The Talking Stick Blog

News, Updates, Program Recaps, and Homeschooling Information

The Stable Marriage Problem (Gale Shapley Algorithm)

(October 2, 2017) I discovered this problem and was so excited – my students would love it, it directly tied in to the topic of our course, and it was a good example of a mathematical algorithm that all of the students would have sufficient math background to work. I wanted to do it right away, so I discarded my…

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PROOFS #6: Math as Art, Collaboration, and Spectator Event

(May 21, 2013)  There’s more than one way to prove the vertical angle theorem:  verbally, numerically, algebraically (with various approaches), intuitively, visually.  Our Math Circle participants debated and attempted them all.  When the theorem was finally proven algebraically, everyone smiled.  It was a satisfying proof.  And it was fun.  And we learned on the way.  Some highlights: N asked “What…

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PROOFS #5: Debating the Merits of Proofs

  THEOREM:          A cat has nine tails. PROOF:                1.  No cat has 8 tails.                                 2.  One cat has one more tail than no cats.  Therefore, a cat has nine tails.1 (May 14, 2013)  We began today’s Math Circle debating the merits of the cat-has-nine-tails “proof.”  N stood at the board diagramming “my” reasoning.  G came up to…

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PROOFS #4: Finally Starting to Prove Something

(May 7, 2013)  It is said that Pythagoras promoted the belief that every number can be expressed as a ratio of whole numbers.  This idea was still a bit confusing to our Math Circle participants, who tried to brainstorm some number that couldn’t be expressed this way.  “How about 1.43?” they asked.  “3.5 over 4?”  “3.5792 over 4?”  That last…

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Math Circle Blog: Signaling Problem Solution via Proof by Contradiction

Signaling Problem Solution via Proof by Contradiction December 11, 2012: We began our final session of our Signalling Problem Math Circle with a few rounds of Exploding Dots, this time in binary.  The large number of explosions in binary (base two) compared to decimal (base ten) was such fun.  I asked the group how many different numbers could be represented…

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