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Interactive Demonstration of Orthocenter and Fractal Geometry

Interactive Demonstration of Orthocenter and Fractal Geometry
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2017-02-15 23:48
TriangleVectorSequenceGeometric Construction
This example demonstrates the interactive relationship between the orthocenter of a triangle and fractal geometry, dynamically constructing geometric phenomena. Core concepts include orthocenter, fractal geometry, equation solving, arithmetic mean, and binomial distribution. Construction highlights the use of GeoGebra commands like Point, Vector, Textfield, Sequence, Intersect, and Segment. Suitable for high school and above learners to understand complex geometric constructions and probability statistics applications.

GeoGebra Commands & Parameters

  1. Point(yAxis) → A_1
  2. Vector(A_1, B) → u
  3. Textfield(f) → inputBox1
  4. Sequence(Vector[(0, k), (2, f(k))], k, -3, 3) → ExpMD
  5. Sequence((2, f(k)), k, -3, 3) → ExpTargPts
  6. Sequence((0, k), k, -3, 3) → SourcePtsMD
  7. Sequence((k, f(k)), k, -3, 3) → ExpGraphpts
  8. Vector(A_1, B_2) → v
  9. Sequence(Vector[(0, f(k)), (2, g(f(k)))], k, -3, 3) → logMD
  10. Sequence((f(k), k), k, -3, 3) → logGraphpts
  11. Sequence(Vector[(2, k), (4, f(k))], k, -3, 3) → InvLogMD
  12. Vector(B_2, A_2) → w
  13. Intersect(f, b, (1.9999999996268363, 19.99999999482685)) → D
  14. Vector(x_*, C_1) → z
  15. Segment(D, X) → j