Oscillating Surfaces
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This example demonstrates the dynamic behavior of oscillating surfaces in three-dimensional space. It involves core mathematical concepts such as surfaces, scatter plots, algebra, trigonometry, arithmetic operations, and differential equations. The construction utilizes GeoGebra commands and objects like a, ellissoide_x, b, ellissoide_y, c, ellissoide_z, text1, start, A, text2. It is suitable for high school and above students to explore the application of spatial geometry and calculus.
GeoGebra Commands & Parameters
Numeric a(0.84)ellissoide_x(u, v) = ((a * cos(v)) * cos(u))Numeric b(1.63)ellissoide_y(u, v) = ((b * cos(v)) * sin(u))Numeric c(1.55)ellissoide_z(u, v) = (c * sin(v))Boolean start(true)Point3d A(-3.168556408202131, -1.9862893283644567, 3.0304462195261923)
AI Drawing Prompt Reference
Draw a dynamic oscillating surface in 3D space defined by parameters a, b, c affecting x, y, z scaling, using trigonometric functions to generate an ellipsoid rotation, and mark a specific 3D point to show its spatial relation to the surface.
The prompt above was compiled from the original drawing commands and is for reference only.