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Holiday Geometric Modeling

Holiday Geometric Modeling
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2017-12-25 11:42
FunctionSolid GeometryTransformationGeometric Construction
In collections GeoGebra 3D & AR: PreCalc & Calculus Resources
This example demonstrates how to create holiday-themed models using geometric shapes like cylinders, squares, and parabolas combined with transformations. Core math concepts include solid geometry, function graphing, dilation, tangent lines, and reflections. Construction highlights include commands like Surface, IntersectPath, Plane, Mirror, and Line from GeoGebra, suitable for high school students and above learning spatial geometry, function modeling, and dynamic transformations, or for math enthusiasts creating visual models.

GeoGebra Commands & Parameters

  1. Surface(((R + (r * cos(u))) * cos(v)), ((R + (r * cos(u))) * sin(v)), (r * sin(u)), u, 0, u_1, v, 0, π / 6) → g
  2. Surface(((R + (r * cos(u))) * cos(v)), ((R + (r * cos(u))) * sin(v)), (r * sin(u)), u, 0, u_1, v, π / 6, π / 3) → b
  3. Surface(((R + (r * cos(u))) * cos(v)), ((R + (r * cos(u))) * sin(v)), (r * sin(u)), u, 0, u_1, v, π / 3, π / 2) → c
  4. Surface(((R + (r * cos(u))) * cos(v)), ((R + (r * cos(u))) * sin(v)), (r * sin(u)), u, 0, u_1, v, π / 2, (2 * π / 3)) → d
  5. Surface(((R + (r * cos(u))) * cos(v)), ((R + (r * cos(u))) * sin(v)), (r * sin(u)), u, 0, u_1, v, (2 * π / 3), (5 * π / 6)) → e
  6. Surface(((R + (r * cos(u))) * cos(v)), ((R + (r * cos(u))) * sin(v)), (r * sin(u)), u, 0, u_1, v, (5 * π / 6), π) → f
  7. IntersectPath(y = 0, i) → k
  8. Surface((-R) + (r * cos(u)), v, (r * sin(u)), u, 0, u_1, v, 0, h / 6) → j
  9. Plane((0, 0, 0), (3, 0, 0), (10, 0, 5)) → l
  10. Mirror(j, l) → j'
  11. Surface((-R) + (r * cos(u)), v, (r * sin(u)), u, 0, u_1, v, h / 6, h / 3) → m
  12. Surface((-R) + (r * cos(u)), v, (r * sin(u)), u, 0, u_1, v, h / 3, h / 2) → n
  13. Surface((-R) + (r * cos(u)), v, (r * sin(u)), u, 0, u_1, v, h / 2, (2 * h / 3)) → o
  14. Surface((-R) + (r * cos(u)), v, (r * sin(u)), u, 0, u_1, v, (2 * h / 3), (5 * h / 6)) → p
  15. Surface((-R) + (r * cos(u)), v, (r * sin(u)), u, 0, u_1, v, (5 * h / 6), h) → q
  16. Mirror(m, l) → m'
  17. Mirror(n, l) → n'
  18. Mirror(o, l) → o'
  19. Mirror(p, l) → p'
  20. Mirror(q, l) → q'
  21. Line((0, 0, 0), (0, 0, 1)) → s
  22. Line((0, 0, 0), (1, 0, 0)) → t
  23. Line((0, 0, 0), (0, 1, 0)) → a