hi, maybe you can try keeping two electrodes at different potentials and subject them in saline solutions. remember, the saline concentration has direct effect on the electrical conductivity. that way you would get the signal you need and the quantitative rigor required in Physics IA. remember to discuss with your teacher the idea before actually gathering data.
hi Bill, for 1) you can do something similar by learning spherical coordinate system and then calculating the distance of a line in the flat space (Minkowski) in two different coordinate planes, thus showing that this line actually corresponds to a curve in the spherical coordinate.