of magic squares.  Next he gave us some partially completed 3x3 magic squares, where three numbers were known, and we needed to determine the other six. This led to the question of when three numbers is enough to determine a magic square, which we explored for some time.  Here is a link to Michael’s slides.

Next, Paul gave us a 5x5 matrix which he called “The Game of 57”.  Three Crooked Mathematicians played in front of the crowd, and sure enough, all three were winners (selecting numbers that added up to 57).  It was quickly believed that this game was impossible to lose, and much of the evening was spent exploring how and why.  This game was taken from Chapter 2 of  Martin Gardner’s 1959 book, Hexaflexagons and Other Mathematical Diversions.

We finished the evening by exploring how matrices are also used to solve systems of equations, and how free software like Octave can be run on a SageMathCell to solve a linear system.

Tell Me More

Thursday, September 21, 2023

The Crooked River Teachers Math Circle met for the first time this school year on Thursday,  September 21st.  Our evening began with the ‘Smileys’ puzzle from the Julia Robinson Mathematics Festivals.  In this puzzle one tries to turn all the frowns turned upside down. ??  Puzzles includes squares, hexagons, and triangles of frowns and smileys. 

After our introductory game of ‘Smileys’, Michael led us in a exercise of ‘slow reveals’.  He began by projecting a graph, but all of the important information was missing.  We had fun trying to guess what data the graph represented.  As Michael would slowly begin revealing parts of the graph, we modified our guesses.  (Hilarity ensued.)  He then taught us how to make our own slow reveal graphs and provided the some websites for sets of slow reveal graphs.

Slow Reveal Graphs: https://slowrevealgraphs.com/ 

Slow Reveal at Math With Bad Drawings:  https://mathwithbaddrawings.com/2020/06/03/what-graphs-reveal-if-you-give-them-the-time/

NYTimes: What's Going On in This Graph?

Our Julia Robinson Math Festival

Saturday, June 17, 2023

A Festival of Math

Thursday, May 18, 2023

We engaged in two activities that are part of our upcoming Julia Robinson Math Festival, which will take place on Saturday, June 17, at the conclusion of our summer immersion.

Sara Good started our evening by passing out Geometiles to each group.  We explored these puzzles for well over an hour, and each group explored our own questions that were raised as we worked on these.

Next, Paul Zachlin led us in a game where we try to place Wolves and Sheep onto an n by n “chess board”.  In addition to the pdf version of this puzzle, you can click here for a jamboard version.

We are excited to engage in these and other similar activities this June!

This is Probably a Good Meeting

Thursday, March 16, 2023

Dr. Edwin Meyer of Baldwin Wallace University, who specializes in helping students become critical thinkers lead us in our main activities.  After sharing a bit about his background and what lead him to teach problem solving, he shared a problem he gives his students on the first day of class.  After allowing us to grapple with the problem he lead the group in an exploration designed to answer the questions:  if a deck of cards is random dealt to four people, what are the odds that 1) each person will have an ace, 2) two people will have an ace and one person will have 2 aces, 3) two people will have 2 aces each, 4) one person will have three aces and one person will have 1, and finally 4) one person will have all four aces.

Numbers Have Personality!

January 19, 2023

These activities were a team effort, courtesy of your Crooked River Math Teacher Circle leadership team!  Here is the Google Slides doc that we used.  Slides 2, 16, and 17 include links to other wonderful resources.

Sara Good started our evening by having participants take their chosen number through a personality test.  We used adjectives to describe numbers where tests for the numbers were available at different stations.  We saw examples of numbers that are abundant, deficient, or perfect, aspiring or sociable, practical, weird, untouchable, or amicable.

Next, Kate Lane had us working to find happy and sad numbers.  Paul Zachlin wrapped things up with a search for vampire numbers.

It was certainly a great way to kick off the year, as we know different groups have different personalities, too!  This group of teachers was full of energy for the entire meeting.

Dr. Melissa Dennison of Baldwin Wallace University introduced us to a two-player game called NIM.  We played a lot, discussed strategy, and then played a number of variations. Here are the slides that she used.

We concluded the evening by viewing and discussing the video Learning and Behavior Characteristics of Gifted students

We read All of the Above in advance of this meeting, in anticipation of our video conference with the author, northeast Ohio native Shelley Pearsall.  We began by building tetrahedrons and other geometric figures using paper plates in the way that artist Bradford Hansen-Smith showed to Paul Zachlin two decades ago.  

We spent the session playing with Lego Mindstorms pieces.  We began by making static geometric shapes before proceeding to dynamic linkages.  Here is a great resource for how to make triangles using Legos.

Paul Zachlin then presented his slides on Lego Linkages, which came from a longer set of slides by Zoltan Kovacs.  Both Paul and Zoltan had been inspired by the book, How Round is Your Circle?   The slides began by showing why linkages are: :important, interesting, useful, beautiful, modern, and challenging.  We viewed a video of the amazing enormous kinetic sculptures called strandbeests (“beach animals” in Dutch) by Theo Jansen.  We ended up using our legos to construct 2-bar, 4-bar, and 6-bar linkages, and we traced algebraic curves corresponding to each.  We learned What Watt sent to Watt (his son) to explain the linkage in his steam engine.  Here is a Desmos simulator for 4-bar linkages.  Here is the Geogebra model of Hart’s Inversor.

In the end, we straightened out which lines were straight, and which were close, but not quite.