MathPlotAI Logo MathPlotAI

Brachistochrone Curve

Brachistochrone Curve
Loading the math board and drawing, please wait…
2024-10-14 20:31
CalculusOptimizationParametric Equation
In collections The Domain of the Time (intuitive kinematics)
This example demonstrates the Brachistochrone curve, involving parametric equations, limits, and calculus. Using GeoGebra commands such as CurveCartesian, Tangent, and UnitVector, the curve's generation process is dynamically shown. Suitable for high school and above students or teachers for teaching or research.

GeoGebra Commands & Parameters

  1. CurveCartesian(((α * r), r) + (r; α + pi / 2), α, 0, (2 * pi)) → c
  2. Point(c) → M
  3. Tangent(M, c) → i
  4. UnitVector(i) → n
  5. Point(c) → P
  6. Segment((0, (2 * r)), P) → f
  7. Point(f) → A
  8. UnitVector(f) → nA
  9. Circle(H, S, P) → d
  10. Point(d) → B
  11. Tangent(B, d) → iB,
  12. UnitVector(iB) → nB
  13. Center(d) → D
  14. Angle(H, D, S) → amp
  15. Segment(D, B) → l

AI Drawing Prompt Reference

Draw a parametric curve and show its generation process with tangents and unit vectors, include a line segment from the origin to a point on the curve, and a circle passing through a point on the curve, showing the center, another point on the circle, and the line segment from the center to that point, finally display the relationship between the tangent and the unit vector.
The prompt above was compiled from the original drawing commands and is for reference only.