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Rotated Polygon

Rotated Polygon
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2015-07-06 03:45
PolygonTransformationGeometric Construction
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This example demonstrates a dynamically rotating polygon. It involves the rotation of polygons and geometric transformations. Using the Sequence command in GeoGebra, a series of rotated polygons are constructed. This example is suitable for middle school and above students, for teaching geometric construction and transformations.

GeoGebra Commands & Parameters

  1. Sequence((((1 - e) * cos(i)), ((1 - e) * sin(i)), 0), i, 0, 6.28319, (2 * π / n)) → liste2
  2. Sequence((cos(i), sin(i), 0), i, 0, 6.28319, (2 * π / n)) → liste1
  3. Sequence((((1 - e) * cos(i)), ((1 - e) * sin(i)), e), i, 0, 6.28319, (2 * π / n)) → liste3
  4. Sequence((cos(i), sin(i), e), i, 0, 6.28319, (2 * π / n)) → liste4
  5. Sequence(Surface[(((x(Element[liste1, i]) * (1 - u)) + (u * x(Element[liste2, i]))) * (1 - v)) + (v * ((x(Element[liste2, i + 1]) * (1 - u)) + (u * x(Element[liste3, i + 1])))), (((y(Element[liste1, i]) * (1 - u)) + (u * y(Element[liste2, i]))) * (1 - v)) + (v * ((y(Element[liste2, i + 1]) * (1 - u)) + (u * y(Element[liste3, i + 1])))), (((z(Element[liste1, i]) * (1 - u)) + (u * z(Element[liste2, i]))) * (1 - v)) + (v * ((z(Element[liste2, i + 1]) * (1 - u)) + (u * z(Element[liste3, i + 1])))), u, 0, U, v, 0, V], i, 1, n) → liste5
  6. Sequence(Surface[(((x(Element[liste2, i]) * (1 - u)) + (u * x(Element[liste3, i]))) * (1 - v)) + (v * ((x(Element[liste3, i + 1]) * (1 - u)) + (u * x(Element[liste4, i + 1])))), (((y(Element[liste2, i]) * (1 - u)) + (u * y(Element[liste3, i]))) * (1 - v)) + (v * ((y(Element[liste3, i + 1]) * (1 - u)) + (u * y(Element[liste4, i + 1])))), (((z(Element[liste2, i]) * (1 - u)) + (u * z(Element[liste3, i]))) * (1 - v)) + (v * ((z(Element[liste3, i + 1]) * (1 - u)) + (u * z(Element[liste4, i + 1])))), u, 0, U, v, 0, V], i, 1, n) → liste6
  7. Sequence(Surface[(((x(Element[liste3, i]) * (1 - u)) + (u * x(Element[liste4, i]))) * (1 - v)) + (v * ((x(Element[liste4, i + 1]) * (1 - u)) + (u * x(Element[liste1, i + 1])))), (((y(Element[liste3, i]) * (1 - u)) + (u * y(Element[liste4, i]))) * (1 - v)) + (v * ((y(Element[liste4, i + 1]) * (1 - u)) + (u * y(Element[liste1, i + 1])))), (((z(Element[liste3, i]) * (1 - u)) + (u * z(Element[liste4, i]))) * (1 - v)) + (v * ((z(Element[liste4, i + 1]) * (1 - u)) + (u * z(Element[liste1, i + 1])))), u, 0, U, v, 0, V], i, 1, n) → liste7
  8. Sequence(Surface[(((x(Element[liste4, i]) * (1 - u)) + (u * x(Element[liste1, i]))) * (1 - v)) + (v * ((x(Element[liste1, i + 1]) * (1 - u)) + (u * x(Element[liste2, i + 1])))), (((y(Element[liste4, i]) * (1 - u)) + (u * y(Element[liste1, i]))) * (1 - v)) + (v * ((y(Element[liste1, i + 1]) * (1 - u)) + (u * y(Element[liste2, i + 1])))), (((z(Element[liste4, i]) * (1 - u)) + (u * z(Element[liste1, i]))) * (1 - v)) + (v * ((z(Element[liste1, i + 1]) * (1 - u)) + (u * z(Element[liste2, i + 1])))), u, 0, U, v, 0, V], i, 1, n) → liste8

AI Drawing Prompt Reference

Draw a dynamically rotating polygon by first creating a sequence of points on a unit circle, then rotating these points around the origin to form a series of rotated polygons. Use these rotated polygons to construct a series of surfaces, demonstrating the dynamic rotation effect of the polygon.
The prompt above was compiled from the original drawing commands and is for reference only.