Arbor Bench

The arch would be made by joining wider straight segments together at an angle, essentially end-to-end, and then cutting the arcs within that width. In other words, you make part of a flat polygon that is wide enough to contain the width of the arc you want, then scribe and cut the arc. The more segments you have, the less initial width you need to get the width of arc you want.

You'd first cut the ends of the polygon segments to the desired angle for the desired polygon, and then join the ends. You could use half-lap joints, bridle joints, a splined butt joint, or a "finger joint" bit like this (only in a router table with a proper sled) across the width of the board ends:

http://www.eagleamerica.com/product/v191...

An angled bridle joint would likely be the strongest, but the arch is decorative, not terribly structural, so the strength of the joints is less of an issue.

Be sure to keep the grain of all segments going in the same direction, so the finished piece can be planed flat.

This link will help with the polygon angles:

http://www.rockler.com/articles/woodwork...