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Earth Model (cities, references, curves)

Earth Model (cities, references, curves)
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2017-07-12 20:26
VectorTrigonometryCoordinate GeometrySolid GeometryParametric Equation
This example demonstrates an Earth model incorporating cities, reference lines, and curves. It involves core mathematical concepts such as spheres, coordinate geometry, vectors, parametric equations, and trigonometry. The construction utilizes GeoGebra commands and objects like Length, Element, Segment, Sequence, KeepIf, Sphere, PointIn, Ray, IntersectPath, Arc, Point, Center, Angle, Vector, Intersect, CircumcircleSector, Circle, OrthogonalPlane, Rotate, If, and CurveCartesian. Suitable for high school students and educators.

GeoGebra Commands & Parameters

  1. Length(capitalesLista) → capitalesNum
  2. Element(tiempo, 7) → año
  3. Segment(PS + (0.075 * PS), PN + (0.075 * PN)) → eje
  4. Length(ciudadesLista) → ciudadesNum
  5. Sequence(If[Element[ciudadesLista, k] > 0, k, 0], k, 1, ciudadesNum) → ciudadesElegidas1
  6. KeepIf(x > 0, ciudadesElegidas1) → ciudadesElegidas2
  7. Length(ciudadesElegidas2) → ciudadesNumElegidas
  8. Sequence((5; Element[ciudadesLongitud, Element[ciudadesElegidas2, k]]°; Element[ciudadesLatitud, Element[ciudadesElegidas2, k]]°), k, 1, ciudadesNumElegidas) → ciudades
  9. Sequence((1.5 * Element[ciudades, k]), k, 1, ciudadesNumElegidas) → baseCiudades
  10. Sequence(Text[Element[ciudadesNombres, Element[ciudadesElegidas2, k]], Element[baseCiudades, k] + (0.03, 0.03, 0.03)], k, 1, ciudadesNumElegidas) → ciudadesNombresVisibles
  11. Sphere((0, 0, 0), (0.999 * 5)) → tierra
  12. PointIn(tierra) → A
  13. Sequence(Segment[(0, 0, 0), Element[baseCiudades, k]], k, 1, ciudadesNumElegidas) → laserOtros
  14. PointIn(tierra) → B
  15. Ray(A, (2 * A)) → laserA
  16. Ray(B, (2 * B)) → laserB
  17. PointIn(tierra) → C
  18. IntersectPath(Plane[(0, 0, 0), A, B], tierra) → ortodromiaAB
  19. Arc(ortodromiaAB, A, B) → arcoOrtodromiaAB
  20. Segment(PN, PS) → eje2
  21. Point(eje2) → L
  22. IntersectPath(Plane[L, A, B], tierra) → circuloLAB
  23. Center(circuloLAB) → D
  24. Segment(A, D) → segmentoDA
  25. Segment(D, B) → segmentoDB
  26. Arc(circuloLAB, A, B) → arcoCirculoLAB
  27. Ray(C, (2 * C)) → laserC
  28. IntersectPath(Plane[(0, 0, 0), A, C], tierra) → ortodromiaAC
  29. IntersectPath(Plane[(0, 0, 0), B, C], tierra) → ortodromiaBC
  30. Arc(ortodromiaAC, A, C) → arcoOrtodromiaAC
  31. Arc(ortodromiaBC, B, C) → arcoOrtodromiaBC
  32. Angle(A, (0, 0, 0), B) → angAOB
  33. Angle(A, (0, 0, 0), C) → angAOC
  34. Angle(B, (0, 0, 0), C) → angBOC
  35. Vector((1; (-rot) + 180°; (-inclinacion))) → dir
  36. Ray((0, 0, 0), Midpoint[A, A']) → g
  37. Intersect(g, tierra) → A'',
  38. CircumcircleSector(A, A'', A') → sectorLatitudA
  39. Ray((0, 0, 0), Midpoint[(5; 0; 0), A']) → h
  40. Intersect(h, tierra) → A''',
  41. CircumcircleSector((5; 0; 0), A''', A') → sectorLongitudA
  42. Circle((0, 0, 0), 5, eje) → ecuador2
  43. Circle((5; 0; (-anguloPolar)), (5; 90°; (-anguloPolar)), (5; 180°; (-anguloPolar))) → antartico
  44. Circle((5; 0; anguloPolar), (5; 90°; anguloPolar), (5; 180°; anguloPolar)) → artico
  45. Circle((5; 0; anguloEcliptica), (5; 90°; anguloEcliptica), (5; 180°; anguloEcliptica)) → cancer
  46. Circle((5; 0; (-anguloEcliptica)), (5; 90°; (-anguloEcliptica)), (5; 180°; (-anguloEcliptica))) → capricornio
  47. Circle((0, 0, 0), 5, eje) → ecuador
  48. Circle(PN, (5; 0; 0), PS) → greenwich
  49. Sequence(Circle[PN, (5; (15° * k); 0), PS], k, 1, 11) → meridianos
  50. Sequence(Circle[(5; 0; (15° * k)), (5; 90°; (15° * k)), (5; 180°; (15° * k))], k, 1, 5) → paralelosN
  51. Sequence(Circle[(5; 0; (-15° * k)), (5; 90°; (-15° * k)), (5; 180°; (-15° * k))], k, 1, 5) → paralelosS
  52. Segment((0, 0, 0), A) → segmentoOA
  53. Segment((0, 0, 0), B) → segmentoOB
  54. Segment((0, 0, 0), (5; 0; 0)) → radio
  55. OrthogonalPlane(A, zAxis) → planoA
  56. IntersectPath(planoA, tierra) → paraleloA
  57. Sphere((0, 0, 0), 5) → esfera
  58. Ray((0, 0, 0), Midpoint[A, B]) → f
  59. Intersect(f, tierra) → AB,
  60. CircumcircleSector(A, AB, B) → sectorOrtodromiaAB
  61. Segment((0, 0, 0), C) → radioC
  62. Sequence(If[Element[capitalesLista, k] > 0, k, 0], k, 1, capitalesNum) → capitalesElegidas1
  63. KeepIf(x > 0, capitalesElegidas1) → capitalesElegidas2
  64. Length(capitalesElegidas2) → capitalesNumElegidas
  65. Sequence((5; Element[capitalesLongitud, Element[capitalesElegidas2, k]]°; Element[capitalesLatitud, Element[capitalesElegidas2, k]]°), k, 1, capitalesNumElegidas) → capitales
  66. Sequence((1.5 * Element[capitales, k]), k, 1, capitalesNumElegidas) → baseCapitales
  67. Sequence(Text[Element[capitalesNombres, Element[capitalesElegidas2, k]], Element[baseCapitales, k] + (0.03, 0.03, 0.03)], k, 1, capitalesNumElegidas) → capitalesNombresVisibles
  68. Sequence(Segment[(0, 0, 0), Element[baseCapitales, k]], k, 1, capitalesNumElegidas) → laserCapital
  69. Rotate(AA + (1, 0), lox, AA) → BB
  70. If(abs(arg(BL) - arg(A)) ≤ 180°, arg(BL) - arg(A), arg(BL) - arg(A) < -180°, 360° + arg(BL) - arg(A), arg(BL) - arg(A) - 360°) → inc
  71. CurveCartesian((5 * cos(t + λ) / cosh((q * t))), (5 * sin(t + λ) / cosh((q * t))), (5 * tanh((q * t))), t, (-20 * pi), (20 * pi)) → loxodromia

AI Drawing Prompt Reference

Draw an Earth model featuring multiple cities, reference lines, and curves. Start by creating a sphere to represent the Earth, then mark several cities on its surface and add name labels for each. Next, draw rays from the center of the sphere to the cities, highlighting the intersection points of these rays with the sphere. Finally, use these points to sketch two sinusoidal curves and an arc to illustrate the Earth's latitude and longitude features.
The prompt above was compiled from the original drawing commands and is for reference only.