Transhumance and Mathematics. Pretexts and links

In this paper, places, routes, things, forms, encounters relating to transhumance are used as a pretext to show how many mathematical ideas are present and can be connected to reality even to what might seem very distant from the world of an hard science. Connections, sheep tracks, are created between two very lateral worlds: mathematics and transhumance. Transhumance, its places, its characters, becomes an opportunity to refer to concepts, principles, theorems explained first with convivial language, like sheep tracks, and then, when necessary, with formal language. We speak, for example, of the theory of fractals to measure the length and windingness of sheep tracks, to draw the mountains or the nature crossed by men and animals or to plot some plants of the territory; of isoperimetric theorems to justify the shape of pens and enclosures for animals; of mathematical curves and surfaces that describe the shepherd's wooden stick or the shape of a local cheese. Finally, by using mathematical techniques, we show and analyze some sounds of transhumance: bleating, bellowing, cowbells and whistles of a shepherd.