Volumes of Pyramid and Sphere in Ancient Chinese Mathematics

Anthony OR 柯志明, Jul 16, 2017

[b]Abstract[/b] In this session the speaker would present how ancient Chinese mathematicians approached the problem of finding the volumes of pyramids and spheres. The speaker would illustrate ancient Chinese mathematicians' ideas with GeoGebra and elaborate the pedagogical value of the ideas through the use of GeoGebra.

Table of Contents

  1. Volume of Pyramids
    1. Aim
    2. Cuboid and "Yangma"（陽馬）
    3. Volume of Pyramids - Liu Hui's (劉徽) Proof
    4. Volume of Pyramids by Democritus
    5. Cavalieri's Principle
  2. Volume of Spheres and Double Box-lid (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 牟合方蓋)
    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
    7. Pedagogical Values of Ancient Math Ideas

1.

Volume of Pyramids

  • 1. Aim
  • 2. Cuboid and "Yangma"（陽馬）
  • 3. Volume of Pyramids - Liu Hui's (劉徽) Proof
  • 4. Volume of Pyramids by Democritus
  • 5. Cavalieri's Principle

1.1.

Aim

[list][*][size=200]Visualize ideas of ancient Chinese mathematicians on volumes of pyramids and spheres with the distinctive features of GeoGebra [/size][/*][*][size=200]Elaborate the pedagogical values of the ideas[br][/size][br][/*][/list][br][br]
– Anthony OR 柯志明

1.2.

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1.3.

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1.4.

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1.5.

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2.

Volume of Spheres and Double Box-lid (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 牟合方蓋)
  • 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
  • 7. Pedagogical Values of Ancient Math Ideas

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.

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2.3.

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2.4.

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2.5.

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2.6.

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2.7.

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