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Mid-sphere in Higher Dimensions

Mid-sphere in Higher Dimensions
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2017-09-19 17:53
Coordinate GeometrySolid GeometryGeometric Construction
In collections surface 3D /3D-Oberflächen 1 surface 3D /3D-Oberflächen 1
This example demonstrates the mid-sphere in higher dimensions. Key mathematical concepts include the geometric construction in high-dimensional space and the properties of mid-spheres. Using GeoGebra commands such as Sphere, Intersect, and Circle, the construction of mid-spheres in higher-dimensional space is illustrated. Suitable for high school students and math enthusiasts to explore geometric constructions in high-dimensional space.

GeoGebra Commands & Parameters

  1. SurdText(sqrt(A2) - 1) → B2
  2. SurdText(sqrt(A3) - 1) → B3
  3. SurdText(sqrt(A4) - 1) → B4
  4. SurdText(sqrt(A5) - 1) → B5
  5. SurdText(sqrt(A6) - 1) → B6
  6. SurdText(sqrt(A7) - 1) → B7
  7. SurdText(sqrt(A8) - 1) → B8
  8. SurdText(sqrt(A9) - 1) → B9
  9. SurdText(sqrt(A10) - 1) → B10
  10. SurdText(sqrt(A11) - 1) → B11
  11. TableText({{A1, B1}, {A2, B2}, {A3, B3}, {A4, B4}, {A5, B5}, {A6, B6}, {A7, B7}, {A8, B8}, {A9, B9}, {A10, B10}, {A11, B11}}, "|_") → Text1
  12. Intersect(xAxis, yAxis) → A
  13. Circle(A, sqrt(2) - 1) → c
  14. Polygon((-2, -2), (2, -2), 4) → QU
  15. Point(yAxis) → B
  16. Point(MP) → C
  17. Polygon(C, B, A) → d1, a, c_1, b
  18. Sphere((0, 0, 0), sqrt(3) - 1) → d
  19. Sphere((-1, -1, -1), 1) → KG_1
  20. Sphere((1, -1, -1), 1) → KG_2
  21. Sphere((1, 1, -1), 1) → KG_3
  22. Sphere((-1, 1, -1), 1) → KG_4
  23. Sphere((-1, -1, 1), 1) → KG_5
  24. Sphere((1, -1, 1), 1) → KG_6
  25. Sphere((1, 1, 1), 1) → KG_7
  26. Sphere((-1, 1, 1), 1) → KG_8
  27. Segment(C, A) → f
  28. Point(PM) → E
  29. Segment(A, E) → g
  30. Segment(E, D) → h
  31. Segment(E, F) → i
  32. Segment(D, F) → j
  33. Cube((-2, -2, -2), (2, -2, -2), (2, 2, -2)) → k, G, Fläche5, FlächeHIJK, Kante2, Kante1, Kante4, Kante6, Kante3, KanteGK, KanteHK, KanteHI, H, Kante5, KanteIJ, Kante7, KanteJK, I, J, K, Fläche1, Fläche3, Fläche2, Fläche4