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Concha (Asteroceras) Geometric Example

Concha (Asteroceras) Geometric Example
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2023-03-15 19:20
TriangleCircleGeometric Construction
In collections geometriadinamica.es
This example demonstrates the geometric construction and properties of Concha (Asteroceras). It involves core mathematical concepts such as circles, similar triangles, intersections, and integer arithmetic. GeoGebra commands like Segment, Point, OrthogonalLine, Circle, Intersect, Ellipse, Angle, CurveCartesian, and Sequence are used in the construction. Suitable for high school mathematics education, it helps understand the integration of analytical geometry and geometric construction.

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, yAxis) → zz1
  10. Circle(C, 0.62) → zz0
  11. Intersect(zz0, zz1, 1) → ZZ1
  12. Intersect(zz0, zz1, 2) → ZZ2
  13. Ellipse(ZZ1, ZZ2, 0.65) → zElipse1
  14. Intersect(zElipse1, zz1) → ZZ5, ZZ6
  15. Point(zElipse1) → XY
  16. Angle(ZZ6, C, XY) → zAngRot
  17. OrthogonalLine(C, xAxis) → zz2
  18. Intersect(zz0, zz2, 2) → ZZ3
  19. Intersect(zz0, zz2, 1) → ZZ4
  20. Ellipse(ZZ3, ZZ4, 0.65) → zElipse2
  21. Intersect(zElipse2, zz2) → ZZ7, ZZ8
  22. Point(zElipse2) → Z
  23. Angle(ZZ8, C, Z) → zAngInc
  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 * ((((exp((f * u)) * (d + (a * cos(α)))) * cos((c * u))) * sin(zAngRot)) + (((exp((f * u)) * (d + (a * cos(α)))) * sin((c * u))) * cos(zAngRot)))), (r * ((((((-exp((f * u))) * (d + (a * cos(α)))) * cos((c * u))) * cos(zAngRot)) * sin(zAngInc)) + ((((exp((f * u)) * (d + (a * cos(α)))) * sin((c * u))) * sin(zAngRot)) * sin(zAngInc)) + ((exp((f * u)) * ((-1.4 * e) + (b * sin(α)))) * cos(zAngInc)))), u, u1, u2) → curva2
  32. CurveCartesian((r * ((((exp((f * β)) * (d + (a * cos(v)))) * cos((c * β))) * sin(zAngRot)) + (((exp((f * β)) * (d + (a * cos(v)))) * sin((c * β))) * cos(zAngRot)))), (r * ((((((-exp((f * β))) * (d + (a * cos(v)))) * cos((c * β))) * cos(zAngRot)) * sin(zAngInc)) + ((((exp((f * β)) * (d + (a * cos(v)))) * sin((c * β))) * sin(zAngRot)) * sin(zAngInc)) + ((exp((f * β)) * ((-1.4 * e) + (b * sin(v)))) * cos(zAngInc)))), v, v1, v2) → a1
  33. CurveCartesian((r * ((((exp((f * max)) * (d + (a * cos(v)))) * cos((c * max))) * sin(zAngRot)) + (((exp((f * max)) * (d + (a * cos(v)))) * sin((c * max))) * cos(zAngRot)))), (r * ((((((-exp((f * max))) * (d + (a * cos(v)))) * cos((c * max))) * cos(zAngRot)) * sin(zAngInc)) + ((((exp((f * max)) * (d + (a * cos(v)))) * sin((c * max))) * sin(zAngRot)) * sin(zAngInc)) + ((exp((f * max)) * ((-1.4 * e) + (b * sin(v)))) * cos(zAngInc)))), v, v1, v2) → curva1
  34. Sequence(CurveCartesian[(r * ((((exp((f * u)) * (d + (a * cos(v)))) * cos((c * u))) * sin(zAngRot)) + (((exp((f * u)) * (d + (a * cos(v)))) * sin((c * u))) * cos(zAngRot)))), (r * ((((((-exp((f * u))) * (d + (a * cos(v)))) * cos((c * u))) * cos(zAngRot)) * sin(zAngInc)) + ((((exp((f * u)) * (d + (a * cos(v)))) * sin((c * u))) * sin(zAngRot)) * sin(zAngInc)) + ((exp((f * u)) * ((-1.4 * e) + (b * sin(v)))) * cos(zAngInc)))), v, v1, v2], u, u1, u2, paso) → list2
  35. Sequence(CurveCartesian[(r * ((((exp((f * u)) * (d + (a * cos(v)))) * cos((c * u))) * sin(zAngRot)) + (((exp((f * u)) * (d + (a * cos(v)))) * sin((c * u))) * cos(zAngRot)))), (r * ((((((-exp((f * u))) * (d + (a * cos(v)))) * cos((c * u))) * cos(zAngRot)) * sin(zAngInc)) + ((((exp((f * u)) * (d + (a * cos(v)))) * sin((c * u))) * sin(zAngRot)) * sin(zAngInc)) + ((exp((f * u)) * ((-1.4 * e) + (b * sin(v)))) * cos(zAngInc)))), u, u1, u2], v, v1, v2, paso) → list1

AI Drawing Prompt Reference

Draw a geometric representation of Asteroceras, incorporating core elements such as circles, similar triangles, intersections, and integer arithmetic. The graph should include two ellipses, two circles, multiple intersection points, multiple angles, and one curve. Please generate a complete geometric graph based on the given construction sequence and key object relationships.
The prompt above was compiled from the original drawing commands and is for reference only.