Geometry

Also called: plane geometry, solid geometry, developing curves, raking mouldings

Practical geometry is the part of mathematics a woodworker needs to work out shapes, angles and curves accurately before any cut is made. It is what lies behind setting out, the step of marking a piece of work with the lines it will be cut to, and it runs quietly under most of the trade's more exacting jobs.

Plane geometry and solid geometry

Geometry splits into two branches. Plane geometry deals only with flat surfaces; solid geometry covers three-dimensional forms such as cubes. For a woodworker, plane geometry is the branch that matters day to day: it covers the setting out of angles, polygons, circles and ellipses, and one long-standing teaching text aimed at the trade deliberately limited its own coverage to this practical core, on the view that a woodworker needs no more than a grounding in plane geometry to carry out the work. Solid and descriptive geometry, which handle three-dimensional problems more fully, go beyond what most joinery calls for.

Where it earns its keep

A student cannot properly prepare or read the working drawings needed for carpentry and joinery without some prior grounding in practical geometry. The same grounding underlies bevels, angled cuts across a piece of timber: a handful of geometric constructions form the basis of the general methods used to set them out. Traditional timber framing leans on it most heavily, calling for elaborate joints, advanced geometric layout and an understanding of the structural forces involved; the more sophisticated mortise-and-tenon joints in this work may lock together by shaped wedges and a precise geometric fit rather than by pegs driven through bored holes, though pegged joints are also used. In regions where timber was historically raised in densely wooded country, the resulting buildings tend to look more vertical, which calls for more elaborate joinery and geometric setting out.

The geometry of a cutting edge

The word also applies to the shape of a tool's edge, not just to lines drawn on a board. A knife-type cutting tool's geometry has to let its edge touch the wood while the tool is held comfortably in the hand, which calls for a smaller sharpness angle, the angle ground onto the edge itself. On a router bit, the maker trades off the hook angle, the clearance angle (the angle left behind the edge so the tool does not rub against the wood it has just cut) and the shear angle against one another, since improving one tends to cost something in the others.

Construction versus instrument

A normal, a line running at right angles to a surface, can be found by geometric construction, but reading it directly off a measuring instrument is reckoned the more workable way to do it in practice.