Q&A #1664

Teachers' Lounge Discussion: Group research project in geometry for students

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From: Tom Hibbs 
To: Teacher2Teacher Public Discussion
Date: 2001012412:32:46
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 non-overlapping "tiles"
(2) the "area" is non-negative
(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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