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Rotating Rectangles

Rotating Rectangles
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2016-04-21 23:55
PolygonTransformationGeometric Construction
This GeoGebra example demonstrates a series of rotating and occasionally aligning rectangles. Key mathematical concepts include geometric transformations and rotation. Using commands such as LineBisector, Point, Midpoint, Mirror, OrthogonalLine, Intersect, Polygon, Rotate, and Sequence, the dynamic rotation of rectangles is constructed. Suitable for middle school and above students to learn about geometric transformations and rotation.

GeoGebra Commands & Parameters

  1. LineBisector(A, B) → a
  2. Point(a) → D
  3. Midpoint(A, B) → E
  4. Mirror(D, E) → D'
  5. OrthogonalLine(D, a) → b
  6. OrthogonalLine(B, b) → c
  7. Intersect(b, c) → F
  8. Mirror(F, B) → F'
  9. Mirror(F, E) → F'_1
  10. Mirror(F, D) → F'_2
  11. Polygon(F'_1, F'_2, F, F') → poly1, f'_1, f'_2, f, f'
  12. Rotate(F'_1, (t * α), E) → G
  13. Rotate(F'_2, (t * α), E) → H
  14. Rotate(F, (t * α), E) → F'_3
  15. Rotate(F', (t * α), E) → F''
  16. Polygon(G, H, F'_3, F'') → poly1', g, h, f'_3, f''
  17. Sequence(Sequence[Polygon[Translate[G, Vector[(spacing * ((i * Vector[A, C]) + (j * Vector[A, B])))]], Translate[H, Vector[(spacing * ((i * Vector[A, C]) + (j * Vector[A, B])))]], Translate[F'_3, Vector[(spacing * ((i * Vector[A, C]) + (j * Vector[A, B])))]], Translate[F'', Vector[(spacing * ((i * Vector[A, C]) + (j * Vector[A, B])))]]], i, (-N), N], j, (-N), N) → list1
  18. Circle(A, B) → e
  19. Textfield(α) → InputBox1

AI Drawing Prompt Reference

Draw a series of rectangles rotating around point E, with sides perpendicular to line segments AB and AC, and vertices F, F', F'_1, F'_2, and F'' rotating with angle t. First, draw the perpendicular bisector of line segment AB to get point D, then find the midpoint E of line segment AB, and use D and E to mirror point D' and draw the perpendicular line b from point D to line segment AB, and the perpendicular line c from point B to line segment AB, and find their intersection point F. Mirror point F to get points F', F'_1, F'_2, and F''. Construct rectangle F'_1F'_2FF', then rotate the rectangle around point E to get rectangle GHHF'_3F''. Finally, use translation and rotation commands to generate a series of rectangles.
The prompt above was compiled from the original drawing commands and is for reference only.