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Mouhefanggai Locus Tracing

Mouhefanggai Locus Tracing
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2017-07-17 14:31
FunctionTrigonometryCoordinate GeometrySolid GeometryGeometric Construction
In collections Volume of Spheres in Ancient Chinese Mathematics
This example demonstrates the locus generation process of the Mouhefanggai (Double Box-lid). It involves core mathematical concepts such as Sphere, Volume, Algebra, Functions, Logarithm, Exponent, and Circle. The construction utilizes GeoGebra commands like Sequence, Sphere, Segment, Point, OrthogonalPlane, IntersectPath, Line, Intersect, Distance, Circle, and Polygon. Suitable for high school students and mathematics enthusiasts studying solid geometry and coordinate geometry.

GeoGebra Commands & Parameters

  1. Sequence((-2, 0, i), i, 0, 2, 2 / n) → list1
  2. Sphere((0, 0, 1), 1) → j
  3. Segment((-2, 0, 0), (-2, 0, 2)) → f
  4. Point(list1) → P
  5. OrthogonalPlane(P, f) → a
  6. IntersectPath(a, j) → c
  7. Line(C, xAxis) → g
  8. Intersect(g, j) → D, E
  9. Distance(C, E) → r
  10. Segment(F, G) → h
  11. Segment(G, H) → i
  12. Segment(H, I) → k
  13. Segment(I, F) → l
  14. Circle((0, 0), r) → d
  15. Polygon(((-r), (-r)), (r, (-r)), (r, r), ((-r), r)) → poly1, m, p, q, s

AI Drawing Prompt Reference

Draw the locus generation process of a double box-lid curve, showing the intersection of a sphere with planes. Start by creating a sphere and a vertical line segment. Generate a series of points along the segment, use them to construct perpendicular planes, and find their intersections with the sphere to form the double box-lid curve. Then, draw lines from the intersection points to the sphere's center, locate their intersections, and use these points to create a circle and a square, finally presenting the dynamic generation of the curve.
The prompt above was compiled from the original drawing commands and is for reference only.