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Exploring Polygon Relationships

Exploring Polygon Relationships
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2019-03-25 22:58
PolygonTrigonometryCoordinate GeometryOptimization
This example demonstrates dynamically constructing one polygon inside another and exploring their geometric relationships. Core math concepts include polygon construction, area calculation, geometric transformations, quadratic equations, equilateral triangles, symmetry, and statistical characteristics. GeoGebra commands used in construction are Intersect, Sequence, Polygon, PointIn, Point, and Append. Suitable for high school and above learners to understand the intrinsic connections and transformation patterns of complex geometric figures.

GeoGebra Commands & Parameters

  1. Intersect(Ray[A, Rotate[B, ca, A]], Ray[B, Rotate[A, (-ca), B]]) → C_1
  2. Sequence(Rotate[A, (i * (360°) / n), C_1], i, 0, n - 1) → l1
  3. Polygon(l1) → q1
  4. PointIn(Polygon[A, B, C_1]) → C
  5. Point(Segment[C, C_1]) → D
  6. Sequence(Rotate[C, (i * (360°) / n), D], i, 0, n - 1) → l2
  7. Append(l1, A) → l1'
  8. Append(l2, C) → l2'
  9. Sequence(Polygon[Element[l1', i], Element[l1', i + 1], Element[l2', i + 1], Element[l2', i]], i, 1, n) → l3
  10. Sequence(Element[l3, (2 * i) - 1], i, 1, n / 2) → l3a
  11. Sequence(Element[l3, (2 * i)], i, 1, n / 2) → l3b
  12. Sequence(Segment[Element[l1, i], Element[l2, i]], i, 1, n) → l4
  13. Sequence(Element[l4, (2 * i) - 1], i, 1, n / 2) → l4a
  14. Sequence(Element[l4, (2 * i)], i, 1, n / 2) → l4b