I understand why a guitar and other such instruments are the form they are, but why has the ukulele taken the figure of 8 form? It doesn't seem to have much economical merit, as say the guitar which has that shape to sit on the players leg for example.
I'm no expert but I'm unsure that's true. From
http://www.fretboard.com/guitarhistory.html: "In Spain of the 13th through 15th centuries, two instruments could be called "guitar": the guitarra moresca, a lute shaped instrument; and the guitarra latina, a more guitar like shaped instrument. As this period ended, the instruments were more commonly called guitarra and chitarra. A third instrument, the vihuela de mano was a similar guitar-like instrument, plucked with the fingers. And as the 15th century came to an end, these instruments began to become more rounded and have more prominent indentations at the waist." I can't find much on the sizes of these instruments, but at
http://home.earthlink.net/~curtis_bouterse/id6.html the guitarra latina appears to be around tenor-to-baritone uke size, or not much larger, and at
http://www.jubilatores.com/guitarra.pdf is mention of a scale length of 46 cm, about 18 inches. So decidedly smaller than modern guitars, and less need to support it on the leg. And in the illustrations on those pages they're consistently shown as being played while standing.
From
http://www.acousticmasters.com/AcousticMasters_GuitarBody1.htm: "The idea of a waisted body, with a square back and sides, may have been inspired by the design of the bowed instruments of the time, where symmetric waist cutaways were introduced to allow clearance for the bow. Some versions of the vihuela (an instrument that is related to the guitar) were played with a bow."
It's also true the guitar shape influences the acoustics. On a quick search all I find is a rather vague statement at
http://entertainment.howstuffworks.com/guitar1.htm but essentially the resonant frequency of the upper bout is higher than that of the lower bout, which are somewhat decoupled by the waist. So maybe the body acts rather like a 3-band equalizer, boosting the upper and lower frequencies relative to the middle, or something along those lines.