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Shortest Perimeter

Shortest Perimeter
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2017-11-20 09:19
Solid GeometryOptimizationParametric EquationGeometric Construction
This example demonstrates the exploration of geometric shapes with the shortest perimeter by constructing polyhedra and calculating the perimeter of their faces. Core mathematical concepts include perimeter calculation, matrix applications, power functions, parametric curves, and similarity transformations. The construction utilizes GeoGebra commands and objects such as Point, Cube, Line, OrthogonalPlane, IntersectPath, and Perimeter. It is suitable for high school and above students to understand spatial geometry, optimization problems, and advanced mathematical applications.

GeoGebra Commands & Parameters

  1. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  2. Cube(A, B, C) → a, D, faceCDHG, faceEFGH, edgeAD, edgeAB, edgeBC, edgeCD, edgeAE, edgeDH, edgeEH, edgeEF, E, edgeBF, edgeFG, edgeCG, edgeGH, F, G, H, faceABCD, faceADHE, faceABFE, faceBCGF
  3. Line(H, B) → f
  4. Point(f) → P
  5. OrthogonalPlane(P, f) → b
  6. IntersectPath(b, a) → poly1, J, j, k, l, K, L, M, N, O, g, h, i
  7. Perimeter(poly1) → c