# The Harmony Learning Community Blog

News, Updates, Program Recaps, and Homeschooling Information

### Algorithms, Algebra, and College Admissions

(October 19 and 26, 2017) “Today we’re going to do something we’ve never done in a math circle here. We’re going to take a quiz.” Stricken looks on faces. “We’ll do it together, it’s just 2 questions, and I think it will be fun.” Relief. “I’m always on the lookout for things related to algorithms to share with you, and…

### PROOFS #7: We Want to Think

(May 28, 2013)  Seventy-five minutes.  No future sessions.  Four kids.  Five proofs.  What to do? This was the dilemma facing our Math Circle today.  I’d been deliberating all week over how best to use our last session.  So many proofs.  So little time. I gave the decision to the kids in attendance, R, P, N, and G.  Our options:  a…

### 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…

### 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…

### 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…