Related papers: A Generalization of Desargues' Involution Theorem

A projective rectangle is like a projective plane that has different lengths in two directions. We develop the basic theory of projective rectangles including incidence properties, projective subplanes, configuration counts, a partial…

We derive a generalized Stokes' theorem, valid in any dimension and for arbitrary loops, even if self intersecting or knotted. The generalized theorem does not involve an auxiliary surface, but inherits a higher rank gauge symmetry from the…

This paper provides a new simple proof of Hesse's theorem in projective geometry for any dimension.

An approach is shown that proves various theorems of plane geometry in an algorithmic manner. The approach affords transparent proofs of a generalization of the Theorem of Morley and other well known results by casting them in terms of…

An algebraic deformation theory of dialgebra morphisms is obtained.

This is a survey of select recent results by a number of authors, inspired by the classical configuration theorems of projective geometry.

Some translations into non-euclidean geometry of classical theorems of planar projective geometry are explored. The existence of some common triangle centers is dedeuced from theorems of Pascal and Chasles. Desargues' Theorem allows to…

A new and easy way of deriving Gauss's Generalized Hypergeometric Theorem is presented by using the Bilateral Binomial Theorem.

Segre's theorem on ovals in projective spaces is an ingenious result from the mid-twentieth century which requires surprisingly little background to prove. This note, suitable for undergraduates with experience of linear and abstract…

In \cite{Sz25} we generalized the famous Menelaus' and Ceva's theorems for translation triangles in each non-constant curvature Thurston geometry. In this paper based on the described method and results, we prove that the classical…

The generalized projection-tensor geometry introduced in an earlier paper is extended. A compact notation for families of projected objects is introduced and used to summarize the results of the previous paper and obtain fully projected…

The object of this paper is to generalize a theorem on the binomial coefficient [4] to the case in an arithmetic progression. We will also give a slightly stronger result than Langevin's [2].

As an extension of projective homology, stereohomology is proposed via an extension of Desargues theorem and the extended Desargues configuration. Geometric transformations such as reflection, translation, central symmetry, central…

The theorem of Mather on generic projections of smooth algebraic varieties is also proved for the singular ones.

We prove a generalization of Lopes's theorem, that is, of the converse of Brolin's theorem.

We study involutions on K3 surfaces under conjugation by derived equivalence and more general relations, together with applications to equivariant birational geometry.

This paper reproves a general form of the Green-Lazarsfeld 'generic vanishing' theorem and more recent strengthenings, as well as giving some new applications.

In this note, we use the disformal transformation to induce a geometry from the manifold which is originally Riemannian. The new geometry obtained here can be considered as a generalization of Weyl integrable geometry. Based on these…

This paper considers dilations and translations of lines in the Desargues affine plane. A dilation of a line transforms each line into a parallel line whose length is a multiple of the length of the original line. In addition to the usual…

We prove a generalized Gauss-Kuzmin-L\'evy theorem for the $p$-numerated generalized Gauss transformation $$T_p(x)=\{\frac{p}{x}\}.$$ In addition, we give an estimate for the constant that appears in the theorem.