3D Rose Curve
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This example demonstrates the 3D visualization of a rose curve by rotating a 2D rose curve. It involves core math concepts like coordinate geometry, quadratic functions, linear equations, parabolas, and arithmetic mean. Constructed using the Surface command with parameters a, h, n, V, c, g, i, j. Suitable for high school and above students to understand the relationship between spatial surfaces and parametric equations.
GeoGebra Commands & Parameters
Surface(((a + v) * cos(t + v) / sqrt(1 + (h^(2) * cos((n * t) + v)^(2)))), ((a + v) * sin(t + v) / sqrt(1 + (h^(2) * cos((n * t) + v)^(2)))), ((c * v) * h) + (((a + v) * h) * cos((n * t) + v) / sqrt(1 + (h^(2) * cos((n * t) + v)^(2)))), t, 0, 6.28319, v, 0, V) → gSurface(((a + v) * cos(t + v) / sqrt(1 + (h^(2) * cos((n * t) + v)^(2)))), ((a + v) * sin(t + v) / sqrt(1 + (h^(2) * cos((n * t) + v)^(2)))), ((c * v) * h) + (((a + v) * h) * cos((n * t) + v) / sqrt(1 + (h^(2) * cos((n * t) + v)^(2)))), t, 0.01, 6.28319, v, 0, V) → iSurface(((a + v) * cos(t + v) / sqrt(1 + (h^(2) * cos((n * t) + v)^(2)))), ((a + v) * sin(t + v) / sqrt(1 + (h^(2) * cos((n * t) + v)^(2)))), ((c * v) * h) + (((a + v) * h) * cos((n * t) + v) / sqrt(1 + (h^(2) * cos((n * t) + v)^(2)))), t, 0, 6.28319, v, 0.01, V) → j
AI Drawing Prompt Reference
Draw a 3D rose curve by rotating a 2D rose curve. Use parameters a, h, n, V, c, g, i, j, where a, h, n, c, and V are constants, and t and v are variables. First, draw a surface with t ranging from 0 to 6.28319 and v from 0 to V. Then, adjust the range of t to 0.01 to 6.28319 and v from 0 to V, and draw another surface. Finally, draw a surface with t from 0 to 6.28319 and v from 0.01 to V.
The prompt above was compiled from the original drawing commands and is for reference only.