Interesting Tile-Like Surface
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This example demonstrates a tile-like 3D surface composed of multiple planes and its tangent lines. Core math concepts include planes, surfaces, tangent lines, general quadrilaterals, derivatives, and hypergeometric distributions. It uses GeoGebra objects 'a' and 'b' to control the surface's shape and parameters, making it suitable for high school and above students to explore spatial geometry, calculus, and parametric equations.
GeoGebra Commands & Parameters
a(x, y) = If[x - 4.81 ≤ y ≤ x + 4.81 ∧ (-x) - 4.81 ≤ y ≤ (-x) + 4.81, (0.5 * cos((6 * ((abs(x) * cos(π / 4)) + (abs(y) * sin(π / 4))))))]b(x, y) = If[x - 4.81 ≤ y ≤ x + 4.81 ∧ (-x) - 4.81 ≤ y ≤ (-x) + 4.81, (-0.5 * cos((6 * ((abs(x) * cos(π / 4)) + (abs(y) * sin(π / 4))))))]
AI Drawing Prompt Reference
Draw a tile-like 3D surface composed of multiple planes with tangent lines. The surface consists of two symmetric wave-like patterns defined by functions within specific regions, controlled by sliders. First, visualize the surface, then plot the tangent lines on it to illustrate the surface's behavior at different points.
The prompt above was compiled from the original drawing commands and is for reference only.