Q: I would like to know what the difference (mathematical anyway) is between an arch and an arc.

A: Rob Johnstone: These are the definitions I found on my favorite online dictionary (dictionary.com) for these two terms. I have nearly finished an arch between my dining room and another room in my house. To build it I drew an arc and then built my arch.
Arch:
1. A structure, especially one of masonry, forming the curved, pointed, or flat upper edge of an open space and supporting the weight above it, as in a bridge or doorway.
2. A structure, such as a freestanding monument, shaped like an inverted U.
3. A curve with the ends down and the middle up: the arch of a raised eyebrow.
Arc:
1. Mathematics. A segment of a circle.

A: Michael Dresdner: Yep, Rob said it best. An arc is an imaginary mathematical shape defined by a segment of a circle, while an arch is an architectural solid, often, but not always, based on one or more arcs. However, when I asked my sarcastic high school son the difference between and arc and an arch, he replied: "Well, the first one is a big boat filled with pairs of animals..."