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**The Question**

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Given a length of square stock and a standard compound miter chop-saw how would you make an equilateral triangle using only 45 degree cuts?

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This is a woodworking math puzzle I invented. For three years now no one I've asked

has been able to answer the question.

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**The Hints**

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You need only set up the saw once

You may fashion a simple length stopYou will make exactly four cuts

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**The Answer**

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Set the saw to a 45 degree x 45 degree compound cut as shown.

Cut off the tail of the stock.

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*partial rotation shown*

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Slide stock to the stop.

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Make the second cut.

rotate stock 180 degrees and slide to stop

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With exactly four cuts you can generate three parts.

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Rotate one part around the fold axis.

Fold the second part over by 90 degrees.

Here is an equilateral triangle made from only 45 degree cuts.

**That's It!**

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**There is More!**

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It's interesting that the two angled sides

of the triangle are not the same.

Depending on the respective orientation from these triangles

one can make edge truncated octahedrons and tetrahedrons.

of the triangle are not the same.

Depending on the respective orientation from these triangles

one can make edge truncated octahedrons and tetrahedrons.

Consequently it follows that one can generate an octet-truss.

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**Photos**

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These alder frames are glued and nailed.

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Three triangles preparing to merge.

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## 1 comment:

Thanks a lot for this puzzle. I was playing to create tetrahedron lamp fixture and was going exactly the way you described in this puzzle.

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