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Cone and Linear Equations with 3D Geometric Transformations

Cone and Linear Equations with 3D Geometric Transformations
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2017-02-15 05:54
VectorFunctionCoordinate GeometrySolid GeometryTransformation
In collections Mapping Diagrams: From AB to C&DE, Resource
This example demonstrates the geometric transformations of a cone in three-dimensional space and its relationship with linear equations. The core math concepts involved include solid geometry, vector operations, linear equations, and three-dimensional coordinate transformations. The construction highlights the use of GeoGebra commands like Point, Vector, Textfield, and Sequence to create objects such as base points, vectors, text fields, and sequences, dynamically showcasing the transformation process. Suitable for high school and above students to understand the integration of spatial geometry and linear equations.

GeoGebra Commands & Parameters

  1. Point(i) → K
  2. Point(yAxis) → A_x
  3. Vector(A_x, B_x) → u
  4. Vector(B_x, C_x) → v
  5. Textfield(m) → inputBox1
  6. Textfield(s) → inputBoxf
  7. Sequence(Vector[(6, m(core(R(i)))), (8, s(m(core(R(i)))))], i, 1, 5) → Quadgvlist
  8. Sequence(Vector[(4, core(R(i))), (6, m(core(R(i))))], i, 1, 5) → Quadmvlist
  9. Sequence(Vector[(0, i), (2, R(i))], i, 1, 5) → QuadRvlist
  10. Sequence(Vector[(2, R(i)), (4, core(R(i)))], i, 1, 5) → Quadqvlist
  11. Vector(K, s_{inv}D) → w
  12. Vector(s_{inv}D, m_{invSinvD}) → z
  13. Vector(m_{invSinvD}, q_{inv+}) → d
  14. Vector(q_{inv+}, I) → h_1
  15. Sequence(Vector[(0, i), (2, m(i))], i, -2, 2) → Linmvlist
  16. Sequence(Vector[(2, m(i)), (4, s(m(i)))], i, -2, 2) → Lingvlist
  17. Textfield(h) → inputBox2
  18. Textfield(k) → inputBox3
  19. Textfield(A) → inputBox4
  20. Textfield(base) → inputBox5
  21. Vector(C_x, D_x) → f
  22. Vector(D_x, E_x) → g