Theorems about quadrilaterals and conics
نویسندگان
چکیده
Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content.
منابع مشابه
Dedicated to Armin Herzer on His 60th Birthday
In a desarguesian projective plane we discuss those degenerate conics whose parameters have degree two over the centre of the underlying skew field. Such degenerate conics are closely related with Baer subplanes. This relationship enables us to improve and reformulate in a geometric language some theorems which previously have been established in a purely algebraic way. A geometric description ...
متن کاملMaharavo Randrianarivony Quadrilateral Removals and Generalized 2-ear Theorems
We aim at splitting a given multiply connected polygon into a set of convex quadrilaterals. Our approach consists in repeatedly removing quadrilaterals from the given polygon. We will first derive theoretical results pertaining to quadrangulation of simple polygons from the usual 2-ear theorem. Unfortunately, that theorem holds only for simply connected polygons while we are interested in quadr...
متن کاملPascal-Brianchon Sets in Pappian Projective Planes Pascal-Brianchon Sets in Pappian Projective Planes
It is well-known that Pascal and Brianchon theorems characterize conics in a Pappian projective plane. But, using these theorems and their modifications we shall show that the notion of a conic (or better a Pascal-Brianchon set) can be defined without any use of theory of projectivities or of polarities as usually.
متن کاملMarden theorem and Poncelet-Darboux curves
The Marden theorem of geometry of polynomials and the great Poncelet theorem from projective geometry of conics by their classical beauty occupy very special places. Our main aim is to present a strong and unexpected relationship between the two theorems. We establish a dynamical equivalence between the full Marden theorem and the Poncelet-Darboux theorem. By introducing a class of isofocal def...
متن کاملPoncelet Theorems
The aim of this note is to collect some more or less classical theorems of Poncelet type and to provide them with short modern proofs. Where classical geometers used elliptic functions (or angular functions), we use elliptic curves (or degenerate elliptic curves decomposing into two rational curves). In this way we unify the geometry underlying these Poncelet type statements. Our starting point...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Int. J. Comput. Math.
دوره 91 شماره
صفحات -
تاریخ انتشار 2014