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Pythagoras, Pythagorean Theorem, 3D Models, 勾股定理, ピタゴラス定理

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3D model description

Pythagoras, Pythagorean Theorem, 3D Models

The Pythagorean Theorem can be illustrated (not proved) using 3D models. In fact, it is a direct implication of a^2 + b^2 = c^2 in a 3D space. Pick an h > 0. Then, ha^2 + hb^2 = hc^2. We could construct a square-end box of a constant height along each side of the right triangle. However, there is much more to it. We could build infinitely many 3D (or 2D) models. As long as the three 3D solids (or corresponding 2D shapes) are similar to each other, the volume of the solid on the hypotenuse is equal to the sum of the volumes of the two solids on the two legs. Some 3D models are aesthetically attractive; others are not so much.

Included here are three 3D models on a right triangle that is 30mm, 50mm, and sqrt(3400)mm—semi-circle, square, and trapezoid. They all have a depth of 30mm. You can use water, sand, or rice to demonstrate the relationships. It is a bit messy and is also fun for students!

3D printing settings






.1 to .2mm



By default, the models are 30mm in depth. Please feel free to scale the height down. It will not affect its properties.

3D printer file information

  • 3D design format: STL Folder details Close
    • Pythagoras3DSquare.stl
    • Pythagoras3DTrapezoid.stl
    • Pythagoras3D_semiCircle.stl

    Learn more about the formats

  • Publication date: 2018/01/31 at 17:45




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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