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Spiral on a Sphere by Steve Phelps

Spiral on a Sphere by Steve Phelps
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2014-07-22 07:43
Coordinate GeometrySolid GeometryGeometric Construction
In collections Spherical Geometry Ideas
This example demonstrates a spiral on a sphere. It involves spatial coordinate geometry concepts, constructed using commands such as Sphere, Intersect, Plane, IntersectPath, Point, and CurveCartesian. Suitable for high school and above students or teachers for teaching and learning about curves and surfaces in three-dimensional space.

GeoGebra Commands & Parameters

  1. Sphere((0, 0, 0), 1) → a
  2. Intersect
  3. Intersect(zAxis, a, 2) → A
  4. Plane(A, yAxis) → b
  5. IntersectPath(b, a) → c
  6. Point(c) → B
  7. CurveCartesian((sqrt(1 - (1 - t)^(2)) * cos((2 * (t - π / 2) / abs(1 - z(B))))), (sqrt(1 - (1 - t)^(2)) * sin((2 * (t - π / 2) / abs(1 - z(B))))), 1 - t, t, 0, 3.141592653589793) → d

AI Drawing Prompt Reference

Draw a sphere with a radius of 1 centered at the origin (0,0,0). Then find the intersection point A of the sphere and the z-axis. Create a plane b using point A and the y-axis. On the intersection curve c of plane b and sphere a, pick a point B. Finally, use point B as a parameter to draw a spiral curve d that spirals around the surface of the sphere.
The prompt above was compiled from the original drawing commands and is for reference only.