Hear this question a lot?
The following are links to some old metalworking (and woodworking) books which show that metalworking and woodworking engineers of the past really knew their stuff.
http://archive.org/details/metalplateworkit00millrich
http://archive.org/details/mechanicsgeometr00ridd
http://archive.org/details/tinsheetironcopp00bliniala
They don't bother much with proofs, but do show some really cool constructions for polygons, circles, ellipses, etc.
Most of the complex constructions are approximations, but this just brings up one of my pet interests, the use of appropriate approximations in mathematics.
When you're building a sheet metal part, does it matter if your shape is 1-2 mm from being a perfect heptagon? Especially when it's pretty difficult to bend a piece of metal to within 1mm tolerances in the first place.
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