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pro vyhledávání: '"Chipalkatti, Jaydeep"'
Autor:
Chipalkatti, Jaydeep
Given six points $A,B,C,D,E,F$ on a nonsingular conic in the complex projective plane, Pascal's theorem says that the three intersection points $AE \cap BF, BD \cap CE, AD \cap CF$ are collinear. The line containing them is called a pascal, and we ge
Externí odkaz:
http://arxiv.org/abs/2303.10319
Autor:
Chipalkatti, Jaydeep, Da Silva, Sergio
Publikováno v:
Beitr\"age zur Algebra und Geometrie (2022)
Let $\mathcal{K}$ denote a nonsingular conic in the complex projective plane. Pascal's theorem says that, given six distinct points $A,B,C,D,E,F$ on $\mathcal{K}$, the three intersection points $AE \cap BF, AD \cap CF, BD \cap CE$ are collinear. The
Externí odkaz:
http://arxiv.org/abs/2202.12975
Autor:
Chipalkatti, Jaydeep, Ryba, Alex
The Pascal Multimysticum is a system of points and lines constructed with a straight edge starting from six points on a conic. We show that the system contains 150 infinite ranges (and 150 infinite pencils) whose projective coordinates are absolutely
Externí odkaz:
http://arxiv.org/abs/2007.04315
Autor:
Chipalkatti, Jaydeep, Dénes, Attila
We extract a two-dimensional dynamical system from the theorems of Pappus and Steiner in classical projective geometry. We calculate an explicit formula for this system, and study its elementary geometric properties. Then we use Artin reciprocity to
Externí odkaz:
http://arxiv.org/abs/1708.04002
Autor:
Chipalkatti, Jaydeep, Kulkarni, Mihir
We carry out a comprehensive analysis of letter frequencies in contemporary written Marathi. We determine sets of letters which statistically predominate any large generic Marathi text, and use these sets to estimate the entropy of Marathi.
Externí odkaz:
http://arxiv.org/abs/1707.08209
Publikováno v:
J. Discrete Comput Geom (2018) 60: 381
Given a sextuple of distinct points $A, B, C, D, E, F$ on a conic, arranged into an array $\left[\begin{array}{ccc} A & B & C F & E & D \end{array}\right]$, Pascal's theorem says that the points $AE \cap BF, BD \cap CE, AD \cap CF$ are collinear. The
Externí odkaz:
http://arxiv.org/abs/1608.05056
Autor:
Chipalkatti, Jaydeep
This paper is a study of the so-called `ricochet configuration' (or $R$-configuration) which arises in the context of Pascal's theorem. We give a geometric proof of the fact that a specific pair of Pascal lines is coincident for a sextuple in $R$-con
Externí odkaz:
http://arxiv.org/abs/1604.08262
Autor:
Chipalkatti, Jaydeep
Let ${\mathbf P}^2$ denote the projective plane over a finite field ${\mathbb F}_q$. A pair of nonsingular conics $({\mathcal A}, {\mathcal B})$ in the plane is said to satisfy the Poncelet triangle condition if, considered as conics in ${\mathbf P}^
Externí odkaz:
http://arxiv.org/abs/1604.00436
Autor:
Chipalkatti, Jaydeep
Given six points on a conic, Pascal's theorem gives rise to a well-known configuration called the \emph{hexagrammum mysticum}. It consists of, amongst other things, twenty Steiner points and twenty Cayley-Salmon lines. It is a classical theorem due t
Externí odkaz:
http://arxiv.org/abs/1505.07144
Autor:
Chipalkatti, Jaydeep
Let ${\mathcal K}$ denote a smooth conic in the complex projective plane. Pascal's theorem says that, given six points $A,B,C,D,E,F$ on ${\mathcal K}$, the three intersection points $AE \cap BF, AD \cap CF, BD \cap CE$ are collinear. This defines the
Externí odkaz:
http://arxiv.org/abs/1407.1447