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Constructing the Earth

Constructing the Earth
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2020-03-30 22:23
TrigonometryCoordinate GeometryParametric Equation
This example demonstrates the latitude and longitude of the Earth using parametric equations. It involves core concepts of trigonometry and coordinate geometry. Using the CurveCartesian command, the latitude and longitude lines of the Earth can be constructed. Suitable for high school and above students to learn about parametric equations and Earth geometry.

GeoGebra Commands & Parameters

  1. CurveCartesian((6.371 * cos(t)), (6.371 * sin(t)), 0, t, 0, (2 * π)) → b
  2. CurveCartesian(((6.371 * cos(π / 18)) * cos(t)), ((6.371 * cos(π / 18)) * sin(t)), (6.371 * sin(π / 18)), t, 0, (2 * π)) → c
  3. CurveCartesian(((6.371 * cos((2 * π / 18))) * cos(t)), ((6.371 * cos((2 * π / 18))) * sin(t)), (6.371 * sin((2 * π / 18))), t, 0, (2 * π)) → c_1
  4. CurveCartesian(((6.371 * cos((4 * π / 18))) * cos(t)), ((6.371 * cos((4 * π / 18))) * sin(t)), (6.371 * sin((4 * π / 18))), t, 0, (2 * π)) → c_3
  5. CurveCartesian(((6.371 * cos((3 * π / 18))) * cos(CLIPBOARDmagicSTRINGt)), ((6.371 * cos((3 * π / 18))) * sin(CLIPBOARDmagicSTRINGt)), (6.371 * sin((3 * π / 18))), CLIPBOARDmagicSTRINGt, 0, (2 * π)) → c_2
  6. CurveCartesian(((6.371 * cos((5 * π / 18))) * cos(t)), ((6.371 * cos((5 * π / 18))) * sin(t)), (6.371 * sin((5 * π / 18))), t, 0, (2 * π)) → d
  7. CurveCartesian(((6.371 * cos((6 * π / 18))) * cos(t)), ((6.371 * cos((6 * π / 18))) * sin(t)), (6.371 * sin((6 * π / 18))), t, 0, (2 * π)) → e
  8. CurveCartesian(((6.371 * cos((7 * π / 18))) * cos(t)), ((6.371 * cos((7 * π / 18))) * sin(t)), (6.371 * sin((7 * π / 18))), t, 0, (2 * π)) → f
  9. CurveCartesian(((6.371 * cos((8 * π / 18))) * cos(t)), ((6.371 * cos((8 * π / 18))) * sin(t)), (6.371 * sin((8 * π / 18))), t, 0, (2 * π)) → g
  10. CurveCartesian((0 * cos(t)), ((6.371 * cos((0 * π / 18))) * cos(t)), (6.371 * sin(t)), t, 0, (2 * π)) → h
  11. CurveCartesian(((6.371 * sin(π / 18)) * cos(t)), ((6.371 * cos(π / 18)) * cos(t)), (6.371 * sin(t)), t, 0, (2 * π)) → i
  12. CurveCartesian(((6.371 * sin((2 * π / 18))) * cos(t)), ((6.371 * cos((2 * π / 18))) * cos(t)), (6.371 * sin(t)), t, 0, (2 * π)) → j
  13. CurveCartesian(((6.371 * sin((3 * π / 18))) * cos(t)), ((6.371 * cos((3 * π / 18))) * cos(t)), (6.371 * sin(t)), t, 0, (2 * π)) → k
  14. CurveCartesian(((6.371 * sin((4 * π / 18))) * cos(t)), ((6.371 * cos((4 * π / 18))) * cos(t)), (6.371 * sin(t)), t, 0, (2 * π)) → l
  15. CurveCartesian(((6.371 * sin((5 * π / 18))) * cos(t)), ((6.371 * cos((5 * π / 18))) * cos(t)), (6.371 * sin(t)), t, 0, (2 * π)) → m
  16. CurveCartesian(((6.371 * sin((6 * π / 18))) * cos(t)), ((6.371 * cos((6 * π / 18))) * cos(t)), (6.371 * sin(t)), t, 0, (2 * π)) → n
  17. CurveCartesian(((6.371 * sin((7 * π / 18))) * cos(t)), ((6.371 * cos((7 * π / 18))) * cos(t)), (6.371 * sin(t)), t, 0, (2 * π)) → o
  18. CurveCartesian(((6.371 * sin((8 * π / 18))) * cos(t)), ((6.371 * cos((8 * π / 18))) * cos(t)), (6.371 * sin(t)), t, 0, (2 * π)) → p
  19. CurveCartesian(((6.371 * sin((9 * π / 18))) * cos(t)), (0 * cos(t)), (6.371 * sin(t)), t, 0, (2 * π)) → q
  20. CurveCartesian(((6.371 * sin((10 * π / 18))) * cos(t)), ((6.371 * cos((10 * π / 18))) * cos(t)), (6.371 * sin(t)), t, 0, (2 * π)) → r
  21. CurveCartesian(((6.371 * sin((11 * π / 18))) * cos(t)), ((6.371 * cos((11 * π / 18))) * cos(t)), (6.371 * sin(t)), t, 0, (2 * π)) → s
  22. CurveCartesian(((6.371 * sin((12 * π / 18))) * cos(t)), ((6.371 * cos((12 * π / 18))) * cos(t)), (6.371 * sin(t)), t, 0, (2 * π)) → t
  23. CurveCartesian(((6.371 * sin((13 * π / 18))) * cos(t)), ((6.371 * cos((13 * π / 18))) * cos(t)), (6.371 * sin(t)), t, 0, (2 * π)) → u
  24. CurveCartesian(((6.371 * sin((14 * π / 18))) * cos(t)), ((6.371 * cos((14 * π / 18))) * cos(t)), (6.371 * sin(t)), t, 0, (2 * π)) → v
  25. CurveCartesian(((6.371 * sin((15 * π / 18))) * cos(t)), ((6.371 * cos((15 * π / 18))) * cos(t)), (6.371 * sin(t)), t, 0, (2 * π)) → w
  26. CurveCartesian(((6.371 * sin((16 * π / 18))) * cos(t)), ((6.371 * cos((16 * π / 18))) * cos(t)), (6.371 * sin(t)), t, 0, (2 * π)) → a_1
  27. CurveCartesian(((6.371 * sin((17 * π / 18))) * cos(t)), ((6.371 * cos((17 * π / 18))) * cos(t)), (6.371 * sin(t)), t, 0, (2 * π)) → b_1
  28. CurveCartesian(((6.371 * cos(π / 18)) * cos(t)), ((6.371 * cos(π / 18)) * sin(t)), (6.371 * sin(π / 18)), t, 0, (2 * π)) → d_1
  29. CurveCartesian(((6.371 * cos(π / 18)) * cos(t)), ((6.371 * cos(π / 18)) * sin(t)), (-6.371 * sin(π / 18)), t, 0, (2 * π)) → e_1
  30. CurveCartesian(((6.371 * cos((2 * π / 18))) * cos(t)), ((6.371 * cos((2 * π / 18))) * sin(t)), (-6.371 * sin((2 * π / 18))), t, 0, (2 * π)) → i_1
  31. CurveCartesian(((6.371 * cos((3 * π / 18))) * cos(t)), ((6.371 * cos((3 * π / 18))) * sin(t)), (-6.371 * sin((3 * π / 18))), t, 0, (2 * π)) → j_1
  32. CurveCartesian(((6.371 * cos((4 * π / 18))) * cos(t)), ((6.371 * cos((4 * π / 18))) * sin(t)), (-6.371 * sin((4 * π / 18))), t, 0, (2 * π)) → k_1
  33. CurveCartesian(((6.371 * cos((5 * π / 18))) * cos(t)), ((6.371 * cos((5 * π / 18))) * sin(t)), (-6.371 * sin((5 * π / 18))), t, 0, (2 * π)) → l_1
  34. CurveCartesian(((6.371 * cos((6 * π / 18))) * cos(t)), ((6.371 * cos((6 * π / 18))) * sin(t)), (-6.371 * sin((6 * π / 18))), t, 0, (2 * π)) → m_1
  35. CurveCartesian(((6.371 * cos((7 * π / 18))) * cos(t)), ((6.371 * cos((7 * π / 18))) * sin(t)), (-6.371 * sin((7 * π / 18))), t, 0, (2 * π)) → n_1
  36. CurveCartesian(((6.371 * cos((8 * π / 18))) * cos(t)), ((6.371 * cos((8 * π / 18))) * sin(t)), (-6.371 * sin((8 * π / 18))), t, 0, (2 * π)) → o_1