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Function Trajectory and Geometric Art

Function Trajectory and Geometric Art
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2023-01-11 18:14
FunctionCoordinate GeometryDerivativeGeometric Construction
This example demonstrates the geometric construction of function trajectories, involving concepts like functions, derivatives, and quadratic equations. The construction uses GeoGebra commands such as Segment, Point, Polygon, and If, with parameter t1 controlling the trajectory. Suitable for high school students to develop mathematical thinking in combining functions and geometry, useful for function graph analysis and geometric construction practice.

GeoGebra Commands & Parameters

  1. Segment(A_{1}, B_{1}) → f
  2. Segment(B_{1}, C_{1}) → g
  3. Segment(C_{1}, D) → h
  4. Segment(D, A_{1}) → i
  5. Point(l1) → A
  6. Point(l1) → C
  7. Point(l1) → B
  8. Polygon(A, B, C) → t1, f_1, e, g_1
  9. If(x(A) ≟ 0, Distance[D, A], y(A) ≟ 4, 4 + Distance[A_{1}, A], x(A) ≟ 4, 8 + Distance[B_{1}, A], y(A) ≟ 0, 12 + Distance[C_{1}, A]) → dE
  10. If(x(C) ≟ 0, Distance[D, C], y(C) ≟ 4, 4 + Distance[A_{1}, C], x(C) ≟ 4, 8 + Distance[B_{1}, C], y(C) ≟ 0, 12 + Distance[C_{1}, C]) → dF
  11. If(x(B) ≟ 0, Distance[D, B], y(B) ≟ 4, 4 + Distance[A_{1}, B], x(B) ≟ 4, 8 + Distance[B_{1}, B], y(B) ≟ 0, 12 + Distance[C_{1}, B]) → dG

AI Drawing Prompt Reference

Draw a geometric art pattern of function trajectories, involving three line segments and four points. Start by drawing three line segments and connect three points to form a triangle. Then, calculate and plot four points based on the positions of the triangle's vertices, where the positions are determined by the coordinates of the triangle's vertices. Finally, combine these points and line segments to create a complex geometric pattern, showcasing the integration of function trajectories and geometric construction.
The prompt above was compiled from the original drawing commands and is for reference only.