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General Solution for Symmetry Numbers on Surfaces-B

General Solution for Symmetry Numbers on Surfaces-B
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2019-05-26 01:41
Solid GeometryTransformationGeometric Construction
This example demonstrates how to find the general solution for symmetry numbers on surfaces. It involves core mathematical concepts such as centroid, circle, sphere, and symmetry. Construction highlights include using GeoGebra commands like Circle, Point, Barycenter, Sphere, PointIn, and Segment. Suitable for high school students and those interested in geometric transformations.

GeoGebra Commands & Parameters

  1. Circle(Sun, a) → c
  2. Point(c) → N
  3. Point(c) → C
  4. Point(c) → L
  5. Point(c) → K
  6. Point(c) → J
  7. Point(c) → I
  8. Point(c) → H
  9. Point(c) → G
  10. Point(c) → F
  11. Point(c) → E
  12. Point(c) → D
  13. Point(c) → B
  14. Point(c) → A
  15. Point(c) → M
  16. Barycenter({A, B, C, D, E, F, G, H, I, J, K, L}, {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}) → Earth
  17. Sphere(Earth, a) → b
  18. PointIn(b) → Moon
  19. Segment(Moon, E) → f
  20. Segment(Moon, D) → g
  21. Segment(Moon, F) → h
  22. Segment(Moon, G) → i
  23. Segment(Moon, H) → j
  24. Segment(Moon, I) → k
  25. Segment(Moon, J) → l
  26. Segment(Moon, K) → m
  27. Segment(Moon, L) → n
  28. Segment(Moon, A) → p
  29. Segment(Moon, B) → r
  30. Segment(Moon, C) → q
  31. Point(c) → O

AI Drawing Prompt Reference

Draw a sphere with Earth as its center, and 12 evenly distributed points A to L on the sphere's surface. Calculate the center Earth using the barycenter command. Then draw a moon around the center, connecting it to Earth with multiple segments to form a symmetrical pattern.
The prompt above was compiled from the original drawing commands and is for reference only.