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Cycloid: Helena of Geometry

Cycloid: Helena of Geometry
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2024-01-11 20:01
Coordinate GeometryParametric EquationGeometric Construction
In collections El dominio del Tiempo (cinemática intuitiva)
This example demonstrates the cycloid, also known as Helena of Geometry. It involves core concepts of parametric equations and coordinate geometry. Using GeoGebra commands such as CurveCartesian, Circle, and Segment, the trajectory of the cycloid is constructed. Suitable for high school mathematics education and learning parametric equations.

GeoGebra Commands & Parameters

  1. Circle(O, r) → cir
  2. Circle((0, 0), r) → cir0
  3. Segment(O, C) → h
  4. Segment((((-2 * pi) * r), r), (((2 * pi) * r), r)) → f
  5. Segment((0, 0), B) → i
  6. CurveCartesian(((α * r), r) + (r; (((2 * inv) - 1) * (α + pi / 2))), α, (-2 * pi), (2 * pi)) → c1
  7. CurveCartesian(((t * r), r) + (r; (((2 * inv) - 1) * (t + pi / 2))), t, (-2 * pi), β) → c0

AI Drawing Prompt Reference

Draw a circle centered at O with radius r. Connect O to a point C on the circle to form segment h. Draw a horizontal line segment f from (-2πr, r) to (2πr, r) on the x-axis. Connect the origin (0, 0) to another point B on the circle to form segment i. Finally, plot the curves c1 and c0 defined by parametric equations, where c1 is for α from -2π to 2π and c0 is for t from -2π to β, with specific equations involving r and trigonometric functions.
The prompt above was compiled from the original drawing commands and is for reference only.