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)