This is going to be an IKEA talk. You will need: a wooden plank, plenty of nails, a hammer, a ruler, and plenty of string. On your plank, tap in nails to form a regular grid. Now take a piece of string, and form a polygon on your plank by fastening the two ends of your piece of string to the same nail. Question: what is the area of your polygon ? We are going to see that this question can be answered by just counting nails. This will also give us the occasion to illustrate the typical process a mathematician (and more generally, a scientist) uses to study a question.