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Q3 Math Example by Anthony OR 柯志明

Q3 Math Example by Anthony OR 柯志明
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2018-03-20 09:50
VectorTrigonometryComplex NumberInequalityGeometric Construction
In collections Exploring the Conditions for Congruence of 2 Triangles Exploring Congruence of Triangles
This example dynamically demonstrates the relationship between geometric shapes and vectors. It involves core mathematical concepts such as vectors, complex numbers, binomial distribution, inequalities, and trapezoids. The construction uses GeoGebra commands and objects like Vector, Sequence, DynamicCoordinates, Point, Rotate, Segment, Polygon, If, and Angle. Suitable for high school students and teachers for teaching demonstrations and explorations.

GeoGebra Commands & Parameters

  1. Vector(A, C1) → u
  2. Sequence((x(A) + (round(Length[u]) * cos(t°)), y(A) + (round(Length[u]) * sin(t°))), t, 0, 355, 5) → VPoints
  3. DynamicCoordinates(C1, x(ClosestPoint[VPoints, C1]), y(ClosestPoint[VPoints, C1])) → C
  4. Point(Sequence[A + (i, 0), i, 1, 20, 1]) → B
  5. Vector(B, C2) → v
  6. Rotate(D + (4, 0), 100°, D) → F
  7. Segment(F, D) → k
  8. Segment(E, F) → j
  9. Segment(A, C) → f
  10. Segment(A, B) → g
  11. DynamicCoordinates(C2, If[Distance[C2, C] < d, x(C), x(C2)], If[Distance[C2, C] < d, y(C), y(C2)]) → C'
  12. Sequence(B + (i * UnitVector[Segment[B, C2]]), i, 1, 20, 1) → UPoints
  13. Segment(C', B) → h
  14. Polygon({A, B, C}) → t1
  15. If(Distance[C', C] < d, true, false) → closed1
  16. Segment(D, E) → i
  17. Polygon(D, E, F) → t3, l, m, n
  18. Angle(E, D, F) → α
  19. Angle(B, A, C) → β