Identities Generalizing the Theorems of Pappus and Desargues

نویسندگان

چکیده

The Theorems of Pappus and Desargues (for the projective plane over a field) are generalized here by two identities involving determinants cross products. These proved to hold in three-dimensional vector space field. They closely related Arguesian identity lattice theory Cayley-Grassmann invariant theory.

منابع مشابه

Pappus-Desargues digraph confrontation

Like the Coxeter graph became reattached into the Klein graph in [3], the Levi graphs of the 93 and 103 self-dual configurations, known as the Pappus and Desargues (k-transitive) graphs P and D (where k = 3), also admit reattachments of the distance-(k − 1) graphs of half of their oriented shortest cycles via orientation assignments on their common (k−1)-arcs, concurrent for P and opposite for ...

متن کامل

On Pappus, Desargues and other C-UH graphs

The notion of a C-ultrahomogeneous (or C-UH) graph, due to D. Isaksen et al., is adapted for digraphs and applied to the cubic distancetransitive graphs, considered as digraphs by replacing each edge by a pair of oppositely oriented arcs, with C formed by shortest oriented cycles and (k−1)-arcs with k = arc-transitivity. Moreover, (k−1)-powers of shortest cycles taken with orientation assignmen...

متن کامل

GENERALIZED THEOREMS OF DESARGUES FOR w-DIMENSIONAL PROJECTIVE SPACE

The purpose of the present note is to generalize to n dimensions the celebrated two-triangle theorem of Desargues and its converse.1 The generalized theorems can be stated in simple forms which, nevertheless, suffice for each of the large number of special cases of the configurations involved. The terms concurrent and collinear will be used in the sense that n lines are concurrent if there is a...

متن کامل

the analysis of the role of the speech acts theory in translating and dubbing hollywood films

از محوری ترین اثراتی که یک فیلم سینمایی ایجاد می کند دیالوگ هایی است که هنرپیش گان فیلم میگویند. به زعم یک فیلم ساز, یک شیوه متأثر نمودن مخاطب از اثر منظوره نیروی گفتارهای گوینده, مثل نیروی عاطفی, ترس آور, غم انگیز, هیجان انگیز و غیره, است. این مطالعه به بررسی این مسأله مبادرت کرده است که آیا نیروی فراگفتاری هنرپیش گان به مثابه ی اعمال گفتاری در پنج فیلم هالیوودی در نسخه های دوبله شده باز تولید...

15 صفحه اول

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Symmetry

سال: 2021

ISSN: ['0865-4824', '2226-1877']

DOI: https://doi.org/10.3390/sym13081382