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Curve Stitching and Transformations 3

Curve Stitching and Transformations 3
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2018-09-16 19:08
FunctionSequenceCoordinate GeometryTransformationGeometric Construction
In collections Geometry Transformation Maths for 8th Grade Units 1 to 3 Learn with Lindy: Transformations Intro
This example demonstrates the creation of complex shapes through curve stitching and transformations. It involves core mathematical concepts such as functions, sequences, coordinate geometry, and geometric transformations. The construction utilizes GeoGebra commands like Sequence, Take, and Segment, along with objects like h, D, E, n, L_1, F, L_2, L_3, a, L_4, f, g, L_5, L_6, L_9, L_{10}, L_{11}, L_7, L_8, L_{12}, L_{13}. Suitable for high school and above, it serves as a practical tool for learning function graphs, sequence applications, and geometric transformations.

GeoGebra Commands & Parameters

  1. Sequence(D + (w * (E - D)), w, 0, 1, 1 / 40) → L_1
  2. Sequence(E + (w * (F - E)), w, 0, 1, 1 / 40) → L_2
  3. Sequence(Segment[L_1(w), L_2(w)], w, 1, Length[L_1]) → L_3
  4. Take(L_3, 1, a) → L_4
  5. Segment(D, E) → f
  6. Segment(E, F) → g
  7. Sequence(Rotate[L_3, ((w * 2) * π / n)], w, 1, n) → L_5
  8. Take(L_5, 1, Length[L_5] - 1) → L_6
  9. Sequence(F + (w * (D - F)), w, 0, 1, 1 / 40) → L_9
  10. Sequence(Segment[L_1(w), L_9(w)], w, 1, Length[L_1]) → L_{10}
  11. Sequence(Segment[L_2(w), L_9(w)], w, 1, Length[L_1]) → L_{11}
  12. Sequence(Rotate[L_{10}, ((w * 2) * π / n)], w, 1, n) → L_7
  13. Take(L_7, 1, Length[L_7] - 1) → L_8
  14. Sequence(Rotate[L_{11}, ((w * 2) * π / n)], w, 1, n) → L_{12}
  15. Take(L_{12}, 1, Length[L_{12}] - 1) → L_{13}

AI Drawing Prompt Reference

Create a complex geometric shape through curve stitching and transformations. First, create two line segments L1 and L2, then generate L3, which is a series of segments between L1 and L2. Next, rotate L3 to generate L5, and then take a part of L5 to form L6. After that, create line segments f and g, and L9, then generate L10 and L11, which are segments between L1 and L9, and L2 and L9, respectively. Then, rotate L10 and L11 to generate L7 and L12, and finally take a part of L12 to form L8. The process involves mathematical concepts such as functions, sequences, coordinate geometry, and geometric transformations.
The prompt above was compiled from the original drawing commands and is for reference only.