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Folium (hoja) Geometric Construction Example

Folium (hoja) Geometric Construction Example
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2023-03-15 20:11
TriangleCircleAngleGeometric Construction
In collections geometriadinamica.es
This example demonstrates geometric construction using GeoGebra, involving concepts like triangles, circles, and angles. It uses commands such as Segment, OrthogonalLine, Circle, Intersect, and Ellipse, along with various points and objects. Suitable for middle or high school mathematics to understand geometric relationships and construction techniques.

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(u) * ((2 * (β - p) / p) - tanh(β - p))) * sin(zAngRot)) + (cos(u + (2 * p / 3)) / cosh(β - p) * cos(zAngRot)))), (r * (((((-cos(u)) * ((2 * (β - p) / p) - tanh(β - p))) * cos(zAngRot)) * sin(zAngInc)) + ((cos(u + (2 * p / 3)) / cosh(β - p) * sin(zAngRot)) * sin(zAngInc)) + (cos(u - (2 * p / 3)) / cosh(β - p) * cos(zAngInc)))), u, u1, u2) → a1
  32. CurveCartesian(((r * cos(u + (2 * p / 3))) * cos(zAngRot)), (r * (((cos(u + (2 * p / 3)) * sin(zAngRot)) * sin(zAngInc)) + (cos(u - (2 * p / 3)) * cos(zAngInc)))), u, u1, u2) → curva1
  33. Sequence(CurveCartesian[(r * (((cos(u) * ((2 * v / p) - tanh(v))) * sin(zAngRot)) + (cos(u + (2 * p / 3)) / cosh(v) * cos(zAngRot)))), (r * (((((-cos(u)) * ((2 * v / p) - tanh(v))) * cos(zAngRot)) * sin(zAngInc)) + ((cos(u + (2 * p / 3)) / cosh(v) * sin(zAngRot)) * sin(zAngInc)) + (cos(u - (2 * p / 3)) / cosh(v) * cos(zAngInc)))), v, v1, v2], u, u1, u2, paso) → list3
  34. CurveCartesian((r * (((cos(α - p) * ((2 * v / p) - tanh(v))) * sin(zAngRot)) + (cos(α - p + (2 * p / 3)) / cosh(v) * cos(zAngRot)))), (r * (((((-cos(α - p)) * ((2 * v / p) - tanh(v))) * cos(zAngRot)) * sin(zAngInc)) + ((cos(α - p + (2 * p / 3)) / cosh(v) * sin(zAngRot)) * sin(zAngInc)) + (cos(α - p - (2 * p / 3)) / cosh(v) * cos(zAngInc)))), v, v1, v2) → curva2
  35. Sequence(CurveCartesian[(r * (((cos(u) * ((2 * v / p) - tanh(v))) * sin(zAngRot)) + (cos(u + (2 * p / 3)) / cosh(v) * cos(zAngRot)))), (r * (((((-cos(u)) * ((2 * v / p) - tanh(v))) * cos(zAngRot)) * sin(zAngInc)) + ((cos(u + (2 * p / 3)) / cosh(v) * sin(zAngRot)) * sin(zAngInc)) + (cos(u - (2 * p / 3)) / cosh(v) * cos(zAngInc)))), u, u1, u2], v, v1, v2, paso) → list1

AI Drawing Prompt Reference

Draw a leaf-shaped graph with two ellipses, two arcs, two angles, a triangle, a center point, two intersection points, and a curve. The ellipses and arcs form the leaf's shape, the center point and angles form the leaf's central part, the triangle and intersection points form the leaf's base, and the curve and intersection points form the leaf's edge.
The prompt above was compiled from the original drawing commands and is for reference only.