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Double Cone Construction and Inequality Demonstration

Double Cone Construction and Inequality Demonstration
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2017-09-13 07:54
FunctionSolid GeometryTransformationInequalityGeometric Construction
This example demonstrates how to construct a double cone and visualize inequality relationships through rotation and geometric construction. Key math concepts include cones, exponent operations, geometric constructions, and inequalities. The construction utilizes GeoGebra commands and objects such as Point, Rotate, CurveCartesian, Surface, and Polygon. Suitable for high school and above, it helps understand the connection between solid geometry and inequalities, as well as mastering dynamic geometry software techniques.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Rotate(A, π / 2, yAxis) → B
  3. Rotate(A, (2 * π / 2), yAxis) → C
  4. Rotate(A, (3 * π / 2), yAxis) → D
  5. CurveCartesian((x(A) * cos(t)), (x(A) * sin(t)), 0, t, 0, π) → a
  6. CurveCartesian((x(A) * cos(t)), (x(A) * sin(t)), 0, t, (-π), 0) → b
  7. Rotate(A, (n * π / 2), yAxis) → A'
  8. Rotate(B, (n * π / 2), yAxis) → B'
  9. Rotate(C, (n * π / 2), yAxis) → C'
  10. Rotate(D, (n * π / 2), yAxis) → D'
  11. Rotate(a, (n * π / 2), yAxis) → a'
  12. Surface((u * x(a'(t))) + ((1 - u) * x(D')), (u * y(a'(t))) + ((1 - u) * y(D')), (u * z(a'(t))) + ((1 - u) * z(D')), t, 0, π, u, 0, 1) → c
  13. Surface((u * x(a'(t))) + ((1 - u) * x(B')), (u * y(a'(t))) + ((1 - u) * y(B')), (u * z(a'(t))) + ((1 - u) * z(B')), t, 0, π, u, 0, 1) → d
  14. Polygon(B', C', D', A') → poly1, b', c', d', a'_1
  15. Surface((u * x(b(t))) + ((1 - u) * x(D)), (u * y(b(t))) + ((1 - u) * y(D)), (u * z(b(t))) + ((1 - u) * z(D)), t, (-π), 0, u, 0, 1) → e
  16. Surface((u * x(b(t))) + ((1 - u) * x(D)), (u * y(b(t))) + ((1 - u) * y(D)), (-((u * z(b(t))) + ((1 - u) * z(D)))), t, (-π), 0, u, 0, 1) → f
  17. Polygon(C, D, A, B) → poly2, c_1, d_1, a_1, b_1