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Tangent Spheres

Tangent Spheres
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2015-02-15 07:47
VectorSolid GeometryGeometric Construction
In collections surface 3D /3D-Oberflächen 1 surface 3D /3D-Oberflächen 1
This example demonstrates the spatial geometric relationships of multiple spheres that are tangent to each other. The core math concepts involved include spheres, tangents, spatial geometry, and vector operations. Construction highlights from the GeoGebra command summary include commands like Intersect, Circle, Rotate, Mirror, Midpoint, Distance, Sphere, Sequence, Element, Plane, Point, and IntersectPath, along with objects such as r, n, O, c, M, A, B, M', a, C, b, lista1, d, A', e, D, f, g, h, k, a', lista3, G, i, H, j. It is suitable for high school and above students studying solid geometry and vector applications in space.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → O
  2. Circle(O, r) → c
  3. Rotate(M, (-180 * ° / n), O) → A
  4. Mirror(A, yAxis) → B
  5. Midpoint(A, B) → M'
  6. Distance(A, M') → a
  7. Sphere(C, a) → b
  8. Sequence(Rotate[b, ((i * 360) * ° / n), zAxis], i, 0, n) → lista1
  9. Element(lista1, 1) → d
  10. Mirror(A, O) → A'
  11. Plane(C, O, A') → e
  12. Point(zAxis) → D
  13. Sphere(D, f) → g
  14. IntersectPath(e, g) → h
  15. IntersectPath(e, b) → k
  16. Element(lista3, 1) → G
  17. Sphere(H, i) → j

AI Drawing Prompt Reference

Draw a spatial geometric diagram showing the relationships of multiple tangent spheres. Start with a sphere centered at the origin, rotate and mirror to create two spheres, find midpoints and distances, then draw multiple tangent spheres. Rotate and mirror to generate a sequence of spheres, and intersect spheres with planes to get intersection lines, demonstrating spatial geometry and vector applications.
The prompt above was compiled from the original drawing commands and is for reference only.