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Cantor Set Geometric Construction and Function Graphing

Cantor Set Geometric Construction and Function Graphing
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2021-08-08 12:03
TransformationGeometric ConstructionLocus
This example demonstrates the geometric properties of the Cantor set through rotation operations, involving concepts of fractal geometry, function graphing, and transformations. Construction requires using GeoGebra commands like Rotate with objects a, L1, button1, etc. Suitable for high school students learning geometric transformations and function visualization, useful in mathematical modeling and visualization teaching.

GeoGebra Commands & Parameters

  1. Rotate(Dilate[Join[{L1, Mirror[L1, x = 30]}], 1 / 3, (0, -1 - 0.5)], (a * 1 / 9), (10, -1 - 0.5)) → L2
  2. Rotate(Dilate[Join[{L2, Mirror[L2, x = 30]}], 1 / 3, (0, -2 - 0.5)], (a * 2 / 9), (10, -2 - 0.5)) → L3
  3. Rotate(Dilate[Join[{L3, Mirror[L3, x = 30]}], 1 / 3, (0, -3 - 0.5)], (a * 3 / 9), (10, -3 - 0.5)) → L4
  4. Rotate(Dilate[Join[{L4, Mirror[L4, x = 30]}], 1 / 3, (0, -4 - 0.5)], (a * 4 / 9), (10, -4 - 0.5)) → L5
  5. Rotate(Dilate[Join[{L5, Mirror[L5, x = 30]}], 1 / 3, (0, -5 - 0.5)], (a * 5 / 9), (10, -5 - 0.5)) → L6
  6. Rotate(Dilate[Join[{L6, Mirror[L6, x = 30]}], 1 / 3, (0, -6 - 0.5)], (a * 6 / 9), (10, -6 - 0.5)) → L7
  7. Rotate(Dilate[Join[{L7, Mirror[L7, x = 30]}], 1 / 3, (0, -7 - 0.5)], (a * 7 / 9), (10, -7 - 0.5)) → L8
  8. Rotate(Dilate[Join[{L8, Mirror[L8, x = 30]}], 1 / 3, (0, -8 - 0.5)], (a * 8 / 9), (10, -8 - 0.5)) → L9
  9. Rotate(Dilate[Join[{L9, Mirror[L9, x = 30]}], 1 / 3, (0, -9 - 0.5)], (a * 9 / 9), (10, -9 - 0.5)) → L10

AI Drawing Prompt Reference

Construct the Cantor set geometrically by first mirroring L1 at x=30, then scaling it by 1/3, and rotating it around point (0, -1.5) to get L2. Repeat this process, mirroring, scaling, and rotating to get L3 through L10, forming the geometric representation of the Cantor set.
The prompt above was compiled from the original drawing commands and is for reference only.