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Dots in the Box

Dots in the Box
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2017-01-18 22:10
TrigonometryCoordinate GeometryGeometric ConstructionLocus
This example demonstrates the process of randomly generating points within a box and constructing polygons. It involves core mathematical concepts such as addition, subtraction, angles, unit circle, trigonometry, diagrams, and similarity transformations. The construction utilizes GeoGebra commands and objects like Flatten, Reverse, Sequence, Point, Random, Polygon, If, and Segment. It is suitable for high school students studying geometric transformations, probability & statistics, and coordinate geometry.

GeoGebra Commands & Parameters

  1. Flatten(Sequence[Sequence[Point[{i, j}], j, 0.5, 4.5], i, 0.5, 4.5]) → list3
  2. Reverse(list3) → list5
  3. Flatten(Sequence[Sequence[Point[{i, j}], i, 0.5, 4.5], j, 0.5, 4.5]) → list2
  4. Reverse(list2) → list4
  5. Sequence(Point[{i, 0}], i, 2, 25) → list1
  6. Point(list1) → A
  7. Point(list1) → B
  8. Random(Min[x(A), x(B)], Max[x(A), x(B)]) → number
  9. Random(1, number - 1) → n1
  10. Polygon((0, 0), (5, 0), (5, 5), (0, 5)) → poly1, g, h, i, j
  11. Point({(4 * cos(π - lidMover)) + 4, (2 * sin(π - lidMover))}) → lidPoint
  12. Polygon(lidPoint, lidPoint + (5, 0), lidPoint + (5, 5), lidPoint + (0, 5)) → poly2, k, l, m, n
  13. If(step ≟ 0, 2, 9) → top
  14. Segment((2, 0), (25, 0)) → f
  15. If(step ≟ 0, 29, 16) → right

AI Drawing Prompt Reference

Draw a square with sides of length 5 and generate random points inside it to form polygons. First, draw the four sides of the square, then place points randomly inside. Next, calculate and draw a moving lid using trigonometric functions based on one side of the square, forming a larger quadrilateral with the square. Finally, connect the random points to create multiple internal polygons.
The prompt above was compiled from the original drawing commands and is for reference only.