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Rhumb Line or Spherical Spiral

Rhumb Line or Spherical Spiral
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2014-10-20 01:36
Solid GeometryGeometric ConstructionLocus
In collections Spherical Geometry Ideas
This example demonstrates the spherical curve traced by a ship traveling from the south pole to the north pole while maintaining a fixed angle. Key mathematical concepts include spherical geometry, constant angle, and spherical curves. Construction involves GeoGebra commands such as Sphere, Segment, Point, Sequence, and CurveCartesian. Suitable for high school students or math enthusiasts learning spherical geometry and geometric constructions.

GeoGebra Commands & Parameters

  1. Sphere((0, 0, 0), 1) → a
  2. Segment((-1.5, 0, 1.5), (1.5, 0, 1.5)) → b
  3. Point(b) → A
  4. Sequence(Rotate[Circle[(1, 0, 0), (0, 0, 1), (0, 0, -1)], n, zAxis], n, 0*°, 330*°, 30*°) → list1
  5. CurveCartesian((cos(t) * cos(atan((x(A) * t)))), (sin(t) * cos(atan((x(A) * t)))), (-sin(atan((x(A) * t)))), t, -100 / ss, 100 / ss) → d

AI Drawing Prompt Reference

Describe a curve from the South Pole to the North Pole where a ship maintains a fixed angle. The figure includes a sphere, a line segment, and a curve. The construction order is to draw the sphere first, then the line segment, then determine the starting point, and finally draw the curve.
The prompt above was compiled from the original drawing commands and is for reference only.