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Surfing on a Surface

Surfing on a Surface
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2018-01-29 03:07
VectorSolid GeometryGeometric Construction
In collections surface 3D /3D-Oberflächen 1 surface 3D /3D-Oberflächen 1
This example demonstrates geometric constructions on a surface. It involves concepts such as surfaces, lines, geometric transformations, and vectors. Using GeoGebra commands like Segment, Line, OrthogonalLine, Point, etc., complex geometric shapes can be constructed. Suitable for high school and above students or teachers.

GeoGebra Commands & Parameters

  1. Segment(B, C) → i
  2. Line(B, C) → h
  3. OrthogonalLine(B, xOyPlane) → g
  4. Point(g) → D
  5. Plane(B, C, D) → a
  6. IntersectPath(a, f) → b
  7. Derivative(f, x) → fx
  8. Derivative(f, y) → fy
  9. OrthogonalPlane(G, Vector[ux ⊗ uy]) → c
  10. CurveCartesian(x(B) + (t * (x(C) - x(B))), y(B) + (t * (y(C) - y(D))), f(x(B) + (t * (x(C) - x(B))), y(B) + (t * (y(C) - y(D)))), t, 0, 1) → d
  11. Segment(G, E) → l
  12. Tangent(H, p) → m
  13. Slope(m) → mpunt
  14. Midpoint(l) → I
  15. Vector(I, I + UnitVector[e]) → v
  16. OrthogonalLine(J, c) → j
  17. Intersect(j, c) → K
  18. Vector(G, K) → n
  19. Rotate(n, π / 4, j) → n'
  20. Rotate(n, ((-π)) / 4, j) → n''
  21. Polygon(Q3, Q4, Q1, Q2) → q1, q3, q4, q1_1, q2