MathPlotAI Logo MathPlotAI

Sphere and Octahedron

Sphere and Octahedron
Loading the math board and drawing, please wait…
2016-01-08 04:52
VectorSolid GeometryGeometric Construction
This example demonstrates the geometric relationship and construction method between a sphere and an octahedron. Core mathematical concepts include solid geometry, vectors, and geometric construction. GeoGebra commands and objects used in the construction are RotateText, Sphere, Intersect, Segment, Polygon, Pyramid, Midpoint, Dilate, Mirror, and Angle. Suitable for high school and above students learning solid geometry, vector operations, and the construction of complex geometric figures, as well as for demonstrating related topics.

GeoGebra Commands & Parameters

  1. RotateText("uStas\;\&\,Т.С.", 90°) → надпись01
  2. Sphere(Q, (3 * m)) → Ω
  3. Intersect(Line[Q, xAxis], Ω) → K_1, K
  4. Intersect(Line[Q, yAxis], Ω) → N_1, N
  5. Intersect(zAxis, Ω) → M_1, M
  6. Segment(K, M) → a
  7. Segment(N, K_1) → b
  8. Polygon(K, N, K_1, N_1) → s1, k, n, k_1, n_1
  9. Pyramid(s1, M) → c, граньKMN, грань2, грань1, грань3, реброKM, реброMN, ребро1, ребро2
  10. Pyramid(s1, M_1) → d, грань7, грань5, грань4, грань6, ребро4, ребро6, ребро3, ребро5
  11. Midpoint(K, N_1) → A
  12. Midpoint(K_1, N) → B
  13. Dilate(M, ch3, A) → C
  14. Mirror(C, Q) → C_1
  15. Polygon(M, B, M_1, A) → s2, m_1, b_1, m_2, a_1
  16. Segment(C, C_1) → e
  17. Angle(M, C, Q) → α
  18. Angle(Q, C_1, M_1) → β