• Ancient Chinese Geometry

    by  • June 11, 2013 • Math • 1 Comment

    Liu Hui was a 3rd century Chinese mathematician. I first stumbled upon him when I saw puzzles based on dissection proofs of the Pythagorean Theorem (Shang Gao Theorem (商高定理)) at ICME11 in 2004. Recently I’ve been exploring the trisection of a cube, so I could give students a way to discover the formula for the volume of a pyramid or cone. After recreating the correct pyramids myself – which took an embarrassingly long time and involved floral foam, lucite boxes, ribbon, and my Dremel tool – I came upon an image that amazed me. (If I show you, it will spoil the surprise.)

    Liu Hui Solids - Nets

    I was so excited when I made and built these nets for Liu Hui’s solids! They hold amazing properties, which I could describe, but instead will leave for you to discover. I have included the nets, which I encourage you to decorate, digitally or not, before you build them. I will be using them in a similar way with students – enjoy!

    Liu Hui's Solids - Silverman

    Liu Hui’s Solids


    P.S. I think we as Western educators, would do well to study the contributions of Eastern scholars, like Liu Hui.


    After teaching for 14 years, I now design curriculum and create digital and print instructional materials for high school and middle school math. I have also invented and am now marketing radian-scale protractors. Check out www.proradian.net! I'm very happily married and have 2 grown sons and a cat named Louie.

    One Response to Ancient Chinese Geometry

    1. July 16, 2013 at 1:31 pm

      Look like a great discovery and yes, education should have no limits, teach which is best for the students, these puzzles by Liu Hui will be help for students.

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