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Curve and Sphere

Curve and Sphere
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2019-02-24 18:45
FunctionTrigonometryCoordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the geometric relationship and relative positions between curves and spheres. It involves core mathematical concepts such as sphere, coordinate geometry, Pythagorean theorem, logarithmic functions, statistics, and tangent function. The construction uses GeoGebra commands/objects like Midpoint, Segment, Mirror, CurveCartesian, and Point. Suitable for high school and above students learning about spatial geometry and intersection problems between function graphs and geometric shapes.

GeoGebra Commands & Parameters

  1. Midpoint(A, B) → C
  2. Segment(C, A) → f
  3. Mirror(D, B) → D'
  4. Segment(D', D) → g
  5. Midpoint(A, C) → E
  6. CurveCartesian((8 * sin(t)), (8 * cos(t)), ((8 * sin(t)) * cos(t)), t, 0, (2 * π)) → c
  7. Point(c) → G
  8. Mirror(H, H) → H'

AI Drawing Prompt Reference

Draw a geometric figure consisting of a curve and a sphere, showing their relative positions. First, create a curve, then draw a sphere. Mark the midpoint of the curve and the segment connecting the midpoint. Next, reflect the sphere along a segment and draw the reflected image. Finally, mark a point on the curve and complete the drawing.
The prompt above was compiled from the original drawing commands and is for reference only.