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Rotating and Dilating Squares

Rotating and Dilating Squares
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2014-07-18 12:23
PolygonCoordinate GeometryTransformation
In collections Symmetry, Transformation and Tessellation
This example demonstrates the dynamic transformation of squares under rotation and dilation. It involves core math concepts like transformations (rotation, dilation), polygon properties, angles, and coordinate geometry. Constructed using GeoGebra commands/objects such as Polygon, Point, Angle, Rotate, and Sequence. Suitable for high school students learning geometric transformations and analytical geometry, or for math clubs' exploratory activities.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 4) → poly1, a, b, c, d, C, D
  2. Point(a) → P
  3. Angle(A, O, P) → α
  4. Rotate(Dilate[poly1, t], α) → poly2
  5. Sequence(Rotate[Dilate[poly1, t^(k)], (k * α)], k, 0, n) → list1

AI Drawing Prompt Reference

Draw a dynamically transforming square by first creating a square, then rotating and dilating it around a point to generate a sequence of successive squares, each rotated and scaled by a certain angle and factor, demonstrating the transformation of the square through rotation and dilation.
The prompt above was compiled from the original drawing commands and is for reference only.