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:- 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) |