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Sherlock's Hat

Sherlock's Hat
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2023-03-15 21:32
FunctionCoordinate GeometryGraphing
In collections geometriadinamica.es
This example demonstrates Sherlock's hat. It involves polynomial functions, logarithmic functions, and normal distribution. Using GeoGebra commands such as Segment, Point, OrthogonalLine, etc., complex geometric shapes can be constructed. Suitable for high school math 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 / 1.5 * ((((1 - v^(3)) * sin(α)) * sin(zAngRot)) + (((1 - v^(3)) * cos(α)) * cos(zAngRot)))), (r / 1.5 * (((((-(1 - v^(3))) * sin(α)) * cos(zAngRot)) * sin(zAngInc)) + ((((1 - v^(3)) * cos(α)) * sin(zAngRot)) * sin(zAngInc)) + (v * cos(zAngInc)))) + 1, v, v1, v2) → curva2
  32. CurveCartesian((r / 1.5 * ((((1 - β^(3)) * sin(u)) * sin(zAngRot)) + (((1 - β^(3)) * cos(u)) * cos(zAngRot)))), (r / 1.5 * (((((-(1 - β^(3))) * sin(u)) * cos(zAngRot)) * sin(zAngInc)) + ((((1 - β^(3)) * cos(u)) * sin(zAngRot)) * sin(zAngInc)) + (β * cos(zAngInc)))) + 1, u, u1, u2) → a1
  33. CurveCartesian((r / 1.5 * ((sin(u) * sin(zAngRot)) + (cos(u) * cos(zAngRot)))), (r / 1.5 * ((((-sin(u)) * cos(zAngRot)) * sin(zAngInc)) + ((cos(u) * sin(zAngRot)) * sin(zAngInc)))) + 1, u, u1, u2) → curva1
  34. Sequence(CurveCartesian[(r / 1.5 * ((((1 - v^(3)) * sin(u)) * sin(zAngRot)) + (((1 - v^(3)) * cos(u)) * cos(zAngRot)))), (r / 1.5 * (((((-(1 - v^(3))) * sin(u)) * cos(zAngRot)) * sin(zAngInc)) + ((((1 - v^(3)) * cos(u)) * sin(zAngRot)) * sin(zAngInc)) + (v * cos(zAngInc)))) + 1, v, v1, v2], u, u1, u2, paso) → list2
  35. Sequence(CurveCartesian[(r / 1.5 * ((((1 - v^(3)) * sin(u)) * sin(zAngRot)) + (((1 - v^(3)) * cos(u)) * cos(zAngRot)))), (r / 1.5 * (((((-(1 - v^(3))) * sin(u)) * cos(zAngRot)) * sin(zAngInc)) + ((((1 - v^(3)) * cos(u)) * sin(zAngRot)) * sin(zAngInc)) + (v * cos(zAngInc)))) + 1, u, u1, u2], v, v1, v2, paso) → list1

AI Drawing Prompt Reference

Draw a Sherlock-style hat. Start with a horizontal baseline, then build the brim outline using segments and points. The crown consists of two intersecting ellipses sharing a vertical centerline, tilted at angles. Fill the interior and surroundings with smooth curves and a grid of curved surfaces to create a 3D effect. The overall shape is symmetric, with interwoven curves forming a complex geometric design.
The prompt above was compiled from the original drawing commands and is for reference only.