The Method of Archimedes in the geometry of quadrics
| dc.creator | Dinca, Ion I. | |
| dc.date | 2006-12-13 | |
| dc.date.accessioned | 2026-07-07T07:34:50Z | |
| dc.date.available | 2026-07-07T07:34:50Z | |
| dc.description | Confocal quadrics capture (encode) and geometrize spectral properties of symmetric operators. Certain metric-projective properties of confocal quadrics (most of them established in the first half of the XIX$^{\mathrm{th}}$ century) {\it carry out} (stick and transfer) by rolling to and influence surfaces {\it applicable} (isometric) to quadrics and surfaces geometrically linked to these, thus providing a wealth of integrable systems and projective transformations of their solutions. We shall mainly follow Bianchi's discussion of deformations (through bending) of quadrics. Interestingly enough, {\it The Method} of Archimedes (lost for 7 centuries and rediscovered in the same year as Bianchi's discovery (1906), so unknown to Bianchi) applies {\it word by word in both spirit and the letter} and may provide the key to generalizations in other settings. | |
| dc.identifier | https://arxiv.org/abs/math/0612375 | |
| dc.identifier | http://arxiv.org/abs/math/0612375 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/119910 | |
| dc.subject | Differential Geometry | |
| dc.title | The Method of Archimedes in the geometry of quadrics | |
| dc.type | text |