### Areas

 XCXC!!! Plan for people who know too much -- give them a card with instructions!!!XCXC can we do this with skype?!XCXC rulesyou 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 BUTwithout giving them knowledge HOW?!?!?! XCXCbelieve a socratic dialogueyou think tools are powerful but they force you to think a certain way...XCXC how do we record thisMaybe people write any question posed, perhaps with a diagram, say who is participating in the discussion (use wave????)XCXC possible tree of discussionArea of 1x1 squareArea of axb rectangle (integers)define multiplicationprove commutativitydevise 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 sidesIs that the same as multiplication? If so define multiplicationProve commutativityWhy 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???XCXCArea of triangleXCXCArea of polygonCan we always triangulate?Even if we can always triangulate how do we add the areas together?XCXCArea of circle?!?!??!XCXC!!!Related to perimeter of circle?XCXCold 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)