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Sphere and Art

Sphere and Art
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2018-10-17 14:35
FunctionCoordinate GeometrySolid Geometry
In collections Color 3D surfaces
This example demonstrates the combination of spheres and art. It involves core mathematical concepts such as polynomial functions, tangents, cylinders, and power functions. Using GeoGebra commands like Intersect, CurveCartesian, Mirror, Surface, Polygon, and Segment, complex geometric shapes can be constructed. Suitable for high school mathematics education and learning, particularly in coordinate geometry and solid geometry.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → O_1
  2. CurveCartesian(x(A) + ((R * f(t)) * cos(t)), y(A) + ((R * f(t)) * sin(t)), z(A), t, 0, 6.39319) → a1
  3. CurveCartesian(x(B) + ((R * f(t)) * cos(t)), y(B), z(B) + ((R * f(t)) * sin(t)), t, 0, 6.28319) → b1
  4. CurveCartesian(x(D), y(D) + ((R * f(t)) * cos(t)), z(D) + ((R * f(t)) * sin(t)), t, 0, 6.28319) → c
  5. Mirror(a1, O) → a'
  6. Mirror(b1, O) → b'
  7. Mirror(c, O) → c'
  8. Surface(x(O) + ((R1 * cos(i)) * cos(j)), y(O) + ((R1 * cos(i)) * sin(j)), z(O) + (R1 * sin(i)), i, 0, 6.28319, j, 0, 0.5236) → d
  9. Surface(x(O) + ((R1 * cos(i)) * cos(j)), y(O) + ((R1 * cos(i)) * sin(j)), z(O) + (R1 * sin(i)), i, 0, 6.28319, j, 0.5236, 1.0472) → e
  10. Surface(x(O) + ((R1 * cos(i)) * cos(j)), y(O) + ((R1 * cos(i)) * sin(j)), z(O) + (R1 * sin(i)), i, 0, 6.28319, j, 1.0472, 1.5708) → g
  11. Surface(x(O) + ((R1 * cos(i)) * cos(j)), y(O) + ((R1 * cos(i)) * sin(j)), z(O) + (R1 * sin(i)), i, 0, 6.28319, j, 1.5708, 2.0944) → i
  12. Surface(x(O) + ((R1 * cos(i)) * cos(j)), y(O) + ((R1 * cos(i)) * sin(j)), z(O) + (R1 * sin(i)), i, 0, 6.28319, j, 2.0944, 2.61799) → j
  13. Surface(x(O) + ((R1 * cos(i)) * cos(j)), y(O) + ((R1 * cos(i)) * sin(j)), z(O) + (R1 * sin(i)), i, 0, 6.28319, j, 2.61799, 3.141592653589793) → k
  14. Polygon(G, E, F, H) → poly1, g_1, e_1, f_1, h_1
  15. Segment(E, J) → a
  16. Intersect(g_1, h_1) → P
  17. Segment(G, K) → b
  18. Segment(J, K) → l
  19. Intersect(h_1, f_1) → N
  20. Segment(M, H) → n
  21. Segment(M, L) → p
  22. Segment(J, L) → q
  23. Segment(K, M) → r
  24. Segment(L, F) → s

AI Drawing Prompt Reference

Create a 3D geometric artwork integrating spheres and artistic elements. The figure features multiple parametric curves based on polynomial and power functions, mirrored for symmetry. It includes segmented surfaces of a sphere, assembled into partial spherical regions. Polygons and segments connect key points to form a complex structure. The illustration demonstrates concepts in coordinate and solid geometry, suitable for high school math education.
The prompt above was compiled from the original drawing commands and is for reference only.