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Parabolic Helix

Parabolic Helix
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2017-12-23 03:02
VectorTrigonometryCoordinate GeometrySolid GeometryParametric Equation
This example demonstrates the generation and properties of a parabolic helix. It involves core mathematical concepts such as exponentials, equilateral triangles, rotation, vectors, and circles. Construction highlights include using CurveCartesian for curves, Point for points, and Surface for surfaces, with objects like rotasi, rotano, ejessi, ejesno, and interactive buttons for animation. Suitable for high school mathematics students and teachers exploring spatial geometry and parametric equations.

GeoGebra Commands & Parameters

  1. CurveCartesian(((a / π * t) * cos((t * n))), ((a / π * t) * sin((t * n))), (t^(2) * h / ((2 * π))^(2)), t, 0, (2 * π)) → c
  2. Point(c) → A
  3. Surface(((a / π * u) * cos(v)), ((a / π * u) * sin(v)), (u^(2) * h / ((2 * π))^(2)), v, 0, (2 * π), u, 0, (2 * π)) → d

AI Drawing Prompt Reference

Draw a parabolic helix to demonstrate its generation and properties, incorporating core mathematical concepts like exponentials, equilateral triangles, rotation, vectors, and circles. Start by plotting a parametric curve, then place a point on it, and generate a surface based on the curve. Finally, use rotation and interactive buttons to show its dynamic behavior, suitable for high school students and teachers exploring spatial geometry and parametric equations.
The prompt above was compiled from the original drawing commands and is for reference only.