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Smallest Perimeter Demonstration

Smallest Perimeter Demonstration
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2016-08-17 20:37
Coordinate GeometryOptimizationParametric EquationGeometric Construction
This example demonstrates how to construct and analyze geometric figures with the smallest perimeter using GeoGebra. It involves core mathematical concepts such as perimeter optimization, parametric curves, coordinate geometry, and geometric transformations. Key construction steps include using commands like Polygon, Point, Segment, and Mirror, along with objects A, B, C, poly1, etc. Suitable for high school and above students exploring geometric optimization problems.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Point(c) → P
  3. Point(b) → Q
  4. Point(a) → R
  5. Segment(R, P) → f
  6. Segment(P, Q) → g
  7. Segment(Q, R) → h
  8. Mirror(R, c) → R'
  9. Mirror(P, c) → P'
  10. Segment(R', P') → f'
  11. Mirror(Q, b) → Q'
  12. Mirror(R, b) → R'_1
  13. Segment(Q', R'_1) → h'
  14. Segment(R', A) → i
  15. Segment(A, R'_1) → j
  16. Segment(R'_1, R') → k