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Bertoia Rectangles

Bertoia Rectangles
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2020-07-24 05:53
VectorFunctionCalculus
This example demonstrates the construction of Bertoia rectangles. Key mathematical concepts include rectangles, integration, and vectors. Using GeoGebra commands such as Point, Polygon, Vector, etc., the dynamic transformation and area calculation of rectangles are showcased. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Point(Ray[B, Rotate[D_1, (-(90°)), B]]) → C
  2. Polygon(A, B, C, C + A - B) → q1, a, b, c, f
  3. Vector(Midpoint[A, C], E) → u
  4. Midpoint(A, C) → F
  5. Rotate(q1, Angle[A, F, E], Line[E, F]) → q1'
  6. Rotate(A, Angle[A, F, E], Line[E, F]) → A'
  7. Rotate(B, Angle[A, F, E], Line[E, F]) → B'
  8. Rotate(C, Angle[A, F, E], Line[E, F]) → C'
  9. Rotate(D, Angle[A, F, E], Line[E, F]) → D'
  10. Sequence(Segment[A + (i / (n - 1) * (B - A)), A' + (i / (n - 1) * (B' - A'))], i, 0, n - 1) → l1
  11. Sequence(Segment[C + (i / (n - 1) * (D - C)), C' + (i / (n - 1) * (D' - C'))], i, 0, n - 1) → l2
  12. Rotate(A, Angle[A, F, E], Line[E, F]) → A'_1
  13. Rotate(B, Angle[A, F, E], Line[E, F]) → B'_1
  14. Segment(A'_1, B'_1) → a'
  15. Rotate(B, Angle[A, F, E], Line[E, F]) → B'_2
  16. Rotate(C, Angle[A, F, E], Line[E, F]) → C'_1
  17. Segment(B'_2, C'_1) → b'
  18. Rotate(c, Angle[A, F, E], Line[E, F]) → c'
  19. Rotate(f, Angle[A, F, E], Line[E, F]) → f'
  20. Sequence(Segment[A + (i / (m - 1) * (D - A)), A' + (i / (m - 1) * (D' - A'))], i, 0, m - 1) → l4
  21. Sequence(Segment[C + (i / (m - 1) * (B - C)), C' + (i / (m - 1) * (B' - C'))], i, 0, m - 1) → l3