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The First Set of Nets: Rotation-Based Polygon Net Construction

The First Set of Nets: Rotation-Based Polygon Net Construction
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2023-11-11 15:25
PolygonAngleTransformationGeometric ConstructionSlider Animation
In collections How many nets of a cuboid are there?
This example demonstrates how a base set of control points and polygons can be transformed to generate a structured “first set of nets.” It visually highlights symmetry and stepwise construction using rigid transformations. The key mathematics concepts include geometric construction (defining points and polygonal outlines), planar transformation—especially rotation—and parameter-based modeling where dimensions and rotation variables control the evolving shape. From the provided GeoGebra construction summary, the build process relies on Point to create key points (A, B, C, and additional controls such as q1, l, w, h, q2–q6, and t), Polygon to form the net-like polygonal faces/edges, and Rotate to generate additional rotated copies (using derived parameters like q2', q3', q4', q5', q6' tied to the rotation variable t). Interactive elements (button1, button2) support switching or animating between construction stages. Suitable for middle school to early university audiences for teaching transformations, symmetry, and geometric construction workflows.

GeoGebra Commands & Parameters

  1. Point(Ray[(1, 0), (3, 0)]) → A
  2. Point(Ray[A + (1, 0), A + (2, 0)]) → C
  3. Point(Ray[A + (0, 1), A + (0, 2)]) → B
  4. Polygon({(0, 0), A, B, (0, y(B))}) → q1
  5. Polygon({A, C, (x(C), y(B)), B}) → q2
  6. Polygon({(0, 0), A, A - (0, h), (0, (-h))}) → q3
  7. Polygon({B, B + (0, h), B + ((-l), h), B + ((-l), 0)}) → q4
  8. Polygon({C, C + (l, 0), C + (l, w), C + (0, w)}) → q5
  9. Polygon({C + (l, 0), C + (l + h, 0), C + (l + h, w), C + (l, w)}) → q6
  10. Rotate(q4, (90° * t), Line[(0, w), B]) → q4'
  11. Rotate(q3, (90° * t), Line[A, (0, 0)]) → q3'
  12. Rotate(q2, (90° * t), Line[B, A]) → q2'
  13. Rotate(Rotate[q5, (90° * t), Line[C + (0, w), C]], (90° * t), Line[B, A]) → q5'
  14. Rotate(Rotate[Rotate[q6, (90° * t), Line[C + (l, w), C + (l, 0)]], (90° * t), Line[C + (0, w), C]], (90° * t), Line[B, A]) → q6'_{1}

AI Drawing Prompt Reference

Draw a net-like structure composed of multiple rotated polygons. Start by creating points A, B, and C, then construct basic polygons q1 to q6 using these points. Next, generate rotated copies of polygons q3', q4', q2', q5', and q6' using rotation parameter t and specific axes to demonstrate rotation and symmetry.
The prompt above was compiled from the original drawing commands and is for reference only.