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Coin Rolling

Coin Rolling
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2018-05-01 02:13
CircleTransformationGeometric Construction
In collections GCSE Higher Ch8 Transformations & Constructions
This example demonstrates the trajectory of a coin rolling on a plane. Key mathematical concepts include the properties of circles, transformations, and loci. Using GeoGebra commands such as Sequence, Rotate, and Dilate, the dynamic process of the coin rolling can be shown. Suitable for students at the junior high school level and above to learn about transformations and loci.

GeoGebra Commands & Parameters

  1. Sequence(10) → listR1
  2. Sequence(i, i, SelectedElement[listR1], 10, 1) → listR2
  3. Circle((0, 0), 1) → fixedCircle
  4. SelectedElement(listR1) → r_1
  5. SelectedElement(listR2) → r_2
  6. If(SelectedIndex[listInOut] ≟ 1, -1, 1) → outside
  7. Rotate((1, 0), ((k * 360))°, (0, 0)) → T
  8. Circle(O, r) → rollCircle
  9. Rotate(T, ((((outside * 1 / r) * k) * 360))°, O) → P
  10. If(outside ≟ 1, x^(2) + y^(2) ≤ 1, x^(2) + y^(2) ≥ 1) → shade
  11. Dilate(Rotate[P, If[outside ≟ 1, 135°, 315°], O], 1.41421, O) → H
  12. Dilate(Rotate[P, If[outside ≟ 1, 45°, 225°], O], 1.41421, O) → K
  13. GCD(r_1, r_2) → hcf
  14. If(lang ≟ 1, "直徑之比", "Ratio of Diameters") → text1

AI Drawing Prompt Reference

Draw a fixed circle with radius 1 centered at the origin. Add a rolling circle with adjustable radius, whose center moves along the circumference of the fixed circle while the rolling circle rotates. Mark a point on the rolling circle that traces a path as it rolls. The path shape differs depending on whether the rolling circle is outside or inside the fixed circle. Also construct two points on the rolling circle after rotations, and connect them to form a segment that changes dynamically. Shade the region inside or outside the fixed circle accordingly, and label the ratio of the diameters.
The prompt above was compiled from the original drawing commands and is for reference only.