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]]>Here’s another, as an MAA Found Math in 2012.

http ://www.maa.org/community/columns/maa-found-math/maa-found-math-2012-week-36 ]]>

Subtracting the number 4 from it we get:

0.123105626

Inverse of this number is:

8.123105625

Subtracting 4 we get back to:

4.123105626 = √ [17]

Panagiotis Stefanides

]]>I found it interesting to notice that it’s not the use of a carpenter’s square, specifically, that is needed in order to perform this construction — it’s the ability to find the point ‘F’, subject to the constraint that angle BFJ is a right angle. A carpenter’s square is one tool for doing that, but any method of ‘inverting’ the problem “BFJ is a right angle. solve for F” will do.

You can do this by binary-searching for the position of F on the line segment ED – but this amounts to constructing an infinite series of points and taking their limit, and that’s equivalent to allowing yourself to compute 1/3 of an angle by using an infinite series of bisections like 1/3 = 1/4+1/16+1/256…, which is a known way of trisecting angles anyway. Infinite series approximations are not allowed, of course, in normal compass+straightedge constructions, so this doesn’t clash with the impossibility proof.

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