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Sphere and Median Line Demo

Sphere and Median Line Demo
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2017-04-06 22:31
FunctionSolid GeometryCalculusGeometric Construction
This example demonstrates the intersection of a sphere with a plane, forming a circular section and its median line. It involves core math concepts: sphere, plane, circular section, median line, functions, median value, indefinite integral, sine function. Construction highlights include using GeoGebra commands like Intersect, Sphere, Plane, PointIn, and Point. Suitable for high school students studying solid geometry, coordinate geometry, and calculus, helping them understand the relationship between spatial geometry and function graphs.

GeoGebra Commands & Parameters

  1. Intersect(yAxis, xAxis) → A
  2. Sphere(B, C) → a
  3. Plane(A, D, E) → b
  4. PointIn(a) → F
  5. Plane(F, b) → c
  6. PointIn(a) → G
  7. Point(zAxis) → H
  8. Point(zAxis) → I

AI Drawing Prompt Reference

Draw a sphere intersecting with a plane to form a circular section and its median line. Start by plotting the intersection point of the x-axis and y-axis, then create a sphere. Define a plane containing this intersection point and two other points, making the sphere intersect with the plane to form a circular section. Select two points on the sphere and draw an auxiliary plane based on one of the points on the section and the defined plane. Finally, mark two points on the z-axis to complete the construction, showcasing the relationship between spatial geometry and function graphs.
The prompt above was compiled from the original drawing commands and is for reference only.