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Bohemia (cúpula de)

Bohemia (cúpula de)
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2023-03-14 04:30
AngleFunctionProbability & StatisticsGeometric Construction
In collections geometriadinamica.es
Bohemia (cúpula de) demonstrates geometric constructions and probability distributions. Key concepts include triangles, circles, angles, vectors, and functions. Construction involves GeoGebra commands like Segment, Point, OrthogonalLine, Circle, Intersect, Ellipse, Angle, CurveCartesian, and Sequence. Suitable for high school or university math courses to explore geometry and probability integration.

GeoGebra Commands & Parameters

  1. Segment(Q3, Q4) → p2
  2. Point(p2) → P3
  3. Segment(P3, Q4) → p4
  4. Point(p4) → P4
  5. Segment(Q1, Q2) → p1
  6. Point(p1) → P1
  7. Segment(P1, Q2) → p3
  8. Point(p3) → P2
  9. OrthogonalLine(C, xAxis) → zz2
  10. Circle(C, 0.62) → zz0
  11. Intersect(zz0, zz2, 1) → ZZ4
  12. Intersect(zz0, zz2, 2) → ZZ3
  13. Ellipse(ZZ3, ZZ4, 0.65) → zElipse2
  14. Point(zElipse2) → Z
  15. Intersect(zElipse2, zz2) → ZZ7, ZZ8
  16. Angle(ZZ8, C, Z) → zAngInc
  17. OrthogonalLine(C, yAxis) → zz1
  18. Intersect(zz0, zz1, 2) → ZZ2
  19. Intersect(zz0, zz1, 1) → ZZ1
  20. Ellipse(ZZ1, ZZ2, 0.65) → zElipse1
  21. Point(zElipse1) → XY
  22. Intersect(zElipse1, zz1) → ZZ5, ZZ6
  23. Angle(ZZ6, C, XY) → zAngRot
  24. Segment(Q5, Q6) → p5
  25. Point(p5) → P5
  26. Segment(ZZ5, ZZ6) → zz4
  27. Segment(ZZ7, ZZ8) → zz3
  28. Intersect(zElipse2, zElipse1, 1) → zPunto1
  29. Intersect(zElipse2, zElipse1, 4) → zPunto2
  30. Segment(zPunto1, zPunto2) → zSeg2
  31. CurveCartesian((r / 2 * (((a * cos(u)) * sin(zAngRot)) + (((b * cos(β)) + (a * sin(u))) * cos(zAngRot)))), (r / 2 * (((((-a) * cos(u)) * cos(zAngRot)) * sin(zAngInc)) + ((((b * cos(β)) + (a * sin(u))) * sin(zAngRot)) * sin(zAngInc)) + ((c * sin(β)) * cos(zAngInc)))), u, u1, u2) → a1
  32. CurveCartesian((r / 2 * (((a * cos(u)) * sin(zAngRot)) + (((-b) + (a * sin(u))) * cos(zAngRot)))), (r / 2 * (((((-a) * cos(u)) * cos(zAngRot)) * sin(zAngInc)) + ((((-b) + (a * sin(u))) * sin(zAngRot)) * sin(zAngInc)))), u, u1, u2) → curva1
  33. Sequence(CurveCartesian[(r / 2 * (((a * cos(u)) * sin(zAngRot)) + (((b * cos(v)) + (a * sin(u))) * cos(zAngRot)))), (r / 2 * (((((-a) * cos(u)) * cos(zAngRot)) * sin(zAngInc)) + ((((b * cos(v)) + (a * sin(u))) * sin(zAngRot)) * sin(zAngInc)) + ((c * sin(v)) * cos(zAngInc)))), u, u1, u2], v, v1, v2, (2 * paso)) → list3
  34. CurveCartesian((r / 2 * (((a * cos(α)) * sin(zAngRot)) + (((b * cos(v)) + (a * sin(α))) * cos(zAngRot)))), (r / 2 * (((((-a) * cos(α)) * cos(zAngRot)) * sin(zAngInc)) + ((((b * cos(v)) + (a * sin(α))) * sin(zAngRot)) * sin(zAngInc)) + ((c * sin(v)) * cos(zAngInc)))), v, v1, v2) → curva2
  35. Sequence(CurveCartesian[(r / 2 * (((a * cos(u)) * sin(zAngRot)) + (((b * cos(v)) + (a * sin(u))) * cos(zAngRot)))), (r / 2 * (((((-a) * cos(u)) * cos(zAngRot)) * sin(zAngInc)) + ((((b * cos(v)) + (a * sin(u))) * sin(zAngRot)) * sin(zAngInc)) + ((c * sin(v)) * cos(zAngInc)))), v, v1, v2], u, u1, u2, paso) → list1

AI Drawing Prompt Reference

Draw a geometric structure with two ellipses and a circle. First, construct the foci of the two ellipses using points and line segments, then use these foci and the center to draw the ellipses. Next, construct two tangents to the ellipses using angles and the center, and use the intersection points of these tangents and the ellipses to draw the ellipses. Finally, use curve equations to draw the curves of the two ellipses and generate a series of curves using the sequence command.
The prompt above was compiled from the original drawing commands and is for reference only.