Teacher2Teacher 
Q&A #1664 
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From: Tom Hibbs To: Teacher2Teacher Public Discussion Date: 2001012411:32:46 Subject: Re: Geometry project I would rather call a figure that does not change shape "rigid" instead of "solid" to keep from confusing it with a solid. Parallelograms with a base angel of 60 degrees would measure well it seems. Still the fundamental properties (1) additive for nonoverlapping "tiles" (2) the "area" is nonnegative (3) rigid transformations are congruent Is their a problem with the area being an irrational compared to the square? If so, it is true that the square is irrational if a unit of area is "triangular". The visualization of area = length times width for a triangular tile is harder. Haven't tried it, but also can't easily visualize it. The visualization of the "square" unit of area is easy because of vertical (we're awake) and horizontal (we're asleep) and perpendiculars and gravity (or other forces).
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