Skip to content

Magic Square, Math, Recreational, Luo Shu Square, Lo Shu, 洛书

3D model description

Magic Square

The Magic Square has a Chinese origin and has for long been used in both school and recreational mathematics. It is simple and engaging: Consider the numbers {1, 2, 3, 4, 5, 6, 7, 8, 9}. How can we arrange them to a square so that the sum of the three numbers along each row, each column, and each diagonal are all the same? As a warm up, one can ask children to add up the following: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 =? There are of course many different ways to add up the numbers! There are certainly magic squares of different orders! As the square gets bigger, however, it quickly gets too complicated for school children.

Although we can use paper and pencil work to play with the magic square, a physical model changes the mode of exploration and may encourage children’s math talks and pattern making or tweaking.

Two sizes: 64mm^2, and 100mm^2 .


Magic Square.

Weisstein, Eric W. "Magic Square." From MathWorld--A Wolfram Web Resource.

3D printing settings






.1 to .2mm


10% to 20%

Nothing special about printing. Please feel free to play with the resolution and infill.

If desired, please change filament to add some color to the numbers around 80% completion.

  • 3D model format: STL


STEAM educator, learning from and working with K-12 STEAM teachers to explore new ideas of teaching and engagement. I firmly believe ART is at the core of STEM learning or all human learning! I owe my ideas and designs to the hundreds of K-12 children and teachers and university professors I have had the pleasure of working with, in multiple disciplines-- math, science,engineering language arts, social studies, early childhood education and more! All mistakes, of course, are mine! There is no warranty or liability whatsoever implied or explicit behind the designs or ideas. They are all posted for their potential educational values.

When working with children, please strictly observe all safety and health procedures! Please refer to the NSTA safety guides:




Add a comment