Geodesic
Teorema di Pick e Serie di Farey
Matematica, cultura e società, Série 1, Tome 7 (2022) no. 2, pp. 159-168

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

Farey sequences are sequences of fractions in increasing order in the interval [0;1] whose denominators are less than or equal to a given value. Pick's theorem provides a formula for the calculation of the area of polygonal regions on a lattice with integer coordinates. Although they seem to be quite unrelated topics there is a deep relationship between them. In particular, the fundamental property of Farey sequences can be inferred from Pick's theorem. Conversely, the same property can be used as a starting point of a proof of Pick's theorem. This paper concerns the analysis of such an interesting relationship. 
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     author = {Cordelli, Alessandro},
     title = {Teorema di {Pick} e {Serie} di {Farey}},
     journal = {Matematica, cultura e societ\`a},
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Cordelli, Alessandro. Teorema di Pick e Serie di Farey. Matematica, cultura e società, Série 1, Tome 7 (2022) no. 2, pp. 159-168. http://geodesic.mathdoc.fr/item/RUMI_2022_1_7_2_a4/