MO, gotta log off soon, just some quick notes.
Scientific Calculator: Ellipse Arc Length ... make sure your calculator angle mode is in radians.
Simpson\'s Rule: Web Based Ellipse Arc Length Calculator
Arch Layout Notes ... the idea was to fit the five sections of the circular arch in 13" wide timbers. My computer was broken and there's a five page "math essay" in addition to those three pages.

PS: In case anyone cares to follow the math here's some more info about the circular arch ("Arch Layout Notes" link) I didn't have time to include in the original post:
Mortises and tenons are 2" circular arc length.
The length of the pendant is 16", bevelled at 45°.