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Optical Squares

Optical Squares
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2015-09-01 10:10
Derivative
This example demonstrates a dynamic geometric construction based on geometrical patterns and optical illusions. Core math concepts include squares, quadratic equations, quadrilaterals, circumcircle, step functions, and derivatives. Construction highlights the use of GeoGebra commands like Segment, Point, Sequence, Textfield, Rotate, Distance, with objects such as N, A, B, a, C, ang, r, list3, u, list2, r_1, inputBox1, inputBox2, D, list2', dst, button1, b. Suitable for high school students and enthusiasts exploring geometric transformations and function graphs.

GeoGebra Commands & Parameters

  1. Segment(B, B - (1 / N * (B - A))) → a
  2. Point(a) → C
  3. Sequence(Square[A + (i / N * (B - A)), A + ((i - 1) / N * (B - A)), ((i - 1) * ang / (N - 1)), 1 - (i / N * (1 - r))], i, 1, N) → list3
  4. Sequence(Translate[list3, Vector[((-i) * u)]], i, 0, ceil(N / 2) - 1) → list2
  5. Textfield(r_1) → inputBox1
  6. Textfield(ang) → inputBox2
  7. Rotate(list2, 180*°, D) → list2'
  8. Distance(A, B) → dst