Abstract
[automatically translated] Reverse transformations quadratic Aldo Brigaglia (University of Palermo) brig@math.unipa.it The reverse (or processing for reciprocal vectors rays) is considered the first birational transformation (non-linear) entry in a stable, among those treated by mathematicians. The same naturalness made nebula the origin of this concept. In fact it is the transformation that, set a point A and a segment r, associates with each point B and point B 'on the half line AB such that AB' is the third proportional between AB and r. Construction of points of this kind are very often: p. eg. in the stereographic projection, in which r is the diameter of the sphere, A is the pole from which is projected, B and B 'are respectively a point on the sphere and its projected in the plane; such constructions are also present in the classic problems of Apollonians Contacts and used explicitly by Viète in his Apollonius Gallus. Of course completely different phases will be those in which switching from a static view of the construction of B 'to the consideration of the transformation taken as a whole, the identification of its fundamental properties (being a "circular transformation" and conforming), and finally being a antilinear transformation in the complex projective line and its connections with the Hermitian forms. My purpose in this communication is to see how a very simple concept and elementary as that of the circular inversion can through successive generalizations and insights, connect to far more profound concepts, give rise to entirely new ideas (such as those of general geometric transformation, of birational or Hermitian forms processing). I will examine in particular the contribution of Bellavitis in this direction, as part of a research project of the Palermo Group aims to deepen the historical origins of the birational transformation concept. Bibliography: G. Bellavitis, derived geometry Wise, New Essays of the Royal Imperial Academy of Arts Sciences and Arts in Padua, IV, 1838, pp. 243-288; B. Patterson, The Origin of the geometric principle of inversion, Isis, 19, 1933, pp. 154-180; F. Viète, Apollonius Gallus, Paris, 1600. The use of computers as a str I will examine in particular the contribution of Bellavitis in this direction, as part of a research project of the Palermo Group aims to deepen the historical origins of the birational transformation concept. Bibliography: G. Bellavitis, derived geometry Wise, New Essays of the Royal Imperial Academy of Arts Sciences and Arts in Padua, IV, 1838, pp. 243-288; B. Patterson, The Origin of the geometric principle of inversion, Isis, 19, 1933, pp. 154-180; F. Viète, Apollonius Gallus, Paris, 1600. The use of computers as a str I will examine in particular the contribution of Bellavitis in this direction, as part of a research project of the Palermo Group aims to deepen the historical origins of the birational transformation concept. Bibliography: G. Bellavitis, derived geometry Wise, New Essays of the Royal Imperial Academy of Arts Sciences and Arts in Padua, IV, 1838, pp. 243-288; B. Patterson, The Origin of the geometric principle of inversion, Isis, 19, 1933, pp. 154-180; F. Viète, Apollonius Gallus, Paris, 1600. The use of computers as a str New Essays of the Royal Imperial Academy of Sciences, Letters and Arts in Padua, IV, 1838, pp. 243-288; B. Patterson, The Origin of the geometric principle of inversion, Isis, 19, 1933, pp. 154-180; F. Viète, Apollonius Gallus, Paris, 1600. The use of computers as a str New Essays of the Royal Imperial Academy of Sciences, Letters
| Original language | Italian |
|---|---|
| Pages | 9-9 |
| Number of pages | 1 |
| Publication status | Published - 2012 |