Optimal Rhombus Demonstration

Optimal Rhombus Demonstration
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2018-03-19 03:28
This example demonstrates how to construct an optimal rhombus and its related geometric properties using GeoGebra. It involves core mathematical concepts such as rhombus, exponential functions, standard deviation, tangent lines, exponential functions, LCM, and GCD. The construction uses commands like Segment, Circle, Intersect, Line, Point, Distance, and Angle, with objects including A, B, f, c, d, C, D, g, h, i, E, F, j, k, distanceFE, TextFE, e, G, l, m, α, β, γ, δ, distanceGA, TextGA, distanceAF, TextAF, distanceFB, TextFB, distanceBG, TextBG. It is suitable for high school students and teachers for geometric construction and function analysis education.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Circle(A, B) → c
  3. Circle(B, Segment[B, A]) → d
  4. Intersect(c, d, 1) → C
  5. Intersect(c, d, 2) → D
  6. Line(C, D) → g
  7. Line(A, g) → h
  8. Line(B, g) → i
  9. Intersect(g, f) → E
  10. Point(g) → F
  11. Segment(A, F) → j
  12. Segment(F, B) → k
  13. Distance(F, E) → distanceFE
  14. Circle(E, F) → e
  15. Intersect(e, g, 2) → G
  16. Segment(A, G) → l
  17. Segment(B, G) → m
  18. Angle(A, F, B) → α
  19. Angle(B, G, A) → β
  20. Angle(G, A, F) → γ
  21. Angle(F, B, G) → δ
  22. Distance(G, A) → distanceGA
  23. Distance(A, F) → distanceAF
  24. Distance(F, B) → distanceFB
  25. Distance(B, G) → distanceBG