• Ancient Chinese Geometry

    by  • June 4, 2016 • Math • 1 Comment

    Note: This is a re-post from 2013, dedicated to Dr. Golden’s students!


    Dissected Cube

    A diagram from the book, “Sherlock Holmes in Babylon”

    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 the image on the right.


    Liu Hui's Solids - Silverman

    Liu Hui’s Solids – by Jen Silverman

    It took a while for me to visualize the relationships between the faces of what I’m calling Liu Hui’s solids, but with grit and GeoGebra, I got it done. Excited doesn’t begin to describe how I felt when I finished and built the nets! They hold amazing properties, which I could describe, but instead will leave for you to discover. If you are not up to the task of recreating them for yourself, I have included a link to the nets and a list of resources to make pretty ones that stick together with magnets!


    Check out this post for nets and directions.


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

    Full SetEtsy5Etsy2


    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. June 5, 2016 at 1:03 pm

      I wrote a little bit about Liu Hui inspiration: http://mathhombre.blogspot.com/2016/05/commentary.html His commentary on the Nine Chapters is such a big idea in addition to great math.

      Your cube has inspired more good 3-D to 2-D connections than I could ever thank you for. It’s so well made in addition to the sweet geometry.

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