Math Arguments

What is a circle?

Taken from Chris Lusto ?@Lustomatical

1. In your groups, answer the question, "What is a circle?"


2. Absolutely no book-looking or Googling.  If all goes well, you will be frustrated.  Your peers will frustrate you.  I will frustrate you.  Don't rob anybody else of this beautiful struggle.  If your definition includes the word locus, you are automatically disqualified from further participation.


3. Each group will have one representative present your definition to the class.  No clarification.  No on-the-fly editing.  No examples.  No pantomime.  Your definition will include, and be limited to, English words in some kind of semantically meaningful order.  Introduce variables at your own risk.


4. If you're going to refer to some other mathematical object (and I suspect you will), make sure it's not an object whose definition requires the concept of circle in the first place.  (Ancillary benefit: you will be one of the approximately .01% of the population who learns what "begging the question" actually means.)


5. Once a group presents a definition, here is your new job: construct a figure that meets the given definition precisely, but is not a circle.  Pick nits.  You are a counterexample machine.  A bonus of my undying respect for the most ridiculous non-circle of the day.


6. When you find a counterexample, make a note of the loophole you exploited.  What is non-circley about your figure?