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Pythagorean Theorem, Visual Proof, Chinese Origin

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3D model description

Update: Added a third STL file with more details to show the rich connections within a Pythagorean Square

The Pythagorean Theorem can be proved or confirmed for a right triangle using numerous ways. The 3D model here can be used to make a well-known visual configuration that has its origin with ancient Chinese mathematicians around 220 BC. The idea can be explored with young children using paper models, cardboard models, or, now, 3D printouts.

The first two STL files each have four right triangles within a 70mm x 70mm square. The first measures 30mm, 40mm, 50mm. The second is 20mm,50mm and about 53.85mm. The third STL file has more details and is closer to the original configuration. There is about some room within the square to allow easy assembling. I put some small triangles along the square to prevent it from warping.

The whole thing is parametrically designed on Fusion 360. This project can be used as an entry point project for middle school or secondary students to learn about 3D design in a STEM setting. Either PLA or ABS can be used.

Swetz, F. J., & Katz, V. J. (2011). "Mathematical Treasures - Zhou Bi SuanJing," MAA Convergence. Available at

3D printing settings











Separate the right triangles from the square and play with them!

  • 3D file format: STL
  • Publication date: 2017/12/26 at 15:32


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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:




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