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Tubes Around Polynomial Regressions

Tubes Around Polynomial Regressions
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2020-01-14 02:29
FunctionCoordinate GeometrySolid Geometry
This example demonstrates constructing tubes around polynomial regressions. Key mathematical concepts include polynomial regression, surface construction, and geometric transformations. Commands used include PointIn, FitPoly, Rotate, Surface, etc. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. PointIn(y > 0) → A
  2. PointIn(y > 0) → B
  3. PointIn(y > 0) → C
  4. PointIn(y > 0) → D
  5. PointIn(y > 0) → E
  6. FitPoly({A, B, C, D, E}, n) → f
  7. Rotate(If[Min[l1] ≤ x ≤ Max[l1], f(x)], π / 2, xAxis) → h_1
  8. Point(h_1) → F
  9. Surface(u, (ra * cos(v)), (ra * sin(v)) + f(u), u, Min[l1], Max[l1], v, 0, (2 * π)) → a
  10. Rotate(G, π / 2, xAxis) → G'
  11. Plane(G, G + (0, 1, 0), G + (0, 0, 1)) → p
  12. Circle(G', ra, p) → c
  13. Radius(c) → b
  14. Segment(G', H) → g