Lessons in geometry

  title={Lessons in geometry},
  author={Jacques Hadamard},
Every entangled stuff has its own avatar
It is demonstrated that some byproducts resulting from entanglement act as a hinge that link both theories making the completeness of QM clear and a thorough analysis of the non-locality of this effect will be carried out. Expand
An Extension of Pythagoras Theorem
This article proves a Pythagoras-type formula for the sides and diagonals of a polygon inscribed in a semicircle having one of the sides of the polygon as diameter.
GeoText: an intelligent dynamic geometry textbook
Based on the use of formalized geometric knowledge data and the integration of powerful methods and software tools of algebraic computation, automated deduction, and graphical presentation for computer geometry, GeoText has achieved a high degree of automation in functionality and intelligence in behavior. Expand
The theory of a convex quadrilateral and a circle that forms "Pascal points" - the properties of "Pascal points" on the sides of a convex quadrilateral
Euclidean geometry is one of the oldest branches of mathematics – the properties of different shapes have been investigated for thousands of years. For this reason, many tend to believe that today itExpand
Necessary and sufficient conditions for orthogonal circles
104.31 Polygons and complex trigonometric identities without complex numbers
Reference 1. B. C. Berndt, An unpublished manuscript of Ramanujan on infinite series identities, J. Ramanujan Math. Soc. 19 (2004) pp. 57-74. 2. S. Kanemitsu, Y. Tanigawa, and M. Yoshimoto, OnExpand
Cyclic quadrilaterals have many famous properties, that is, necessary conditions. However, what is not so well-known is that most of their properties are also sufficient conditions for suchExpand
Chaos as a symmetry-breaking phenomenon
Chaos is an ubiquitous and fundamental phenomenon with a wide range of features pointing to a similar phenomenology. Although apparently distinct, it is natural to ask if all these features emergeExpand
Necessary and sufficient properties for a cyclic quadrilateral
ABSTRACT There are many problems whose solution requires proof that a quadrilateral is cyclic. The main reason for writing this paper is to offer a number of new tools for proving that a particularExpand
New points that belong to the nine-point circle
In the present paper, we show that the point of intersection of the bimedians of a cyclic quadrilateral belongs to the nine-point circle (Euler’s circle) of the triangle with one vertex at the pointExpand