Surface and Cylinder Construction
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This example demonstrates the generation of a surface of revolution and a cylinder. Key mathematical concepts include logarithms, arithmetic, linear equations, and random experiments. The Surface command is used to construct the surface of revolution, while the Cylinder command generates the cylinder. Suitable for high school mathematics education and learning.
GeoGebra Commands & Parameters
Surface((((d * v) * cos(u)) * cos((((2 * π) * tor) * (1 - ℯ^(((-v)) / tau))))) - (((sin((((2 * π) * tor) * (1 - ℯ^(((-v)) / tau)))) * d) * v) * sin(u)), (((d * v) * cos(u)) * sin((((2 * π) * tor) * (1 - ℯ^(((-v)) / tau))))) + (((cos((((2 * π) * tor) * (1 - ℯ^(((-v)) / tau)))) * d) * v) * sin(u)), (a * ℯ^((-(sin((n / 2 * u)) / b)^(2)))) - a / 2 + (aa * ℯ^(((-((d * v))^(2))) / bb^(2))), u, (-π), π, v, h + 0.05, 1) → iSurface((((d * v) * cos(u)) * cos((((2 * π) * tor) * (1 - ℯ^(((-v)) / tau))))) - (((sin((((2 * π) * tor) * (1 - ℯ^(((-v)) / tau)))) * d) * v) * sin(u)), (((d * v) * cos(u)) * sin((((2 * π) * tor) * (1 - ℯ^(((-v)) / tau))))) + (((cos((((2 * π) * tor) * (1 - ℯ^(((-v)) / tau)))) * d) * v) * sin(u)), (a * ℯ^((-(sin((n / 2 * u)) / b)^(2)))) - a / 2 + (aa * ℯ^(((-((d * v))^(2))) / bb^(2))), u, (-π) + 0.05, π, v, h, 1) → cSurface((((d * v) * cos(u)) * cos((((2 * π) * tor) * (1 - ℯ^(((-v)) / tau))))) - (((sin((((2 * π) * tor) * (1 - ℯ^(((-v)) / tau)))) * d) * v) * sin(u)), (((d * v) * cos(u)) * sin((((2 * π) * tor) * (1 - ℯ^(((-v)) / tau))))) + (((cos((((2 * π) * tor) * (1 - ℯ^(((-v)) / tau)))) * d) * v) * sin(u)), (a * ℯ^((-(sin((n / 2 * u)) / b)^(2)))) - a / 2 + (aa * ℯ^(((-((d * v))^(2))) / bb^(2))), u, (-π), π, v, h, 1) → k