An objective and practical method for describing and understanding ratios
Mathématiques et Sciences humaines, Tome 124 (1993) , pp. 5-18.

Cet article explore l'utilisation de l'algorithme euclidien comme moyen très utile pour manipuler les rapports, surtout dans les cas où de bonnes approximations rationnelles sont nécessaires. Cette discussion est illustrée à partir d'une analyse de l'architecture grecque par JJ. Coulton. Cet article veut être un compte-rendu pratique, mais il comprend aussi une discussion de certains aspects théoriques, ainsi que de la relation de cette procédure à une nouvelle interprétation des mathématiques grecques de l'époque de Platon.

This article explores the use of the euclidian algorithm as a most useful way of handling ratios, especially when good rational approximations are required. Illustrations are taken from a discussion of the analysis of greek architecture by J.J Coulton. Although this is intended as a practical account, some discussions of theoretical aspects are included, and also of the relationship of this procedure to a new interpretation of early greek mathematics.

@article{MSH_1993__124__5_0,
     author = {Fowler, D. H.},
     title = {An objective and practical method for describing and understanding ratios},
     journal = {Math\'ematiques et Sciences humaines},
     pages = {5--18},
     publisher = {Ecole des hautes-\'etudes en sciences sociales},
     volume = {124},
     year = {1993},
     zbl = {0835.01001},
     mrnumber = {1282235},
     language = {en},
     url = {http://www.numdam.org/item/MSH_1993__124__5_0/}
}
Fowler, D. H. An objective and practical method for describing and understanding ratios. Mathématiques et Sciences humaines, Tome 124 (1993) , pp. 5-18. http://www.numdam.org/item/MSH_1993__124__5_0/

Coulton J.J., "Towards Understanding Greek Temple Design: General Considerations ", Annual of the British School of Athens,70 (1975), 59-99; Corrigenda, ibid., 51 (1976), 149-50.

Fletcher T., "Approximating by vectors", Mathematics Teaching 63 (1973), 4-9 & 64 (1973), 42-44.

Fowler D.H., The Mathematics of Plato's Academy: A New Reconstruction, Oxford, Clarendon Press, 1987; revised paperback reprint, 1991. | MR 932963 | Zbl 0627.01002

Fowler D.H., "Logistic and fractions", pp133-147 in Benoit, P., Chemla K., & Ritter J., edd., Histoire de Fractions, Fractions d'Histoire, Basel etc., Birkhäuser, 1992. | MR 1278497 | Zbl 1067.01511

Fowler D.H., "How to find the golden number without really trying", Mathematics Review, 34 (April 1993), 2-7.

Freyl L., "Médiétés et approximations chez Vitruve", Revue Archéologique, 1990, 285-330.

Freyl L., "Pour un modèle du chapiteau ionique vitruvien", Revue Archéologique, 1992, 37-63.

Freyl L., "La transmission d'un canon: les temples ioniques", to appear in Le Projet de Vitruve: Object, Destination et Reception du De Architectura, Rome, Ecole Française de Rome.

Heath T.L., A History of Greek Mathematics, 2 vols., Oxford, Clarendon Press, 1921, reprinted New York, Dover 1981. | JFM 48.0046.01

Herz-Fischler R., A Mathematical History of Division in Extreme and Mean Ratio, Waterloo (Ontario), Wilfred Laurier University Press, 1987. | MR 907871

Herz-Fischler R. "How to find the golden number without really trying", Fibonacci Quarterly, 19 (1981), 406-10.