Sine Wave on One Sheet Hyperboloid

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2022-04-19 11:39

In collections Sine Wave on Surfaces

This example demonstrates the generation of a sine wave on a one-sheet hyperboloid surface. It involves core mathematical concepts such as trigonometric functions, parametric equations, and surface plotting. The construction uses GeoGebra commands like Surface and CurveCartesian, along with objects a, b, c, d, e, n, amplitude, g. It is suitable for high school students and those interested in spatial geometry and calculus.

GeoGebra Commands & Parameters

Surface(((a * u) * cos(v)), ((b * u) * sin(v)), (c * (u^(2) - 1)^(1 / 2)), u, (-π), π, v, (-2 * π), (2 * π)) → d
Surface(((a * u) * cos(v)), ((b * u) * sin(v)), ((-c) * (u^(2) - 1)^(1 / 2)), u, (-π), π, v, (-2 * π), (2 * π)) → e
CurveCartesian(((a^(2) + (amplitude^(2) * (cos((n * t)))^(2)))^(1 / 2) * cos(t)), ((a^(2) + (amplitude^(2) * (cos((n * t)))^(2)))^(1 / 2) * sin(t)), (amplitude * cos((n * t))), t, 0, (2 * π)) → g

AI Drawing Prompt Reference

Draw a one-sheet hyperboloid and a sine wave on it. First, draw the one-sheet hyperboloid using the parametric equations (a*u*cos(v), b*u*sin(v), c*(u^2-1)^(1/2)) and (a*u*cos(v), b*u*sin(v), -c*(u^2-1)^(1/2)), with u ranging from -π to π and v from -2π to 2π. Then, draw a sine wave on the hyperboloid using the parametric equations ((a^2 + (amplitude^2 * (cos(n*t))^2))^(1/2) * cos(t), (a^2 + (amplitude^2 * (cos(n*t))^2))^(1/2) * sin(t), amplitude * cos(n*t)), with t ranging from 0 to 2π.

The prompt above was compiled from the original drawing commands and is for reference only.