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Huevo: Geometric Construction and Symmetry Exploration

Huevo: Geometric Construction and Symmetry Exploration
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2023-03-15 20:37
CircleAngleGeometric Construction
In collections geometriadinamica.es
The Huevo example demonstrates how to explore symmetry and standard deviation through geometric constructions. Key mathematical concepts include symmetry, standard deviation, geometric construction, and ellipses. Construction involves using GeoGebra commands such as Segment, Point, OrthogonalLine, Circle, Intersect, Ellipse, etc. Suitable for middle school and above students to learn geometry and statistical foundations.

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(((2 * r) * ((((0.7 * sqrt(((u * (u - 1.4)) * (u - 1)))) * sin(α)) * sin(zAngRot)) + (((0.7 * sqrt(((u * (u - 1.4)) * (u - 1)))) * cos(α)) * cos(zAngRot)))), ((2 * r) * (((((-0.7 * sqrt(((u * (u - 1.4)) * (u - 1)))) * sin(α)) * cos(zAngRot)) * sin(zAngInc)) + ((((0.7 * sqrt(((u * (u - 1.4)) * (u - 1)))) * cos(α)) * sin(zAngRot)) * sin(zAngInc)) + (u * cos(zAngInc)))) - 3, u, u1, u2) → curva2
  32. CurveCartesian(((2 * r) * ((((0.7 * sqrt(((β * (β - 1.4)) * (β - 1)))) * sin(v)) * sin(zAngRot)) + (((0.7 * sqrt(((β * (β - 1.4)) * (β - 1)))) * cos(v)) * cos(zAngRot)))), ((2 * r) * (((((-0.7 * sqrt(((β * (β - 1.4)) * (β - 1)))) * sin(v)) * cos(zAngRot)) * sin(zAngInc)) + ((((0.7 * sqrt(((β * (β - 1.4)) * (β - 1)))) * cos(v)) * sin(zAngRot)) * sin(zAngInc)) + (β * cos(zAngInc)))) - 3, v, v1, v2) → a1
  33. CurveCartesian(((2 * r) * ((((0.7 * sqrt(((0.5 * (0.5 - 1.4)) * (0.5 - 1)))) * sin(v)) * sin(zAngRot)) + (((0.7 * sqrt(((0.5 * (0.5 - 1.4)) * (0.5 - 1)))) * cos(v)) * cos(zAngRot)))), ((2 * r) * (((((-0.7 * sqrt(((0.5 * (0.5 - 1.4)) * (0.5 - 1)))) * sin(v)) * cos(zAngRot)) * sin(zAngInc)) + ((((0.7 * sqrt(((0.5 * (0.5 - 1.4)) * (0.5 - 1)))) * cos(v)) * sin(zAngRot)) * sin(zAngInc)) + (0.5 * cos(zAngInc)))) - 3, v, v1, v2) → curva1
  34. Sequence(CurveCartesian[((2 * r) * ((((0.7 * sqrt(((u * (u - 1.4)) * (u - 1)))) * sin(v)) * sin(zAngRot)) + (((0.7 * sqrt(((u * (u - 1.4)) * (u - 1)))) * cos(v)) * cos(zAngRot)))), ((2 * r) * (((((-0.7 * sqrt(((u * (u - 1.4)) * (u - 1)))) * sin(v)) * cos(zAngRot)) * sin(zAngInc)) + ((((0.7 * sqrt(((u * (u - 1.4)) * (u - 1)))) * cos(v)) * sin(zAngRot)) * sin(zAngInc)) + (u * cos(zAngInc)))) - 3, u, u1, u2], v, v1, v2, (3 * paso)) → list1
  35. Sequence(CurveCartesian[((2 * r) * ((((0.7 * sqrt(((u * (u - 1.4)) * (u - 1)))) * sin(v)) * sin(zAngRot)) + (((0.7 * sqrt(((u * (u - 1.4)) * (u - 1)))) * cos(v)) * cos(zAngRot)))), ((2 * r) * (((((-0.7 * sqrt(((u * (u - 1.4)) * (u - 1)))) * sin(v)) * cos(zAngRot)) * sin(zAngInc)) + ((((0.7 * sqrt(((u * (u - 1.4)) * (u - 1)))) * cos(v)) * sin(zAngRot)) * sin(zAngInc)) + (u * cos(zAngInc)))) - 3, v, v1, v2], u, u1, u2, paso) → list2

AI Drawing Prompt Reference

Draw an egg-shaped outline formed by two intersecting ellipses, one oriented horizontally and one vertically, sharing the same center. At the center, place a small circle and draw horizontal and vertical lines through it, intersecting the circle at four points that serve as the major axis endpoints of the ellipses. On each ellipse, take a moving point and connect it to the intersection of the ellipse with the auxiliary line, creating angle markers. Inside the egg, fill with multiple parametric curves forming a grid-like or rotational surface, symmetric about the center, with angle labels to illustrate symmetry.
The prompt above was compiled from the original drawing commands and is for reference only.