The Harmony Learning Community Blog

News, Updates, Program Recaps, and Homeschooling Information

PROOFS #5: Debating the Merits of Proofs

Posted by Rodi Steinig 
· Thursday, May 23rd, 2013 

  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…

Read More→

PROOFS #4: Finally Starting to Prove Something

Posted by Rodi Steinig 
· Monday, May 13th, 2013 

(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…

Read More→

PROOFS #3: Irrational Numbers, Hippasus, and Visual Proofs

Posted by Rodi Steinig 
· Monday, May 6th, 2013 

(April 30, 2013)  As I entered the building, L, one of my Math Circle lurkers, asked excitedly, “Are you studying The Pythagorean theorem?”  I never erase the board work at the end of class so that L (and other building users) can study and think about it throughout the week.  L does not participate in our Circle, but follows it…

Read More→