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Rotational Symmetry by GeoGebra Institute of Hong Kong

Rotational Symmetry by GeoGebra Institute of Hong Kong
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2016-10-28 11:46
Coordinate GeometryTransformationGeometric Construction
This example demonstrates rotational symmetry. It involves key mathematical concepts such as rotational symmetry, angles, and geometric transformations. Using GeoGebra commands like Sequence, Rotate, and Segment, it dynamically shows how shapes change at different rotation angles. Suitable for middle school and above students to learn about geometric transformations and symmetry.

GeoGebra Commands & Parameters

  1. Sequence(Rotate[A, i°], i, 1, 360) → list1
  2. Circle(O, A) → k
  3. Point(list1) → B
  4. Angle(A, O, B) → α
  5. Rotate(pic1, α, O) → pic1'
  6. Rotate(pic2, α, O) → pic2'
  7. Rotate(pic3, α, O) → pic3'
  8. Rotate(pic4, α, O) → pic4'
  9. Rotate(pic5, α, O) → pic5'
  10. Rotate(pic6, α, O) → pic6'
  11. Rotate(pic7, α, O) → pic7'
  12. Rotate(pic8, α, O) → pic8'
  13. Rotate(pic9, α, O) → pic9'
  14. Segment(O, A) → j
  15. Segment(O, B) → l
  16. If(e, 180°, If[b ∨ c ∨ i, 90°, If[a, 72°, 0°]]) → matchAngle

AI Drawing Prompt Reference

Create a rotationally symmetric figure by first drawing a circle and a point A. Then, generate a sequence of point A rotated around point A by 360 degrees. Draw the line segment from point O to point A, and then create point B by rotating point A. Measure the angle AOB. Based on the angle AOB, rotate a series of shapes, including triangles, squares, pentagons, and nonagons, each time by the angle AOB.
The prompt above was compiled from the original drawing commands and is for reference only.