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Geometric Series in Quarter Squares

Geometric Series in Quarter Squares
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2018-02-27 18:32
SequenceCoordinate GeometryGeometric Construction
This example demonstrates the construction of geometric series within a quarter square, integrating concepts like geometric series, square, difference and slope, integers, set theory, curve sketching, and equilateral triangles. It utilizes GeoGebra commands such as Intersect, Point, Polygon, Segment, Vector, Translate, and Sequence to create the visual representation, making it suitable for high school mathematics education to explore the intersection of geometric series and geometric figures.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
  4. Segment(C, D) → j
  5. Segment(D, A) → k
  6. Vector(A, B) → u
  7. Vector(A, D) → v
  8. Translate(poly1, u) → poly2
  9. Translate(poly1, v) → poly3
  10. Vector(A, C) → w
  11. Translate(C, w) → E
  12. Sequence(Dilate[poly1, (1 / 2)^(k), E], k, 0, n) → L_1
  13. Sequence(Dilate[poly2, 0.5^(k), E], k, 0, n) → L_2
  14. Sequence(Dilate[poly3, 0.5^(k), E], k, 0, n) → L_3