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Crossed Beret

Crossed Beret
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2023-03-15 17:55
FunctionCoordinate GeometryGeometric Construction
In collections geometriadinamica.es
This example demonstrates the geometric construction of a crossed beret. It involves quadratic functions, geometric constructions, and indefinite integrals. Using GeoGebra commands such as Segment, Point, Intersect, etc., the shape of the beret can be constructed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Segment(Q5, Q6) → p5
  2. Point(p5) → P5
  3. Segment(Q3, Q4) → p2
  4. Point(p2) → P3
  5. Segment(P3, Q4) → p4
  6. Point(p4) → P4
  7. Segment(Q1, Q2) → p1
  8. Point(p1) → P1
  9. Segment(P1, Q2) → p3
  10. Point(p3) → P2
  11. OrthogonalLine(C, xAxis) → zz2
  12. Circle(C, 0.62) → zz0
  13. Intersect(zz0, zz2, 1) → ZZ4
  14. Intersect(zz0, zz2, 2) → ZZ3
  15. Ellipse(ZZ3, ZZ4, 0.65) → zElipse2
  16. Point(zElipse2) → Z
  17. Intersect(zElipse2, zz2) → ZZ7, ZZ8
  18. Angle(ZZ8, C, Z) → zAngInc
  19. OrthogonalLine(C, yAxis) → zz1
  20. Intersect(zz0, zz1, 2) → ZZ2
  21. Intersect(zz0, zz1, 1) → ZZ1
  22. Ellipse(ZZ1, ZZ2, 0.65) → zElipse1
  23. Point(zElipse1) → XY
  24. Intersect(zElipse1, zz1) → ZZ5, ZZ6
  25. Angle(ZZ6, C, XY) → zAngRot
  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 / 2) * sin((2 * v))) * sin(zAngRot)) + ((sin(α / 2) * sin((2 * v))) * cos(zAngRot)))), (r * (((((-cos(α / 2)) * sin((2 * v))) * cos(zAngRot)) * sin(zAngInc)) + (((sin(α / 2) * sin((2 * v))) * sin(zAngRot)) * sin(zAngInc)) - (((cos(v))^(2) - ((cos(α))^(2) * (sin(v))^(2))) * cos(zAngInc)))), v, v1, v2) → curva2
  32. CurveCartesian((r * (((cos(u / 2) * sin((2 * 3.14159 / 4))) * sin(zAngRot)) + ((sin(u / 2) * sin((2 * 3.14159 / 4))) * cos(zAngRot)))), (r * (((((-cos(u / 2)) * sin((2 * 3.14159 / 4))) * cos(zAngRot)) * sin(zAngInc)) + (((sin(u / 2) * sin((2 * 3.14159 / 4))) * sin(zAngRot)) * sin(zAngInc)) - (((cos(3.14159 / 4))^(2) - ((cos(u))^(2) * (sin(3.14159 / 4))^(2))) * cos(zAngInc)))), u, u1, u2) → curva1
  33. CurveCartesian((r * (((cos(u / 2) * sin((2 * β))) * sin(zAngRot)) + ((sin(u / 2) * sin((2 * β))) * cos(zAngRot)))), (r * (((((-cos(u / 2)) * sin((2 * β))) * cos(zAngRot)) * sin(zAngInc)) + (((sin(u / 2) * sin((2 * β))) * sin(zAngRot)) * sin(zAngInc)) - (((cos(β))^(2) - ((cos(u))^(2) * (sin(β))^(2))) * cos(zAngInc)))), u, u1, u2) → a1
  34. Sequence(CurveCartesian[(r * (((cos(u / 2) * sin((2 * v))) * sin(zAngRot)) + ((sin(u / 2) * sin((2 * v))) * cos(zAngRot)))), (r * (((((-cos(u / 2)) * sin((2 * v))) * cos(zAngRot)) * sin(zAngInc)) + (((sin(u / 2) * sin((2 * v))) * sin(zAngRot)) * sin(zAngInc)) - (((cos(v))^(2) - ((cos(u))^(2) * (sin(v))^(2))) * cos(zAngInc)))), u, u1, u2], v, v1, v2, paso) → list2
  35. Sequence(CurveCartesian[(r * (((cos(u / 2) * sin((2 * v))) * sin(zAngRot)) + ((sin(u / 2) * sin((2 * v))) * cos(zAngRot)))), (r * (((((-cos(u / 2)) * sin((2 * v))) * cos(zAngRot)) * sin(zAngInc)) + (((sin(u / 2) * sin((2 * v))) * sin(zAngRot)) * sin(zAngInc)) - (((cos(v))^(2) - ((cos(u))^(2) * (sin(v))^(2))) * cos(zAngInc)))), v, v1, v2], u, u1, u2, (3 * paso)) → list1

AI Drawing Prompt Reference

Draw a crossed beret consisting of two intersecting ellipses. Start by creating two line segments as bases, then find their midpoints and draw perpendicular lines that intersect a circle to get four points. Use these points to form two ellipses. Next, identify the intersection points on the ellipses and connect them to outline the beret's edges. Finally, use curves to connect the points on the ellipses for a smoother appearance.
The prompt above was compiled from the original drawing commands and is for reference only.