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Rotating a Triangle Around an Axis

Rotating a Triangle Around an Axis
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2012-12-31 00:13
TriangleSolid GeometryTransformation
In collections Area, Surface Area, Volume, Cross Section, 3D Rotations
This example demonstrates the solid of revolution formed by rotating a triangle around an axis. Key mathematical concepts include rotation geometry and solid geometry. Using GeoGebra commands such as Intersect, Vector, and Polygon, the rotation process is visually illustrated. Suitable for high school math education to help students understand spatial geometric transformations.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → O
  2. Vector(O, 6 * X) → px
  3. Vector(O, 6 * Y) → py
  4. Vector(O, 6 * Z) → pz
  5. Polygon(O, 4 * X, 3 * Y + 4 * X) → poly1, a, b, c
  6. CurveCartesian(x(4 * X + 3 * cos(n) * Y + 3 * sin(n) * Z), y(4 * X + 3 * cos(n) * Y + 3 * sin(n) * Z), n, 0, Rotate) → d
  7. Sequence(Segment[O, (x(4 * X + 3 * cos(n) * Y + 3 * sin(n) * Z), y(4 * X + 3 * cos(n) * Y + 3 * sin(n) * Z))], n, 0, Rotate, 0.01) → list1
  8. Segment(O, A) → g
  9. Sequence(Segment[4 * X, (x(4 * X + 3 * cos(n) * Y + 3 * sin(n) * Z), y(4 * X + 3 * cos(n) * Y + 3 * sin(n) * Z))], n, 0, Rotate, 0.01) → list2
  10. Polygon(O, A, 4 * X) → poly2, h, o, a_1
  11. CurveCartesian(x(4 * cos(n) * X + 0 * Y + 4 * sin(n) * Z), y(4 * cos(n) * X + 0 * Y + 4 * sin(n) * Z), n, 0, Rotate) → f
  12. CurveCartesian(x(4 * cos(n) * X + 3 * Y + 4 * sin(n) * Z), y(4 * cos(n) * X + 3 * Y + 4 * sin(n) * Z), n, 0, Rotate) → e
  13. Sequence(Segment[O, (x(4 * cos(n) * X + 3 * Y + 4 * sin(n) * Z), y(4 * cos(n) * X + 3 * Y + 4 * sin(n) * Z))], n, 0, Rotate, 0.1) → list3
  14. Sequence(Segment[O, (x(4 * cos(n) * X + 0 * Y + 4 * sin(n) * Z), y(4 * cos(n) * X + 0 * Y + 4 * sin(n) * Z))], n, 0, Rotate, 0.1) → list4
  15. Sequence(Segment[(x(4 * cos(n) * X + 0 * Y + 4 * sin(n) * Z), y(4 * cos(n) * X + 0 * Y + 4 * sin(n) * Z)), (x(4 * cos(n) * X + 3 * Y + 4 * sin(n) * Z), y(4 * cos(n) * X + 3 * Y + 4 * sin(n) * Z))], n, 0, Rotate, 0.1) → list5
  16. Polygon(O, B, C) → poly3, c_1, o_1, b_1
  17. Sequence(Segment[n * X + 6 * Y, n * X - 6 * Y], n, -6, 6) → list9
  18. Sequence(Segment[-6 * X + n * Y, 6 * X + n * Y], n, -6, 6) → list10
  19. Sequence(CurveCartesian[x(4 / 3 * i * cos(n) * X + i * Y + 4 / 3 * i * sin(n) * Z), y(4 / 3 * i * cos(n) * X + i * Y + 4 / 3 * i * sin(n) * Z), n, 0, Rotate], i, 0, 3, 0.1) → list8
  20. Sequence(CurveCartesian[x(i * cos(n) * X + 0 * Y + i * sin(n) * Z), y(i * cos(n) * X + 0 * Y + i * sin(n) * Z), n, 0, Rotate], i, 0, 4, 0.1) → list7
  21. Sequence(CurveCartesian[x(4 * cos(n) * X + i * Y + 4 * sin(n) * Z), y(4 * cos(n) * X + i * Y + 4 * sin(n) * Z), n, 0, Rotate], i, 0, 3, 0.1) → list6

AI Drawing Prompt Reference

Draw a solid of revolution formed by rotating a triangle around the X-axis, illustrating the geometric transformation during rotation. Start by plotting the coordinate axes and origin, then draw the rotation axis and the triangle. Connect the origin to each vertex of the triangle with line segments and sketch the rotation paths. Finally, fill the solid with curves and lines to create a 3D effect.
The prompt above was compiled from the original drawing commands and is for reference only.