Measuring hard things with easy experiments
Here are some links to experiments that allow you to measure impossibly-difficult-sounding things using everyday objects:
Measuring the thickness of a human hair using a laserpointer and a tape measure.
Measuring the speed of light using chocolate chips and a microwave oven
Calculating PI with a box of toothpicks
Take a box of N toothpicks - each of length L. Find a floor with parallel lines on it - a tiled floor or one made of planks will do. (If you use tiles you need to pick one set of parallel lines to use. eg pick just the 'north-south' lines between them and ignore the east-west lines.) The distance between the parallel lines is D - and D must be bigger than L.
Now - dump out all of the toothpicks onto the floor from a good height so they land pretty much at random. Now, count the number of toothpicks that cross one of the lines on the floor...call that number 'C'.
OK - so all you need to do is to calculate:
PI = 2 x L x N / ( D x C )
...tadaaaa! Of course you need to drop an awful lot of toothpicks to get a precise answer...especially if the distance between the lines on your floor is much bigger than the length of the toothpicks. Under good circumstances, you should be able to get within a few percent using a box of 100 toothpicks. Doing the experiment lots of times and averaging the results will help.
To understand why - look up "Buffons' Needle" in Wikipedia.