Sunday 21 July 2013

A Zometool model for an astrologer's platform

In ancient China, the solid as shown in the picture is called chutong 芻童, which can be roughly translated as "truncated hill". As the reader can see, it has a bottom face and a top face, both of which are oblongs with unequal lengths and widths. On its four side faces are four trapezoids. This solid is often used as an astrologer's platform for observing the heavens, or as an emperor's mausoleum.


If the length and width of the top face are a and b, the length and width of the bottom face are c and d, and the height of this solid is h, then its volume formula is given in the Nine Chapters of Mathematical Art (1st century) as

Saturday 6 July 2013

Liu Hui's derivation for the volume of pyramids (with a photo of a Zometool model!)

Liu Hui 劉徽 (ca. 263 AD) was a mathematician from the Wei Empire (魏國) in modern-day Northern China. His most important contribution was his commentary on the Nine Chapters of Mathematical Art (九章算術). One of the most interesting pieces of his commentary is his demonstration of the volume formulae of two kinds of  pyramids: yangma 陽馬 and bienao 鼈臑.