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Square – Octagon Dissection
von lgbu
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#####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.
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.
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