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Exploring Geometry - Cube-a-rama

Tuesday, July 18, 2006
Homeschool: exploring geometry - 1

(Image Source: Nika's Flickr)

Q disappeared into her room yesterday and things were very quiet for a while. Such quiet is a nice change and if she were still an only child I would have checked to see what was happening up there. But she is not the only kid anymore and so she was left to her quiet devices! Just about every time this happens she comes back downstairs with some marvelous thing that she put together. Today I share what she brought us: an exploration in geometrical space.

We are calling it a skewed cube. We were thinking it might be called by some other more difficult to pronounced word like a trapezoidehedron or, who knows, a multidimensional transinfinite cube from some other reality. *winks*

To learn more about cubes and for patterns of interesting ones visit this Wolfram MathWorld page on cubes.

You could also use this Wolfram MathWorld polygon online classroom to explore this shape.

Mostly, this skewed cube was a chance for Q to use her hands to create a shape and the space around the shape and understand the restrictions necessary to form a particular shape. What I mean by that is that she had to adjust the sides and add various additional supports (extra cross bars and the purple clay) to stabilize the shape.

Homeschool: exploring geometry - 2

(Image Source: Nika's Flickr)

She could also see that some sides, due to the length of side members (sticks) would simply never form a flat face.

Homeschool: exploring geometry - 3

(Image Source: Nika's Flickr)

We could have talked about this but her doing it in a tactile way teaches lessons that even adults may not be able to articulate.

I remember as a small child holding and rotating a puzzle piece for a long time (maybe 30 minutes, that's a long time for a 5 year old) and intuiting chirality.

From the Wikipedia Chirality page:

"Chirality (Greek handedness, derived from the word stem χειρ~, ch[e]ir~ - hand~) is an asymmetry property important in several branches of science. An object or a system is called chiral if it differs from its mirror image. Such objects then come in two forms, which are mirror images of each other, and these pairs of mirror image objects are called enantiomorphs (Greek opposite forms) or, when referring to molecules, enantiomers. A non-chiral object is called achiral (sometimes also amphichiral)."

From the Wikipedia Chemistry Chirality page:

"A molecule is chiral when it cannot be superimposed on its mirror image (see diagram) with the two mirror image forms referred to as enantiomers. A mixture of equal amounts of the two enantiomers is said to be a racemic mixture. Chirality is of interest because of its application to stereochemistry in inorganic chemistry, organic chemistry, physical chemistry and biochemistry. The study of chirality falls in the domain of stereochemistry."

Puzzle pieces are lovely little lessons in chirality because you are forced to deal with chirality as you assemble the puzzle. I did not get a name for the handedness of shapes until undergrad organic chemistry when I learned about the chirality of molecules and how very important the orientation of shapes are to the molecular interplay between various species of reactants. This is especially true in biochemistry. An example is invert sugar. Some inverted sugars are not usable (metabolized) by the body because the chirality of the sugar doesn't fit into the enzymes that make the sugar useful to the body.

As I sat in that organic chemistry class I had no problem with understanding chirality because I sat and marveled over a puzzle piece as a tiny child.

Teachable moments wash over our children constantly. Without the chaos and cacophony of an over-crowded class room, my child was able to explore geometry in a way that is likely deeply integrated into her understanding of the world.

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