Volumes in Ancient Chinese Mathematics 中國古算中的體積

Anthony OR 柯志明, May 27, 2016

Table of Contents

  1. Volume of Pyramids 錐體體積
    1. Cuboid and "Yangma" 長方體與「陽馬」
    2. Volume of Pyramids - Liu Hui's Proof 劉徽的錐體體積證明
    3. Cavalieri's Principle (祖暅原理)
    4. Volume of Pyramids
  2. Volume of Spheres and Double Box-lid 球體體積與牟合方蓋
    1. Volume of Spheres in Nine Chapters on the Mathematical Art《九章算術》的球體體積公式
    2. Tracing Double Box-lid (Mouhefanggai) 追蹤蓋合方蓋
    3. Double Box-lid (Mouhefanggai) 牟合方蓋面面觀
    4. Double Box-lid (Mouhefanggai 牟合方蓋) as Intersection of 2 Cylinders
    5. Volumes of Mouhefanggais and Spheres 牟合方蓋和球體的體積
    6. Volume of Spheres with Proof

1.

Volume of Pyramids 錐體體積

  • 1. Cuboid and "Yangma" 長方體與「陽馬」
  • 2. Volume of Pyramids - Liu Hui's Proof 劉徽的錐體體積證明
  • 3. Cavalieri's Principle (祖暅原理)
  • 4. Volume of Pyramids

1.1.

Cuboid and "Yangma" 長方體與「陽馬」

– Anthony OR 柯志明

1.2.

–

1.3.

–

1.4.

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2.

Volume of Spheres and Double Box-lid 球體體積與牟合方蓋

  • 1. Volume of Spheres in Nine Chapters on the Mathematical Art《九章算術》的球體體積公式
  • 2. Tracing Double Box-lid (Mouhefanggai) 追蹤蓋合方蓋
  • 3. Double Box-lid (Mouhefanggai) 牟合方蓋面面觀
  • 4. Double Box-lid (Mouhefanggai 牟合方蓋) as Intersection of 2 Cylinders
  • 5. Volumes of Mouhefanggais and Spheres 牟合方蓋和球體的體積
  • 6. Volume of Spheres with Proof

2.1.

Volume of Spheres in Nine Chapters on the Mathematical Art《九章算術》的球體體積公式

– Anthony OR 柯志明

2.2.

–

2.3.

–

2.4.

–

2.5.

–

2.6.

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