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Curvature from Derivatives

Curvature from Derivatives
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2017-02-05 06:46
CalculusDerivativeGeometric Construction
This example demonstrates how to calculate the curvature of a curve using derivatives. Key mathematical concepts include derivatives and curvature. Using GeoGebra commands such as Derivative and OsculatingCircle, the example provides a visual understanding of how curvature changes at a point on a curve. Suitable for high school calculus education.

GeoGebra Commands & Parameters

  1. Derivative(cy) → cy'
  2. Derivative(cx) → cx'
  3. CurveCartesian(cx(p), cy(p), p, 0, 1) → C
  4. Point(C, q) → X
  5. Length(cp) → lcp
  6. Integral(euclidianDistance, 0, 1) → L
  7. LaTeX(L, true, true) → text2
  8. Integral(euclidianDistance, 0, q) → l
  9. LaTeX(qL, true, true) → text5
  10. Derivative(csx) → cssx
  11. Derivative(csy) → cssy
  12. Length(css) → kappa
  13. LaTeX(cx, false, true) → text8
  14. LaTeX(cy, false, true) → text9
  15. LaTeX(l, true, true) → text10
  16. Derivative(cx') → cx''
  17. Derivative(cy') → cy''
  18. LaTeX(q, true, true) → text6
  19. OsculatingCircle(X, C) → osculatingCircle
  20. LaTeX(Radius[osculatingCircle] / Length[r]) → text16