While one set of measurements yielded a value of pi as impressive (to me) as 3.38, overall I observed poor consistency of measurements among adjacent squares near the center of the page, and poor repeatability of measurements for the squares tested. Nevertheless, I hope that you, dear reader, will consider trying this experiment for yourself. I will tell you how I did it, and perhaps you will take more care than I to apply the paint accurately and precisely; otherwise, you will too observe a high variance of resistance among your resistors. Note also that the resistance of the Bare Paint decreases as it dries, so be sure to allow ample time for drying (tens of minutes) before measurements.
Submitted by Ace Monster Toys Hackerspace in Oakland, CA for the Instructables Sponsorship Program
Step 1: Materials
Step 2: Folding the Paper to Make "guide Lines" for Drawing
Then, for each of the two axes of the sheet, successively fold the sheet in half four times and unfold it completely.
Step 3: Draw the Grid!
You can clearly see than my drawn grid lacked uniformity, but I didn't know then how much that would matter. Hopefully you will do better than me.
Also, note how I drew "dangling" resistors at the edges of the sheet. These are useful to estimate the resistance of an isolated stretch of the paint equal in length to a side of one square; you need this value to estimate pi.
Step 4: Measure!
There are three simple measurements to do. Using your multimeter in "ohmmeter" mode (the units of resistance are Ohms, symbolized by the Greek capital letter Omega), you can measure (1) the resistance across an isolated "dangling" resistor that is not part of the grid; let's call this resistance R. Next, you can measure (2) the resistance across one side of a square near the center of the paper; the resistance should theoretically be R_side = R / 2. Finally, you can measure (3) the resistance across the diagonal of one square; the resistance should theoretically be R_diag = R * (2 / pi). So, pi should equal 2 * (R / R_diag). Is it close to 3.14? Note that I can list at most three significant digits because my pictured multimeter only provided three. I got as close as 3.38 for one set of measurements.