Sphere Construction and Demonstration
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P1 P2 立體圖形 / 3D Shapes
This example dynamically demonstrates the geometric construction and properties of a sphere using GeoGebra, involving core concepts like solid geometry, rotation, sphere equations, and inequalities. Key GeoGebra commands and objects used include Line, If, Sphere, and Rotate. Suitable for high school students and math enthusiasts exploring spatial geometry and dynamic geometry demonstrations.
GeoGebra Commands & Parameters
Line((0, 1, 0), (0, 0, 0)) → RotateAxisIf(ShowChi, "立體位置(高低)", "Vertical Position") → TextSlider3If(ShowChi, "立體位置(橫向)", "Horizontal Position") → TextSlider4If(ShowChi, "透明度", "Transparency") → TextSlider6If(ShowChi, "旋轉立體", "Rotate the shape") → TextSlider5If(ShowChi, "立體大小", "Solid Size") → TextSlider2If(ShowChi, "球", "Sphere") → TextName1Sphere(ShapePt1, S2) → ShapeBaseRotate(ShapeBase, S5, ShapePt1, RotateAxis) → Shape
AI Drawing Prompt Reference
Draw a 3D sphere with a dynamic demonstration: first define a rotation axis using a line from (0,1,0) to (0,0,0). Include text sliders that switch on/off to control the solid’s vertical position, horizontal position, transparency, a toggle for rotating the solid, and the solid size. Use a reference point as the sphere’s center, construct the sphere whose radius matches the solid size, and then apply the rotation of the sphere around the rotation axis according to the chosen rotation settings and the rotation toggle.
The prompt above was compiled from the original drawing commands and is for reference only.