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Rotating Polygons by Patrick Clément

Rotating Polygons by Patrick Clément
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2014-05-21 00:56
PolygonCoordinate GeometryTransformation
This example demonstrates the rotation of polygons on a plane. It involves rotation transformations, matrices, and geometric construction of polygons. By using the Sequence command to generate a series of rotated polygons, one can observe the changes in the polygons at different angles. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Append(First[{A, B, C, D, E, F, G, H, I, J, K, L}, n], A) → P
  2. Sequence(Segment[Element[P, i], Element[P, i + 1]], i, 1, n) → seg
  3. Append(Sequence[Point[Element[seg, i], p], i, 1, n], Point[Element[seg, 1], p]) → Pin
  4. Sequence(Segment[Element[Pin, i], Element[Pin, i + 1]], i, 1, n) → segin
  5. Append(Sequence[Line[Element[P, i + 1], Element[segin, i]], i, 1, n], Line[Element[P, 2], Element[segin, 1]]) → dte
  6. Sequence(Intersect[Element[dte, i], Element[dte, i + 1]], i, 1, n) → Pout
  7. Polygon(P) → poly1, , , ,
  8. Polygon(Pin) → poly2, , , ,
  9. Polygon(Pout) → poly3, , ,

AI Drawing Prompt Reference

Draw a polygon with multiple vertices, then rotate this polygon around a central point to observe how the rotated polygons change. First, draw the original polygon, then generate a series of rotated polygons, and finally draw a polygon based on the intersection points of the rotated polygons.
The prompt above was compiled from the original drawing commands and is for reference only.