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Rotating Lines

Rotating Lines
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2020-05-11 10:29
Coordinate GeometryTransformationGeometric Construction
This example demonstrates the dynamic process of lines rotating around a fixed point. Core mathematical concepts include rotation, geometric transformation, and coordinate geometry. Construction highlights involve commands/objects like Circle, Sequence, Rotate, and Line from GeoGebra. Suitable for high school mathematics teaching or student exploration of geometric transformation properties.

GeoGebra Commands & Parameters

  1. Circle(A, 1) → c
  2. Circle(B, 1) → d
  3. Sequence(Rotate[D, π / 4 + b + (i * π / e), A], i, 0, e) → l1
  4. Sequence(Line[A, Element[l1, i]], i, 1, e) → l2
  5. Rotate(C, (h * b), B) → C'
  6. Sequence(Rotate[D, ((-π)) / 2 - b - (i * π / e), A], i, 0, e) → l3
  7. Line(B, C') → f
  8. Sequence(Line[A, Element[l3, i]], i, 1, e) → l4
  9. Sequence(Intersect[f, Element[l4, i]], i, 1, e) → l5
  10. Sequence(Intersect[f, Element[l2, i]], i, 1, e) → l6

AI Drawing Prompt Reference

Draw a dynamic process of lines rotating around a fixed point, including two concentric circles, multiple line segments rotating around the inner circle and extending outward, and multiple line segments rotating around the outer circle, with the inner and outer rotating line segments intersecting a fixed line segment to demonstrate the dynamic effects of rotation and geometric transformation.
The prompt above was compiled from the original drawing commands and is for reference only.