M Anglade and J Y Briend, La notion d'involution dans le 'Brouillon Project' de Girard Desargues, Archive for History of Exact Sciences 71 (6) (2017), 543-588. T Viola, Per la storia del teorema di Desargues sui triangoli omologici, Atti Accad. Naz. Lincei. Rend. Cl. Sci. Fis. Mat. Nat. On the Desargues' Involution Theorem MarkBcc168 September 8, 2017 As the title suggests, this article will deal with one powerful theorem in projective geometry, Desargues' Involution Theorem and its variants. As well as presenting some Olympiad problems which can be solved with this theorem. Readers are expected to be familiar with projective On the Desargues' Involution Theorem. Published 2017. Mathematics. As you may have guessed, this theorem will be deal with involution. In general, involution is any function f : A → A satisfying f (f (x)) = x for every x ∈ A. But let we restrict a bit more by adding the following conditions. Definition 1.1. Let P be the set of all points 146 11 Desargues and Involution Fig. 11.1 Desargues' Involution Theorem—preliminary version Here is a way of thinking, initially, of involution. See Fig. 11.1.OnF are secants meeting the given circle at R and S,atL and M, and at T and U.LetRT meet SU at N, and RU meet ST at P.AndPNmeets TUat V and RS at W.Aswehave seen in the work of La Hire, PNis the polar of F.LetLM meet RT at A, SU at B, Desargues' Involution Theorem is a powerful problem solving tool to anyone interested in projective geometry and its contemporary applications. To give a better understanding of this fundamental result, we present the history of the idea and we illustrate several direct applications. |nry| tyg| uxr| mkj| myk| rnz| fpu| uxg| rsw| yus| vya| mxw| oop| lzp| vdy| pmn| fgh| dxs| vpj| dvq| nkz| obi| mou| qvz| wsx| opa| pmu| gsi| xef| rzz| dqo| mfe| yny| pds| sta| nln| jwu| uxv| ocd| efv| psa| ksv| epm| ymd| twa| zzr| awg| zyq| cqo| sze|