Square –Octagon Dissection: A Beautiful Problem!

Given a square, how do we dissect it and reassemble the parts into an octagon? It is a simple and complex problem! Using the illustrated method, there is only one way to do it. I had to use a bit of algebra to find the dimensions of the squares. In short, \text{InnerSquareDim}= \frac{1}{2}\sqrt{2 \sqrt{2} - 2)} \cdot \text{OuterSquareDim} . It is a satisfying process to figure out how things are related in such an formula!

There might be other methods to do that, though. It turns out to be a great design project, integrating school geometry, algebra, and a bit of design heuristics. Three square sizes are included, 60mm, 80mm, and 100mm; the thickness is 3mm. Have fun!

Reference

Cundy, H. M., & Rollett, A. P. (1961). Mathematical models (2nd ed.). London, UK: Oxford University Press.

Rafts:

No

Supports:

No

Resolution:

.1 to .2mm

Infill:

5-20%

- 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: http://www.nsta.org/safety/.

LGBU Contact: LGBU@SIU.EDU

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