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Almohada

Almohada
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2023-03-14 04:26
CircleCoordinate GeometryGeometric Construction
In collections geometriadinamica.es
This example demonstrates how to draw a circular almohada. An almohada is a traditional Arabic pillow with a circular appearance. The core mathematical concepts involved include the geometric properties of circles and the equation of a circle. The construction involves using GeoGebra's Circle and Ellipse commands to draw the circular almohada. This example is suitable for middle school or high school students learning about the geometric properties of circles and the equation of a circle.

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)) + (cos(v) * cos(zAngRot)))), (r * ((((-cos(α)) * cos(zAngRot)) * sin(zAngInc)) + ((cos(v) * sin(zAngRot)) * sin(zAngInc)) + (((a * sin(α)) * sin(v)) * cos(zAngInc)))), v, v1, v2) → curva2
  32. CurveCartesian((r * ((cos(u) * sin(zAngRot)) + cos(zAngRot))), (r * ((((-cos(u)) * cos(zAngRot)) * sin(zAngInc)) + (sin(zAngRot) * sin(zAngInc)))), u, u1, u2) → curva1
  33. CurveCartesian((r * ((cos(u) * sin(zAngRot)) + (cos(β - 3.14159) * cos(zAngRot)))), (r * ((((-cos(u)) * cos(zAngRot)) * sin(zAngInc)) + ((cos(β - 3.14159) * sin(zAngRot)) * sin(zAngInc)) + (((a * sin(u)) * sin(β - 3.14159)) * cos(zAngInc)))), u, u1, u2) → a1
  34. Sequence(CurveCartesian[(r * ((cos(u) * sin(zAngRot)) + (cos(v) * cos(zAngRot)))), (r * ((((-cos(u)) * cos(zAngRot)) * sin(zAngInc)) + ((cos(v) * sin(zAngRot)) * sin(zAngInc)) + (((a * sin(u)) * sin(v)) * cos(zAngInc)))), v, v1, v2], u, u1, u2, paso) → list2
  35. Sequence(CurveCartesian[(r * ((cos(u) * sin(zAngRot)) + (cos(v) * cos(zAngRot)))), (r * ((((-cos(u)) * cos(zAngRot)) * sin(zAngInc)) + ((cos(v) * sin(zAngRot)) * sin(zAngInc)) + (((a * sin(u)) * sin(v)) * cos(zAngInc)))), u, u1, u2], v, v1, v2, paso) → list1

AI Drawing Prompt Reference

In a Cartesian plane, draw a circle centered at the origin with radius 0.62. Through the origin, draw two perpendicular lines along the coordinate axes, then mark their intersection points with the circle to define the needed directions. Using the two points determined from these intersections, construct two ellipses whose size parameter is 0.65: one ellipse uses the appropriate pair aligned with one axis direction, and the other ellipse uses the pair aligned with the orthogonal direction. Take intersection points of the ellipses with the corresponding axis lines and use the circle center together with those points to define an inclination angle and a rotation angle. Finally, generate two parametric curves using the variables and parameters r, a, α, β, v, and u together with the two angles, and connect them via parameter sequences to form a rounded “almohada”-like shape.
The prompt above was compiled from the original drawing commands and is for reference only.