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Minimizing Surface Area Example by ILC Curriculum

Minimizing Surface Area Example by ILC Curriculum
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2016-10-29 00:18
Solid GeometryCalculusOptimizationGeometric ConstructionGraphing
This example demonstrates dynamically minimizing surface area using GeoGebra, focusing on a pyramid. Key math concepts include area calculation, tangent functions, quadratic equations, curve sketching, and logarithmic functions. Construction highlights points, segments, ellipses, lines, intersections, and other GeoGebra commands/objects. Suitable for high school mathematics teaching on optimization problems and geometric relationships.

GeoGebra Commands & Parameters

  1. Point(Circle[A, (r * 2)]) → B
  2. Segment(A, B) → a
  3. Ellipse(A, B, C) → c
  4. Point(Circle[D, (r * 2)]) → E
  5. Ellipse(D, E, F) → d
  6. Segment(A, D) → b
  7. Segment(B, E) → e
  8. Point(b) → G
  9. Point(e) → H
  10. Line(G, H) → f
  11. Point(b) → I
  12. Point(e) → J
  13. Line(I, J) → g
  14. Intersect(c, f) → K, L
  15. Intersect(d, g) → M, N
  16. Segment(L, N) → i
  17. Segment(K, M) → j