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Cylinder by JM Arranz, JA Mora, M Sada y R Losada

Cylinder by JM Arranz, JA Mora, M Sada y R Losada
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2023-03-15 19:00
CircleSolid GeometryGeometric Construction
In collections geometriadinamica.es
This example demonstrates the construction of a cylinder. Key mathematical concepts include circles, solid geometry, and geometric construction. Using GeoGebra commands such as Segment, Circle, and Intersect, various parts of the cylinder can be constructed. Suitable for middle school and above students or teachers.

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 * ((cos(α) * sin(zAngRot)) + (sin(α) * cos(zAngRot)))), (r * ((((-cos(α)) * cos(zAngRot)) * sin(zAngInc)) + ((sin(α) * sin(zAngRot)) * sin(zAngInc)) + (v * cos(zAngInc)))), v, v1, v2) → curva2
  32. CurveCartesian((r * ((cos(u) * sin(zAngRot)) + (sin(u) * cos(zAngRot)))), (r * ((((-cos(u)) * cos(zAngRot)) * sin(zAngInc)) + ((sin(u) * sin(zAngRot)) * sin(zAngInc)) + (β * cos(zAngInc)))), u, u1, u2) → a1
  33. CurveCartesian((r * ((cos(u) * sin(zAngRot)) + (sin(u) * cos(zAngRot)))), (r * ((((-cos(u)) * cos(zAngRot)) * sin(zAngInc)) + ((sin(u) * sin(zAngRot)) * sin(zAngInc)))), u, u1, u2) → curva1A
  34. Sequence(CurveCartesian[(r * ((cos(u) * sin(zAngRot)) + (sin(u) * cos(zAngRot)))), (r * ((((-cos(u)) * cos(zAngRot)) * sin(zAngInc)) + ((sin(u) * sin(zAngRot)) * sin(zAngInc)) + (v * cos(zAngInc)))), v, v1, v2], u, u1, u2, paso) → list2
  35. Sequence(CurveCartesian[(r * ((cos(u) * sin(zAngRot)) + (sin(u) * cos(zAngRot)))), (r * ((((-cos(u)) * cos(zAngRot)) * sin(zAngInc)) + ((sin(u) * sin(zAngRot)) * sin(zAngInc)) + (v * cos(zAngInc)))), u, u1, u2], v, v1, v2, paso) → list1

AI Drawing Prompt Reference

Draw a 3D cylinder with an elliptical base and top, connected by a curved surface. Start by constructing two intersecting ellipses representing the bottom and top faces, and determine their centers and rotation axes. Pick a point on the bottom ellipse and use the line from it to the center to set the tilt angle. Then generate a series of parallel curves extending from the bottom ellipse outline to the top ellipse, forming the cylinder's side. Finally, add two auxiliary segments connecting corresponding points on the top and bottom ellipses to indicate the cylinder's height and direction. The overall figure includes two ellipses, several surface curves, and auxiliary segments, showing a solid cylinder.
The prompt above was compiled from the original drawing commands and is for reference only.