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Dilation and Definite Integral

Dilation and Definite Integral
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2014-07-30 21:08
CalculusIntegralTransformation
This example demonstrates the effect of dilation and the application of definite integrals. By adjusting parameters, you can observe how the shape changes under different dilation ratios. Key mathematical concepts include geometric transformations, specifically dilation, and the calculation of areas using definite integrals. GeoGebra commands used include Dilate, Intersect, and Length. Suitable for high school mathematics education, particularly for learning calculus and geometric transformations.

GeoGebra Commands & Parameters

  1. Segment(D, E) → w
  2. Segment(D, F) → L
  3. Segment(F, A) → h
  4. Dilate(D, k, C) → D'
  5. Dilate(E, k, C) → E'
  6. Segment(D', E') → w'
  7. Dilate(D, k, C) → D'_1
  8. Dilate(F, k, C) → F'
  9. Segment(D'_1, F') → L'
  10. Dilate(F, k, C) → F'_1
  11. Dilate(A, k, C) → A'
  12. Segment(F'_1, A') → h'
  13. Point(h) → G
  14. Intersect(L, h) → H
  15. Line(G, H) → a
  16. Intersect(w, L) → I
  17. Line(H, I) → b
  18. Point(w) → J
  19. Line(I, J) → c
  20. Dilate(c, k, C) → c'
  21. Dilate(b, k, C) → b'
  22. Dilate(a, k, C) → a'
  23. Length(h) → g
  24. Intersect(xAxis, yAxis) → K
  25. Dilate(pic1, k, C) → pic1'