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Using Sequences : Squares with reducing sizes

Using Sequences : Squares with reducing sizes
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2017-02-04 23:35
PolygonSequenceGeometric Construction
This example demonstrates how to dynamically draw a sequence of squares with decreasing side lengths using GeoGebra. Key math concepts include sequences, polygons, area, perimeter, and similarity transformations. It uses commands like Distance, Polygon, and Sequence. Suitable for high school mathematics education to understand sequence applications and geometric transformations.

GeoGebra Commands & Parameters

  1. Distance(A, B) → a
  2. Polygon(A, B, 4) → poly1stSquare, f, g, h, i, C, D
  3. Sequence(Polygon[(x(A) + (a * (1 - (l_2 / l_1)^(i)) / (1 - l_2 / l_1)), y(A) + (a * (1 - (l_2 / l_1)^(i)) / (1 - l_2 / l_1))), (x(A) + a + ((a * l_2 / l_1) * (1 - (l_2 / l_1)^(i)) / (1 - l_2 / l_1)), y(A) + (a * (1 - (l_2 / l_1)^(i)) / (1 - l_2 / l_1))), 4], i, 1, n - 1, 1) → listSquares
  4. Sequence((4 * sqrt(Element[listSquares, i])), i, 1, n - 1, 1) → listPerimeters