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Palm Tree Construction

Palm Tree Construction
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2018-09-16 01:10
FunctionCoordinate GeometryTransformationGeometric Construction
This example demonstrates how to construct a palm tree shape using rotations and combinations. It involves core mathematical concepts like rotation, set theory, parabola, standard deviation, and pyramid. The construction uses commands and objects such as Rotate, Join, Intersect, Sequence, and PolyLine in GeoGebra. It is suitable for high school mathematics learning and exploring the combination of geometric transformations and function graphs.

GeoGebra Commands & Parameters

  1. Rotate(B, (360 * ° / n), A) → B'
  2. Join({{A}, Sequence[Sequence[(i / j * (A + (j * (B - A)))) + ((1 - i / j) * (A + (j * (B' - A)))), i, 0, j], j, 1, m]}) → L_1
  3. Intersect(Ray[Rotate[E, (-0.5 * (180° - (360 * ° / n))), E], Rotate[F, (-0.5 * (180° - (360 * ° / n))), E]], Ray[Rotate[F, (0.5 * (180° - (360 * ° / n))), F], Rotate[E, (0.5 * (180° - (360 * ° / n))), F]]) → G
  4. Sequence(Rotate[L_1, ((k * 360) * ° / n), G], k, 0, n - 1) → L_2
  5. PolyLine(C + ((m + 1) * (B' - A)), C, C + ((m + 1) * (B - A))) → f
  6. Sequence(Rotate[f, ((k * 360) * ° / n), G], k, 0, n - 1) → L_3
  7. Rotate(H, (360 * ° / n), G) → H'
  8. Sequence(Sequence[(i / j * (G + (j * (H - G)))) + ((1 - i / j) * (G + (j * (H' - G)))), i, 0, j - 1], j, 1, q - 1) → L_4
  9. Sequence(Rotate[L_4, ((k * 360) * ° / n), G], k, 0, n - 1) → L_5