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Rotating a Pencil Geometric Demo

Rotating a Pencil Geometric Demo
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2017-08-07 15:02
VectorTrigonometryCoordinate GeometrySolid GeometryGeometric Construction
In collections surface 3D /3D-Oberflächen 1 surface 3D /3D-Oberflächen 1
This example dynamically demonstrates the 3D geometric shapes formed by rotating a pencil, involving core math concepts like linear equations, solid geometry, Pythagorean theorem, area calculation, and linear programming. It uses GeoGebra commands such as Circle, CurveCartesian, OrthogonalLine, Point, Segment, Tangent, Midpoint, Line, Rotate, Vector, Radius, and Surface for construction, suitable for elementary and advanced students to understand 3D graphics and related math principles.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. CurveCartesian(x(A) + (Radius[c] * cos(t)), y(A) + (Radius[c] * sin(t)), 0, t, 0, (2 * π)) → a
  3. OrthogonalLine(C, xOyPlane) → f
  4. Point(f) → D
  5. Segment(C, D) → g
  6. Tangent(C, c) → h,
  7. Midpoint(g) → E
  8. Line(E, h) → i
  9. Rotate(C, t / 2, i) → C'
  10. Rotate(D, t / 2, i) → D'
  11. Segment(C', D') → g'
  12. Vector(C', D') → u
  13. Radius(c) → R
  14. Surface(x(A) + (R * cos(t)) + (k * x(u)), y(A) + (R * sin(t)) + (k * y(u)), z(E) + (k * z(u)), k, -0.5, 0.5, t, 0, (2 * π)) → b
  15. Vector(C, F) → v

AI Drawing Prompt Reference

In 3D space, draw a circle on a horizontal plane with its center and a point on the circumference. From a point outside the circle, construct a line perpendicular to the plane, and pick a point on this line; connect this point to the outside point to form a segment. Draw a tangent line to the circle from the outside point, take the midpoint of the segment, and through this midpoint draw a line parallel to the tangent. Rotate both the outside point and the point on the perpendicular line around this parallel line by a certain angle, obtaining two new points; connect them to form a new segment and derive its direction vector. Finally, sweep a surface along the circular path using this vector as the direction, and also draw a vector from the circle's center to a given point, creating a dynamic 3D geometric demonstration of rotation.
The prompt above was compiled from the original drawing commands and is for reference only.