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Rectangular Envelope

Rectangular Envelope
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2018-01-17 01:37
PolygonTransformationGeometric Construction
This example demonstrates the concept of rectangular envelope. Core mathematical concepts include geometry of rectangles and polygons. Using GeoGebra commands such as Midpoint, Circle, Point, Line, etc., the construction of rectangular envelope is illustrated. Suitable for students at junior high school level and above for geometric construction.

GeoGebra Commands & Parameters

  1. Midpoint(A, B) → C
  2. Circle(C, B) → c
  3. Point(c) → D
  4. Line(D, C) → f
  5. Intersect(c, f, 2) → E
  6. Polygon(A, D, B, E) → q1, a, d, b, e
  7. Segment(A, B) → g
  8. OrthogonalLine(D, g) → h
  9. OrthogonalLine(E, g) → i
  10. Intersect(i, g) → F
  11. Intersect(h, g) → G
  12. Segment(E, F) → j
  13. Segment(D, G) → k

AI Drawing Prompt Reference

Draw the envelope of a rectangle. First, find the midpoint C of AB, draw a circle with C as the center and B as the radius, and pick any point D on the circle. Draw line CD, and the other intersection point of the circle and line CD is E. Connect A, D, B, and E to form a quadrilateral. Then, draw the perpendicular bisector f of AB, and draw perpendicular lines h from D and i from E to f. The intersection of h and f is F, and the intersection of i and f is G. Finally, connect EF and DG to form the envelope of the rectangle.
The prompt above was compiled from the original drawing commands and is for reference only.