Microworld: Group
Actions and Orbits
Click the Hyperlink
above to visit the Microworld.
Authors:
Kate
Johnson and
J.T.
Ratnanather
Applying
an action to a point results in a transformed point. Similarly, applying an
action to a group of points results in a transformed group. In the two examples
to the left, the point and the group of points are part of the same space,
the 2-D real space. The scale and shear actions can be thought of in both
examples as acting on the entire space. The concept is a simple one, but is
an important starting point to understanding how one member of an anatomical
"family" (orbit) can be transformed into another member of that "family".
Two different actions have been applied to the space of the stomach on the
left, resulting in two significantly different looking stomachs. The top group
action is a 20 degree horizontal shear. The bottom group action is a 20 degree
vertical shear.
In
the example above, obviously infinitely many group actions on the 2-D real
space may be explored. We owe this geometric description of morphology to
D'Arcy Wentworth Thompson.
Number
of Pages: 7
Animation: Yes
Grade Level:15-16
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| author of this website, Mathwright 2000, MindScapes, | ||
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