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Steiner Points (4 Points)

Steiner Points (4 Points)
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2018-05-23 08:53
Coordinate GeometryTransformationGeometric Construction
In collections Besondere Punkte/Special Points
This example demonstrates the geometric construction and properties of Steiner points through four given points. It involves core mathematical concepts such as quadratic equations, similarity transformations, exponential functions, conic sections, and statistical characteristics. GeoGebra commands and objects like Polygon, Segment, Rotate, Angle, Distance, Circle, and Intersect are used in the construction process. Suitable for high school and above mathematics learners to understand the application of Steiner points in geometric optimization.

GeoGebra Commands & Parameters

  1. Polygon(B, A, 3) → poly1, n, q, r, M
  2. Polygon(D, C, 3) → poly2, s, t, a, N
  3. Segment(M, N) → b
  4. Segment(B, C) → m_1
  5. Segment(A, B) → n_1
  6. Segment(D, C) → p_1
  7. Segment(A, D) → c
  8. Rotate(I, 60°, B) → I'
  9. Angle(I, B, I') → ν
  10. Rotate(J, -60°, C) → J'
  11. Angle(J', C, J) → ξ
  12. Segment(I, J) → d
  13. Segment(I', I) → q_1
  14. Segment(M, I') → r_1
  15. Segment(B, I) → s_1
  16. Segment(A, I) → t_1
  17. Segment(J, C) → a_1
  18. Segment(J, J') → b_1
  19. Segment(J, D) → c_1
  20. Segment(J', N) → d_1
  21. Distance(M, N) → u
  22. Segment(I', B) → e_1
  23. Segment(J', C) → f_2
  24. Polygon(A, D, 3) → poly3, g_2, h_2, i_2, K
  25. Polygon(C, B, 3) → poly4, j_2, k_2, l_2, L
  26. Segment(K, L) → m_2
  27. Circle(K, A, D) → c_2
  28. Circle(B, L, C) → d_2
  29. Intersect(c_2, m_2, 2) → R
  30. Intersect(d_2, m_2, 2) → S
  31. Segment(A, R) → f
  32. Segment(R, D) → g
  33. Segment(R, S) → h
  34. Segment(B, S) → i
  35. Segment(S, C) → j
  36. Circle(M, B, A) → e
  37. Circle(D, C, N) → k
  38. Intersect(e, b, 2) → E
  39. Intersect(k, b, 2) → F
  40. Segment(A, E) → l
  41. Segment(B, E) → m
  42. Segment(E, F) → p
  43. Segment(F, D) → f_1
  44. Segment(F, C) → g_1
  45. Angle(F, E, A) → α
  46. Angle(E, F, C) → β
  47. Distance(K, L) → KL