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Sphere Volume Formula in Nine Chapters

Sphere Volume Formula in Nine Chapters
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2016-05-26 00:38
FunctionSolid GeometryGeometric Construction
In collections Volumes and Surface Areas of Pyramids, Cones and Spheres Volumes in Ancient Chinese Mathematics 中國古算中的體積 Volumes of Pyramid and Sphere in Ancient Chinese Mathematics Volume of Spheres in Ancient Chinese Mathematics
This example demonstrates the geometric derivation of the sphere volume formula from the Nine Chapters on the Mathematical Art. It involves core concepts like sphere volume, geometric construction, and integral ideas. Constructed using commands such as Circle, Polygon, Prism, Cylinder, Sphere. Suitable for high school solid geometry teaching and introductory mathematical modeling.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Polygon((-1, -1), (1, -1), (1, 1), (-1, 1)) → poly1, f, g, h, i
  3. Prism(poly1, 2) → a, C, edge1, edge2, edge3, edge4, edgeCD, edgeDE, edgeEF, edgeCF, D, E, F, face1, face3, face4, face2, faceCDEF
  4. Cylinder(c, 2) → b, d, e
  5. Sphere((0, 0, 1), 1) → j