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The Elevator Problem

The Elevator Problem
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2016-10-12 11:51
VectorFunctionGeometric Construction
This example demonstrates the movement of an elevator between different floors. It involves key mathematical concepts such as functions, vectors, and loci. Using GeoGebra commands like Point, Vector, Sequence, and Polygon, the dynamic path of the elevator can be shown. Suitable for high school mathematics education, particularly in coordinate geometry and function graphing.

GeoGebra Commands & Parameters

  1. Point(xAxis) → C
  2. Point(xAxis) → G
  3. Point(xAxis) → A
  4. Point(xAxis) → E
  5. Point(xAxis) → D
  6. Point(xAxis) → B
  7. Vector((0, 0), (0, a)) → v
  8. Sequence(Segment[Element[points, i] + (v * i), G + (v * i)], i, 1, 5) → list2
  9. Vector((0, 0), (0, b)) → w
  10. Sequence(If[x(Element[points, i]) ≤ x(G), Polygon[Element[points, i] + (v * i), G + (v * i), 4], Polygon[G + (v * i), Element[points, i] + (v * i), 4]], i, 1, 5) → list4
  11. Vector((0, 0), F) → u
  12. Sequence(Text[x(Element[points, i]), Element[points, i] + u], i, 1, Length[points]) → list1
  13. Line((0, 0), (1, 0)) → d
  14. Line((m, 4 + h), d) → e
  15. Circle((m, 4 + h), Sum[list2] / 2) → c
  16. Intersect(c, e) → H, I
  17. Polygon((m + s / 2, (-b)), (m - s / 2, (-b)), 4) → poly1
  18. Segment(H, I) → f
  19. Sequence(If[x(Element[points, i]) > x(G), x(Element[points, i]) - x(G), 0], i, 1, 5) → above
  20. Sequence(If[x(Element[points, i]) < x(G), x(G) - x(Element[points, i]), 0], i, 1, 5) → below
  21. Sum(above) → abv
  22. Sum(below) → bel
  23. Segment((x(A), -1.4), (x(A) + abv, -1.4)) → p
  24. Segment((x(A), -1.7), (x(A) + bel, -1.7)) → q