Surface of Revolution from 2D Function with AR
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This GeoGebra example demonstrates how to create a surface of revolution from a 2D function. By defining a function f(x), setting rotation axis, upper and lower limits, and rotation angle, the Surface command generates a 3D rotational surface. Core mathematical concepts include: surface equations formed by revolving function graphs around coordinate axes, parametric representations, and volume calculation of solids of revolution in solid geometry. Construction details: Using the Surface command based on function f and angle α to create the surface, with InputBox1, InputBox2, and InputBox3 for entering function expressions, rotation axis parameters, and angle values respectively, while Textfield displays real-time numerical values. Suitable for high school and college students learning solid geometry, calculus (volumes of solids of revolution), and parametric equations, also serves as a teaching case for AR applications in mathematics visualization.
GeoGebra Commands & Parameters
Surface(g, α, xAxis) → dTextfield(f) → InputBox1Textfield(lowerlimit) → InputBox2Textfield(upperlimit) → InputBox3
AI Drawing Prompt Reference
Create a rotational surface generated by revolving a function f(x) around the x-axis. First, input the function expression, then set the rotation angle and limits, and finally use the Surface command to generate the surface. InputBox1 is for the function expression, InputBox2 and InputBox3 are for the lower and upper limits respectively.
The prompt above was compiled from the original drawing commands and is for reference only.