Start with a small 4x4 square.
Sketch a continuous series of line segments (no curves) to divide the square neatly in half.
(Be interesting, please: no fair drawing a straight vertical or horizontal line or a simple diagonal.)
Prove that the two sections do indeed take up the same area.
Check to see if the figure has rotational symmetry. (That is, if it looks exactly the same when it's rotated any distance less than 360 degrees.)
Color the two sections contrasting colors.
Repeat the process 3 times. You may transform the original design by a) rotating (turning) the design 90, 180, or 270 degrees, or b) reflecting (flipping) the design as if it were appearing in a mirror. You may also keep the design oriented exactly the same as the original.
Arrange the four squares into a larger square.
Repeat this larger square four times. Place these together to create a sixteen-square unit.
Write a description of what you did.
The pictures show the results.
And the answer to the equation? Well, we could say "Fractions + Transformations = An Example of Applied Mathematics." Or, we could also say simply "Fractions + Transformations = Art." Your choice!
No comments:
Post a Comment