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Visser Unit Circle

Visser Unit Circle
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2018-10-29 10:26
CircleFunctionTrigonometryCalculusGeometric Construction
This example demonstrates the geometric construction of the Visser Unit Circle and related graphical phenomena. It involves core mathematical concepts such as Circle, Unit Circle, Parabola, Logarithm, Upper and Lower Sum or Riemann Sum, Poisson Distribution, and Histogram. The construction utilizes GeoGebra commands and objects like Intersect, Circle, Point, Ray, OrthogonalLine, Polygon, Segment, Angle, and Line. It is suitable for high school and above students to visualize complex geometric and functional relationships.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, 1) → c
  3. Point(c) → P
  4. Ray(A, P) → f
  5. OrthogonalLine(P, xAxis) → g
  6. Intersect(g, xAxis) → C
  7. Polygon(P, C, A) → t1, a, b, c_1
  8. Segment(A, P) → h
  9. Segment(A, C) → i
  10. Segment(P, C) → j
  11. Intersect(c, xAxis) → D, E
  12. OrthogonalLine(E, xAxis) → k
  13. Intersect(k, f) → F
  14. Segment(E, F) → l
  15. Angle(E, A, P) → θ
  16. Intersect(i, j) → B
  17. Intersect(c, l, 1) → G
  18. Intersect(f, l) → P_2
  19. Line(G, P_2) → m
  20. Point(h) → H
  21. Line(P_2, H) → n
  22. Intersect(m, n) → I
  23. Ray(P, H) → p
  24. Intersect(c, xAxis, 2) → J
  25. OrthogonalLine(J, xAxis) → q
  26. Intersect(q, p) → K
  27. Intersect(c, q, 1) → L
  28. Segment(L, K) → r