Areas

XCXC!!! Plan for people who know too much -- give them a card with instructions!!!
XCXC can we do this with skype?!

XCXC rules
  • you can always ask and you must get a response! if not find someone that will, or me!
  • if you can help someone you must do so BUT
    • without giving them knowledge HOW?!?!?! XCXC
      • believe a socratic dialogue
      • you think tools are powerful but they force you to think a certain way...
XCXC how do we record this
  • Maybe people write any question posed, perhaps with a diagram, say who is participating in the discussion (use wave????)

XCXC possible tree of discussion
  • Area of 1x1 square
  • Area of axb rectangle (integers)
    • define multiplication
      • prove commutativity
        • devise axiom of "rotation and movement don't change 
    • Area of axb rectangle (non-integers)
      • What is measurement? If we believe a, b are rationals:
        • Find area of rectangle with rational sides
          • Is that the same as multiplication? If so define multiplication
            • Prove commutativity
            • Why is that different than the original multiplication? What does this mean?
      • What if a, b are not rationals?
        • Can this happen?
          • XCXC!!!
        • Then what is multiplication?!?!?!
          • You can do estimates, but can it be defined???
            • XCXC
  • Area of triangle
    • XCXC
  • Area of polygon
    • Can we always triangulate?
    • Even if we can always triangulate how do we add the areas together?
      • XCXC
  • Area of circle?!?!??!
    • XCXC!!!
    • Related to perimeter of circle?
      • XCXC


old notes:

(to be completed)

- area of rectangle (with integer sides)
- area of rectangle (with fractional sides)
- area of rectangle (with any length sides)
- area of triangle
- area of any polygon?
- what about curved shapes? circles? (see Vieta's value for pi)
Comments