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Luna creciente: Geometry and Probability Exploration

Luna creciente: Geometry and Probability Exploration
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2023-03-15 20:43
Coordinate GeometryProbability & StatisticsGeometric Construction
In collections geometriadinamica.es
This example demonstrates how to explore mathematical phenomena through geometric figures and probability concepts. Key mathematical concepts include ellipses, linear equations, Pythagorean theorem, and probability statistics. Construction involves GeoGebra commands such as Segment, OrthogonalLine, Circle, Ellipse, and Angle. Suitable for middle or high school mathematics learning, used for geometric construction and probability analysis exercises.

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. CurveCartesian((r / 2.2 * ((((a + (sin(((b * 3.14) * u)) * sin(((b * 3.14) * 0.25)))) * sin(((c * 3.14) * 0.25))) * sin(zAngRot)) + (((a + (sin(((b * 3.14) * u)) * sin(((b * 3.14) * 0.25)))) * cos(((c * 3.14) * 0.25))) * cos(zAngRot)))), (r / 2.2 * (((((-(a + (sin(((b * 3.14) * u)) * sin(((b * 3.14) * 0.25))))) * sin(((c * 3.14) * 0.25))) * cos(zAngRot)) * sin(zAngInc)) + ((((a + (sin(((b * 3.14) * u)) * sin(((b * 3.14) * 0.25)))) * cos(((c * 3.14) * 0.25))) * sin(zAngRot)) * sin(zAngInc)) + (((cos(((b * 3.14) * u)) * sin(((b * 3.14) * 0.25))) + (4 * 0.25) - 2) * cos(zAngInc)))), u, u1, u2) → curva1
  27. Segment(ZZ5, ZZ6) → zz4
  28. Segment(ZZ7, ZZ8) → zz3
  29. Intersect(zElipse2, zElipse1, 1) → zPunto1
  30. Intersect(zElipse2, zElipse1, 4) → zPunto2
  31. Segment(zPunto1, zPunto2) → zSeg2
  32. CurveCartesian((r / 2.2 * ((((a + (sin(((b * 3.14159) * α)) * sin(((b * 3.14159) * v)))) * sin(((c * 3.14159) * v))) * sin(zAngRot)) + (((a + (sin(((b * 3.14159) * α)) * sin(((b * 3.14159) * v)))) * cos(((c * 3.14159) * v))) * cos(zAngRot)))), (r / 2.2 * (((((-(a + (sin(((b * 3.14159) * α)) * sin(((b * 3.14159) * v))))) * sin(((c * 3.14159) * v))) * cos(zAngRot)) * sin(zAngInc)) + ((((a + (sin(((b * 3.14159) * α)) * sin(((b * 3.14159) * v)))) * cos(((c * 3.14159) * v))) * sin(zAngRot)) * sin(zAngInc)) + (((cos(((b * 3.14159) * α)) * sin(((b * 3.14159) * v))) + (4 * v) - 2) * cos(zAngInc)))), v, v1, v2) → curva2
  33. Sequence(CurveCartesian[(r / 2.2 * ((((a + (sin(((b * 3.14159) * u)) * sin(((b * 3.14159) * v)))) * sin(((c * 3.14159) * v))) * sin(zAngRot)) + (((a + (sin(((b * 3.14159) * u)) * sin(((b * 3.14159) * v)))) * cos(((c * 3.14159) * v))) * cos(zAngRot)))), (r / 2.2 * (((((-(a + (sin(((b * 3.14159) * u)) * sin(((b * 3.14159) * v))))) * sin(((c * 3.14159) * v))) * cos(zAngRot)) * sin(zAngInc)) + ((((a + (sin(((b * 3.14159) * u)) * sin(((b * 3.14159) * v)))) * cos(((c * 3.14159) * v))) * sin(zAngRot)) * sin(zAngInc)) + (((cos(((b * 3.14159) * u)) * sin(((b * 3.14159) * v))) + (4 * v) - 2) * cos(zAngInc)))), v, v1, v2], u, u1, u2, paso) → list2
  34. CurveCartesian((r / 2.2 * ((((a + (sin(((b * 3.14159) * u)) * sin(((b * 3.14159) * β)))) * sin(((c * 3.14159) * β))) * sin(zAngRot)) + (((a + (sin(((b * 3.14159) * u)) * sin(((b * 3.14159) * β)))) * cos(((c * 3.14159) * β))) * cos(zAngRot)))), (r / 2.2 * (((((-(a + (sin(((b * 3.14159) * u)) * sin(((b * 3.14159) * β))))) * sin(((c * 3.14159) * β))) * cos(zAngRot)) * sin(zAngInc)) + ((((a + (sin(((b * 3.14159) * u)) * sin(((b * 3.14159) * β)))) * cos(((c * 3.14159) * β))) * sin(zAngRot)) * sin(zAngInc)) + (((cos(((b * 3.14159) * u)) * sin(((b * 3.14159) * β))) + (4 * β) - 2) * cos(zAngInc)))), u, u1, u2) → a1
  35. Sequence(CurveCartesian[(r / 2.2 * ((((a + (sin(((b * 3.14159) * u)) * sin(((b * 3.14159) * v)))) * sin(((c * 3.14159) * v))) * sin(zAngRot)) + (((a + (sin(((b * 3.14159) * u)) * sin(((b * 3.14159) * v)))) * cos(((c * 3.14159) * v))) * cos(zAngRot)))), (r / 2.2 * (((((-(a + (sin(((b * 3.14159) * u)) * sin(((b * 3.14159) * v))))) * sin(((c * 3.14159) * v))) * cos(zAngRot)) * sin(zAngInc)) + ((((a + (sin(((b * 3.14159) * u)) * sin(((b * 3.14159) * v)))) * cos(((c * 3.14159) * v))) * sin(zAngRot)) * sin(zAngInc)) + (((cos(((b * 3.14159) * u)) * sin(((b * 3.14159) * v))) + (4 * v) - 2) * cos(zAngInc)))), u, u1, u2], v, v1, v2, paso) → list1

AI Drawing Prompt Reference

Draw a figure consisting of two ellipses and two perpendicular lines, one vertical and one horizontal. The ellipses rotate around these lines, creating a dynamic effect. Mark several key points on the ellipses and connect them with curves to illustrate the combination of geometry and probability.
The prompt above was compiled from the original drawing commands and is for reference only.