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Archimedean Principle Demo

Archimedean Principle Demo
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2019-05-11 20:27
Solid GeometryCalculusGeometric Construction
This example dynamically demonstrates the volume relationships between cones, cylinders, and spheres, visually showcasing the Archimedean Principle. Core math concepts include volume calculation, linear equations, random variables, rhombus, surface, and indefinite integral. GeoGebra commands used in construction are Segment, Cone, Intersect, Point, Cylinder, Sphere. Suitable for high school students and math enthusiasts for learning solid geometry and calculus.

GeoGebra Commands & Parameters

  1. Segment(H, I) → t
  2. Cone(A, B, 1) → b, d, e
  3. Cone(C, B, 1) → f, g, h
  4. Intersect(yAxis, xAxis) → D
  5. Point(zAxis) → E
  6. Cylinder(D, E, 1) → i, k, p, j
  7. Sphere(F, 1) → l
  8. Point(t) → G
  9. Point(q) → K
  10. Point(r) → O
  11. Point(s) → P
  12. Segment(J, K) → a_1
  13. Segment(L, O) → b_1
  14. Segment(M, P) → c_1
  15. Segment(G, N) → d_1
  16. Segment(S, Q) → e_1
  17. Segment(T, R) → f_1
  18. Segment(B, S) → g_1
  19. Segment(F, T) → h_1