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Rotation vs. Time - Addition Subtraction Example

Rotation vs. Time - Addition Subtraction Example
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2017-09-27 09:59
FunctionTransformationGeometric Construction
This example demonstrates the relationship between rotation and time, involving addition and subtraction operations. Using GeoGebra commands such as Rotate, Segment, and Textfield, it dynamically shows the changes in rotating figures. Suitable for middle school and above students to learn geometric transformations and function graphs.

GeoGebra Commands & Parameters

  1. Textfield(f) → InputBox1
  2. Textfield(a) → InputBox2
  3. Textfield(b) → InputBox3
  4. Segment(A, B) → g
  5. Rotate(A, (f(t))°, A) → A'
  6. Rotate(B, (f(t))°, A) → B'
  7. Segment(A', B') → g'
  8. Rotate(A, (h(t) / ((2 * π)) * 360), A) → A'_{1}
  9. Rotate(B, ((h(t) / 360 * 2) * π), A) → B'_{1}
  10. Segment(A'_{1}, B'_{1}) → g'_{1}
  11. Textfield(t) → InputBox4
  12. Circle(A, B) → e

AI Drawing Prompt Reference

Draw a circle e, then take two points A and B on the circle. Use InputBox1 to input function f(t), and rotate point B around point A by f(t) degrees to get points A' and B'. Connect A' and B' to form line segment g'. Then input function h(t) into InputBox2, and rotate point B around point A by h(t) radians converted to degrees to get points A'₁ and B'₁. Connect A'₁ and B'₁ to form line segment g'₁. Finally, use InputBox4 to input the value of t and observe how the figure changes over time.
The prompt above was compiled from the original drawing commands and is for reference only.