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Square Pattern

Square Pattern
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2014-08-05 12:32
PolygonFunctionCalculusGeometric ConstructionSlider Animation
In collections Symmetry, Transformation and Tessellation
This example demonstrates how to construct a dynamic square pattern using GeoGebra, involving core math concepts like polygon construction, function graphing, integral calculus, continuity, angle calculations, and function applications. Key GeoGebra commands/objects used include Polygon, Point, Angle, and Sequence, making it suitable for high school and above students to explore the integration of geometric constructions and function graphs.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 4) → poly1, a, b, c, d, C, D
  2. Point(poly1) → P
  3. Polygon(A, P, 4) → poly2, e, f, g, h, E, F
  4. Angle(B, A, P) → α
  5. Sequence(Rotate[Dilate[poly1, r^(n), A], (n * α), A], n, 0, 12) → list1

AI Drawing Prompt Reference

Create a dynamic square pattern by repeatedly rotating and scaling a square to form a complex geometric design. Start with a square, then calculate the angle between one vertex and the adjacent side. Use this angle to sequentially rotate and scale the original square, generating multiple squares to form a dynamic pattern. Incorporate a slider to control the scaling factor and observe how the pattern changes with different values.
The prompt above was compiled from the original drawing commands and is for reference only.