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Rotate Rectangle

Rotate Rectangle
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2019-05-16 19:41
Solid GeometryTransformationGeometric Construction
This example demonstrates the process of rotating a rectangle around an axis to form a cylinder. Key mathematical concepts include rotation, solid geometry, and volume calculation. Using GeoGebra commands such as Vector, Translate, and Rotate, the dynamic transformation of a rectangle into a cylinder is illustrated. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Vector(B_1, X) → u
  2. Vector(B_1, Y) → v
  3. OrthogonalLine(view, yAxis) → a_1
  4. OrthogonalLine(view, xAxis) → b
  5. Vector(B_1, Z) → w
  6. Sequence((x(O), y(O)) - (Radius * (((sin(0°) * sin(i°)) * w) + ((cos(0°) * sin(i°)) * u) - (cos(i°) * v))), i, 0, k, n) → liste1
  7. Translate(O, Vector[(Height * w)]) → F
  8. Sequence((x(F), y(F)) - (Radius * (((sin(0°) * sin(i°)) * w) + ((cos(0°) * sin(i°)) * u) - (cos(i°) * v))), i, 0, k, n) → liste5
  9. Sequence(Polygon[O, Element[liste1, i], Element[liste5, i], F], i, 0, Rotate) → liste6
  10. CurveCartesian(x(F - (Radius * (((0 * sin(i)) * w) + (sin(i) * u) - (cos(i) * v)))), y(F - (Radius * (((0 * sin(i)) * w) + (sin(i) * u) - (cos(i) * v)))), i, 0, 6.283185307179586) → f
  11. CurveCartesian(x(O - (Radius * (((0 * sin(i)) * w) + (sin(i) * u) - (cos(i) * v)))), y(O - (Radius * (((0 * sin(i)) * w) + (sin(i) * u) - (cos(i) * v)))), i, 0, 6.283185307179586) → d
  12. Polygon(O, F, Element[liste5, Rotate], Element[liste1, Rotate]) → poly2, m, p, q, s
  13. Segment(F, O) → f_1

AI Drawing Prompt Reference

Draw a rectangle rotating around one of its sides to form a cylinder, demonstrating the rotation process. Start by drawing the rectangle and its rotation axis, using vectors to represent the sides and axis direction. Then, translate one side of the rectangle along the axis to get two parallel rectangles. Rotate to generate a series of connecting quadrilaterals between these two rectangles, forming the cylinder's side. Finally, represent the top and bottom of the cylinder with circular arcs to complete the drawing.
The prompt above was compiled from the original drawing commands and is for reference only.