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Dissection of Circle

Dissection of Circle
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2015-04-27 09:28
CircleTransformationGeometric Construction
In collections Circumference, Area, and Volume
This example demonstrates how to dissect a circle through rotation and division, illustrating the concept of similarity transformation. Key mathematical concepts include circles, similarity, and angles. Using GeoGebra commands such as Circle, Rotate, CircleSector, and Angle, a series of circles and angles are constructed to show the process of circle dissection. Suitable for middle school and above students to learn geometric transformations and similarity.

GeoGebra Commands & Parameters

  1. Circle(A, p) → c
  2. Rotate(B, (360 / n)°, A) → B'
  3. CircleSector(A, B, B') → d
  4. Angle(B, A, B') → α
  5. Sequence(Rotate[d, 360° - (i * 360 / n)°, A], i, 1, n, 1) → list1
  6. Point(xAxis) → C
  7. OrthogonalLine(C, xAxis) → a
  8. Circle(C, p) → e
  9. Rotate(B, 225*°, A) → B'_1
  10. Rotate(B', 225*°, A) → B''
  11. Rotate(D, (-α) / 2, C) → D'
  12. Rotate(C, α, D') → C'
  13. CircleSector(D', C, C') → f
  14. Vector(C, C') → u
  15. Midpoint(D', C') → E
  16. Sequence(Translate[f, Vector[i / 2 * u]], i, 2, n, 2) → list2
  17. Mirror(f, E) → f'
  18. Sequence(Translate[f', Vector[i / 2 * u]], i, 2, n, 2) → list3
  19. Point(list2) → F
  20. Point(list3) → G
  21. Segment(F, G) → b

AI Drawing Prompt Reference

Draw a circle and then rotate and divide it around the center to form a series of similar arcs and angles. First, draw a circle, then rotate it around the center to generate multiple arcs and angles. Next, construct a series of circles similar to the original one using rotation and angle transformations. Finally, use translation and mirroring operations to generate a series of arcs, and connect the endpoints of these arcs to form a line segment.
The prompt above was compiled from the original drawing commands and is for reference only.