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Cones, Statistics, and Isosceles Triangles

Cones, Statistics, and Isosceles Triangles
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2023-03-15 21:28
TrigonometryCoordinate GeometrySolid GeometryProbability & StatisticsGeometric Construction
In collections geometriadinamica.es
This example demonstrates the geometric relationships between cones, statistical data, and isosceles triangles. It involves core concepts like cone sections, statistical analysis, and the orthocenter of isosceles triangles. Construction highlights include using commands such as Segment, Point, OrthogonalLine, Circle, Intersect, Ellipse, Angle, CurveCartesian, and Sequence. Suitable for high school mathematics education, focusing on the integration of solid geometry and analytical geometry.

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 * (((sin((2 * v)) * (cos(α))^(2)) * sin(zAngRot)) + ((sin(v) * sin((2 * α))) * cos(zAngRot)))), (r * (((((-sin((2 * v))) * (cos(α))^(2)) * cos(zAngRot)) * sin(zAngInc)) + (((sin(v) * sin((2 * α))) * sin(zAngRot)) * sin(zAngInc)) + ((cos(v) * sin((2 * α))) * cos(zAngInc)))), v, v1, v2) → curva2
  32. CurveCartesian(0, (r * ((-sin((2 * u))) * cos(zAngInc))), u, u1, u2) → curva1
  33. CurveCartesian((r * (((sin((2 * β)) * (cos(u))^(2)) * sin(zAngRot)) + ((sin(β) * sin((2 * u))) * cos(zAngRot)))), (r * (((((-sin((2 * β))) * (cos(u))^(2)) * cos(zAngRot)) * sin(zAngInc)) + (((sin(β) * sin((2 * u))) * sin(zAngRot)) * sin(zAngInc)) + ((cos(β) * sin((2 * u))) * cos(zAngInc)))), u, u1, u2) → a1
  34. Sequence(CurveCartesian[(r * (((sin((2 * v)) * (cos(u))^(2)) * sin(zAngRot)) + ((sin(v) * sin((2 * u))) * cos(zAngRot)))), (r * (((((-sin((2 * v))) * (cos(u))^(2)) * cos(zAngRot)) * sin(zAngInc)) + (((sin(v) * sin((2 * u))) * sin(zAngRot)) * sin(zAngInc)) + ((cos(v) * sin((2 * u))) * cos(zAngInc)))), v, v1, v2], u, u1, u2, (2 * paso)) → list2
  35. Sequence(CurveCartesian[(r * (((sin((2 * v)) * (cos(u))^(2)) * sin(zAngRot)) + ((sin(v) * sin((2 * u))) * cos(zAngRot)))), (r * (((((-sin((2 * v))) * (cos(u))^(2)) * cos(zAngRot)) * sin(zAngInc)) + (((sin(v) * sin((2 * u))) * sin(zAngRot)) * sin(zAngInc)) + ((cos(v) * sin((2 * u))) * cos(zAngInc)))), u, u1, u2], v, v1, v2, paso) → list1

AI Drawing Prompt Reference

Draw a graph that includes cone sections, statistical data, and isosceles triangles. The graph should have the cone's axis, ellipses, angles, and curves. The construction order should include drawing the axis, circles, ellipses, intersection points, angle calculations, and curve drawing.
The prompt above was compiled from the original drawing commands and is for reference only.