Related papers: A Generalization of Desargues' Involution Theorem
This paper provides a uniform explanation of different extensions and generalizations of the butterfly theorem based on the Desargues involution theorem.
In this article we present a generalization of a Leibniz's geometrical theorem and an application of it.
Using techniques of projective geometry, we give elementary proofs of two theorems concerning Hagge configurations.
The large variety of Fourier transforms in geometric algebras inspired the straight forward definition of ``A General Geometric Fourier Transform`` in Bujack et al., Proc. of ICCA9, covering most versions in the literature. We showed which…
The Theorems of Pappus and Desargues are generalized by two special formulas that hold in the three-dimensional vector space over a field.
This text is a survey of derived algebraic geometry. It covers a variety of general notions and results from the subject with a view on the recent developments at the interface with deformation quantization.
We propose a general definition of unprojection, and prove that it indeed generalizes previous efforts.
A generalization of the law of total covariance is presented and proved.
In this paper, by using analytical methods we obtain a generalization of the famous Kodaira embedding theorem.
We solve a long-standing problem by enumerating the number of non-degenerate Desargues configurations. We extend the result to the more difficult case involving Desargues blockline structures in Section 8. A transparent proof of Desargues…
This work is, in part, a generalization of the article by A.A. Bruen ,T.C Bruen and J.M.McQuillan on Desargues Theorem in arXiv:2007.09175[mathCO]July 17,2020. We prove the extension of Desargues theorem in all dimensions, using 4 different…
Pappus' Involution Theorem is a powerful tool for proving theorems about non-euclidean triangles and generalized triangles in Cayley-Klein models. Its power is illustrated by proving with it some theorems about euclidean and non-euclidean…
In this article we will represent some ideas and a lot of new theorems in Euclidean plane geometry.
We develop a general deformation theory of objects in homotopy and derived categories of DG categories. The main result is a general pro-representability theorem for the corresponding deformation functor.
In this paper we prove two general results related to Marstrand's projection theorem in a quite general formulation over separable metric spaces under a suitable transversality hypothesis (the "projections" are in principle only measurable)…
This paper proves a generalization of the Butterfly Theorem, a classical Euclidean result, which is valid in the complex projective plane.
In this paper, we prove some foundational results on the deformation theory of E-infinity ring spectra.
In this paper we give a generalization of injective and projective complexes.
In the present paper we generalise transference theorems from the classical geometry of numbers to the geometry of numbers over the ring of adeles of a number field. To this end we introduce a notion of polarity for adelic convex bodies.
In this paper we present a set transformation of points in a line of the Desargues affine plane in a additive group. For this, the first stop on the meaning of the Desargues affine plane, formulating first axiom of his that show proposition…