MathPlotAI Logo MathPlotAI

Cross Sections of Cylinders by Alfred Estberg

Cross Sections of Cylinders by Alfred Estberg
Loading the math board and drawing, please wait…
2016-07-29 02:12
Solid GeometryTransformationGeometric Construction
This example demonstrates the cross-sectional shapes of cylinders. Key mathematical concepts include solid geometry and geometric construction. Using GeoGebra commands such as Intersect, Point, Segment, etc., it dynamically shows different cross-sectional shapes. Suitable for middle school and above students to learn solid geometry.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(Circle[A, b]) → B
  3. Segment(A, B) → c
  4. Line(P, yAxis) → p
  5. Line(P, xAxis) → q
  6. Point(p) → Q
  7. Point(q) → R
  8. Rotate(R, α, p) → R'
  9. Rotate(Q, (-β), q) → Q'
  10. Plane(P, Q', R') → n
  11. Rotate(n, γ, zAxis) → i_1
  12. Intersect(xAxis, yAxis) → D_1
  13. Circle(D_1, b) → f_1
  14. Cylinder(f_1, l) → g_1, h_1, j_1
  15. IntersectPath(i_1, g_1) → d
  16. Plane(p, x = 0) → e
  17. Translate(e, Vector[(0, 0, 0), (w, 0, 0)]) → e'
  18. IntersectPath(e', g_1) → f