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Constant Perimeter... Changing Area?

Constant Perimeter... Changing Area?
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2016-07-08 11:52
PolygonOptimizationGeometric Construction
This example demonstrates how the area of a polygon changes while maintaining a constant perimeter. Key math concepts include perimeter, area, polygons, and optimization. It is constructed using GeoGebra commands like Polygon, Area, Circle, Point, Segment, OrthogonalLine, Intersect, Perimeter, Distance, If. Suitable for high school mathematics education to understand area maximization under fixed perimeter conditions.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 3) → poly1, a, b, c, C
  2. Area(poly1) → areaT
  3. Circle(D, perim / 2) → d
  4. Point(d) → E
  5. Segment(D, E) → e
  6. Point(e) → F
  7. OrthogonalLine(F, e) → f_1
  8. OrthogonalLine(D, e) → g
  9. Circle(F, E) → h
  10. Intersect(h, f_1, 2) → G
  11. OrthogonalLine(G, f_1) → i
  12. Intersect(g, i) → H
  13. Polygon(D, F, G, H) → poly2, d_1, f, g_1, f_2
  14. Perimeter(poly2) → k
  15. Circle(D, perim / 3) → p
  16. Intersect(p, d_1, 1) → I
  17. Segment(D, I) → a_1
  18. Segment(I, F) → b_1
  19. Segment(F, G) → b_2
  20. Segment(D, F) → l
  21. Intersect(r, xAxis, 2) → K
  22. Distance(I, K) → n
  23. Circle(F, a - l) → s
  24. OrthogonalLine(F, xAxis) → t
  25. Intersect(s, t) → L, M
  26. Segment(F, M) → e_1
  27. Segment(H_2, D) → c_2
  28. If(poly2 > poly1, 1, 0) → q
  29. Segment(H_2, H) → c_1
  30. Segment(M, G) → h_1
  31. Circle(H, c - c_2) → k_1
  32. Intersect(k_1, i) → J, N
  33. Segment(H, J) → i_1
  34. Segment(J, G) → j_1