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Regular Tetrahedron by Loizos Loizou

Regular Tetrahedron by Loizos Loizou
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2018-01-27 05:49
PolygonVectorSolid Geometry
This example demonstrates the construction of a regular tetrahedron. Key mathematical concepts include regular polygons, median lines, and solid geometry. Using GeoGebra commands such as Intersect, Circle, and Point, various elements of the tetrahedron can be constructed. Suitable for middle school and above students or teachers.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, a) → c
  3. Intersect(c, xAxis) → B_1, B
  4. Circle(A, b) → d
  5. Intersect(d, yAxis) → D, E
  6. Point(c) → Δ
  7. Segment(A, Δ) → e
  8. Line(B, e) → f
  9. Line(Δ, xAxis) → g
  10. Intersect(f, g) → Γ
  11. Segment(Δ, B) → h
  12. Segment(Γ, A) → i
  13. Intersect(h, i) → O
  14. Line(O, xAxis) → j
  15. Intersect(f, j) → M
  16. OrthogonalLine(O, xAxis) → k
  17. Line(D, i) → l
  18. Intersect(k, l) → K
  19. Segment(A, K) → m
  20. Segment(K, Γ) → n
  21. Segment(K, Δ) → p
  22. Segment(K, B) → q
  23. Segment(Γ, B) → r
  24. Segment(Δ, Γ) → s
  25. Segment(A, B) → t
  26. Segment(K, M) → a_1
  27. Segment(O, M) → b_1
  28. Segment(K, O) → c_1
  29. Polygon(O, M, K) → poly1, k_1, h_1, i_1
  30. Polygon(Δ, Γ, B, A) → poly2, f_1, g_1, c_2, a_2
  31. Angle(O, A, K) → ω
  32. Angle(K, M, O) → φ
  33. Point(m) → C
  34. Point(c_1) → G
  35. Point(h_1) → I
  36. Point(g_1) → P
  37. Vector(P, Q) → u
  38. Vector(I, L) → v
  39. Vector(G, H) → w
  40. Vector(C, F) → z
  41. Vector(N, R) → u_1