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Geogebra Parametric Curves & Integral Demo

Geogebra Parametric Curves & Integral Demo
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2020-01-08 02:00
Coordinate GeometryCalculusIntegralParametric EquationGeometric Construction
In collections Color 3D surfaces
This example dynamically demonstrates parametric curves, their geometric forms, and definite integral calculations. Core math concepts include parametric equations, coordinate geometry, definite integrals from calculus, and constructions involving line segments and spheres. Key GeoGebra commands and objects used are CurveCartesian, Segment, Midpoint, Surface, and Sphere, as listed in the construction summary. Suitable for high school and above students to understand parametric curves, integral applications, and 3D geometric constructions.

GeoGebra Commands & Parameters

  1. CurveCartesian(x(B) + (open * cos(t + k)) + (0.5 * cos((7 * t))) + (1 / 3 * cos((-17 * t) + 3.142 / 2)), y(B) + 2.5, z(B) + (open * sin(t + k)) + (0.5 * sin((7 * t))) + (1 / 3 * sin((-17 * t) + 3.142 / 2)), t, 0, theta) → b
  2. Segment(C, D) → e
  3. Segment(A, E) → i
  4. CurveCartesian(x(A) + (a_1 * cos(i + k)), y(A), z(A) + (a_1 * sin(i + k)), i, 0, theta) → a
  5. Midpoint(i) → G
  6. Surface(x(A) + ((j * cos(i°)) * cos(((m * i))°)), y(A) + ((0.5 * (j - 1)) * cos(((m * i))°)^(2)), z(A) + ((j * sin(i°)) * cos(((m * i))°)), i, 0, 720, j, 0, 4.8) → l
  7. Surface(x(A) + 0.45 + (u * x(a(t))) + ((1 - u) * x(b(t))), y(A) + 3.5 + (u * y(a(t))) + ((1 - u) * y(b(t))), z(A) + (u * z(a(t))) + ((1 - u) * z(b(t))), t, 0, theta, u, 0, c) → d
  8. Surface(x(G) + ((j * cos(i°)) * cos(((m / 4 * i))°)), y(G) + ((j - 1) * cos(((m / 4 * i))°)^(2)), z(G) + ((j * sin(i°)) * cos(((m / 4 * i))°)), i, 0, 720, j, 0, 4.8) → n
  9. Sphere(A + (0, 0, 1), a_1 - 0.01) → g
  10. Surface(x(A) + ((a_1 * cos(i)) * cos(j)), y(A) + ((a_1 * cos(i)) * sin(j)), z(A) + (a_1 * sin(i)), i, 0, (2 * π), j, 0, π) → o
  11. Surface(x(A) + (((a_1 - 0) * cos(i)) * cos(j)), y(A) + 0.1 + (((a_1 - 0) * cos(i)) * sin(j)), z(A) + ((a_1 - 0) * sin(i)), i, (-π), π, j, (-0.5 * π), (0.5 * π)) → f

AI Drawing Prompt Reference

Draw a parametric curve with a sphere and multiple surfaces. First, draw a parametric curve, then a sphere, followed by two line segments, two surfaces, and finally two rotational surfaces.
The prompt above was compiled from the original drawing commands and is for reference only.