scholarly journals Data with Non-Euclidean Geometry and its Characterization

2021 ◽  
Author(s):  
Prem Kumar Singh
Keyword(s):  
Euclidean Geometry ◽  
Real Life ◽  
Data Sets ◽  
The Third ◽  
Non Euclidean Geometry ◽  
True False

Recently, dealing the Non-Euclidean data and its characterization is considered as one of the major issues by researchers. The first problem arises while distinction of among Euclidean and non-Euclidean geometry. The second problem arises with dealing the Non-Euclidean geometry in true, false and uncertain regions. The third problem arises while investigating some pattern in Non-Euclidean data sets. This paper focused on tackling these issues with some real life examples.

Anti-Geometry and NeutroGeometry Characterization of Non-Euclidean Data

2021 ◽  
pp. 24-33
Author(s):  
Prem Kumar Singh ◽  
Keyword(s):  
Euclidean Geometry ◽  
Current Paper ◽  
Data Sets ◽  
Knowledge Processing ◽  
Non Euclidean Geometry ◽  
Precise Representation

Recently, a problem is addressed while dealing with fourth dimensional or non-Euclidean data sets. These are the data sets does not follow one of the postulates established by Euclid specially the parallel postulates. In this case, the precise representation of these data sets is major issues for knowledge processing tasks. Hence, the current paper tried to introduce some non-Euclidean geometry or Anti-Geometry methods and its examples for various applications.

scholarly journals Taylor's Cubics associated with a Triangle in Non-Euclidean Geometry

1914 ◽  
Vol 33 ◽  
pp. 85-99
Author(s):  
D. M. Y. Sommerville
Keyword(s):  
Euclidean Geometry ◽  
Famous Theorem ◽  
The Third ◽  
Non Euclidean Geometry ◽  
Straight Line ◽  
Second Degree

§ 1. The famous theorem of the pedal line of a triangle in ordinary geometry can be stated as follows:—“Given a triangle ABC and a point P such that the feet of the perpendiculars X, Y, Z, dropped from P on the sides of the triangle, are collinear, then the locus of P is the circumcircle.” In noneuclidean geometry this locus is not a circle or even a curve of the second degree, but a cubic; and in both cases the envelope of the line XYZ is a curve of the third class. The explanation of the inconsistency in ordinary geometry is that the complete locus consists of the circumcircle together with the straight line at infinity.

scholarly journals “I have Learned Non-Euclidean Geometry Just from this Book” - Some facets of the correspondence between Friedrich Engel and David Hilbert

2021 ◽  
Vol 76 (3) ◽  
Author(s):  
Peter Ullrich
Keyword(s):  
Present Article ◽  
19Th Century ◽  
Euclidean Geometry ◽  
Academic Life ◽  
David Hilbert ◽  
Non Euclidean Geometry ◽  
The 19Th Century

AbstractFriedrich Engel and David Hilbert learned to know each other at Leipzig in 1885 and exchanged letters in particular during the next 15 years which contain interesting information on the academic life of mathematicians at the end of the 19th century. In the present article we will mainly discuss a statement by Hilbert himself on Moritz Pasch’s influence on his views of geometry, and on personnel politics concerning Hermann Minkowski and Eduard Study but also Engel himself.

scholarly journals Langevin simulations of protoplasmic streaming in non-Euclidean geometry

2021 ◽  
Vol 1730 (1) ◽  
pp. 012037
Author(s):  
Shuta Noro ◽  
Masahiko Okumura ◽  
Satoshi Hongo ◽  
Shinichiro Nagahiro ◽  
Toshiyuki Ikai ◽  
...  
Keyword(s):  
Euclidean Geometry ◽  
Protoplasmic Streaming ◽  
Non Euclidean Geometry

Practical Non-Euclidean Geometry

1925 ◽  
Vol 12 (177) ◽  
pp. 422 ◽  
Author(s):  
T. C. J. Elliott
Keyword(s):  
Euclidean Geometry ◽  
Non Euclidean Geometry

scholarly journals An Interoperability Platform Enabling Reuse of Electronic Health Records for Signal Verification Studies

2016 ◽  
Vol 2016 ◽  
pp. 1-18 ◽  
Author(s):  
Mustafa Yuksel ◽  
Suat Gonul ◽  
Gokce Banu Laleci Erturkmen ◽  
Ali Anil Sinaci ◽  
Paolo Invernizzi ◽  
...  
Keyword(s):  
Real Life ◽  
Case Series ◽  
Background Information ◽  
Data Sets ◽  
Local Data ◽  
Lombardy Region ◽  
Common Information ◽  
Spontaneous Reports ◽  
Wide Range ◽  
Common Information Model

Depending mostly on voluntarily sent spontaneous reports, pharmacovigilance studies are hampered by low quantity and quality of patient data. Our objective is to improve postmarket safety studies by enabling safety analysts to seamlessly access a wide range of EHR sources for collecting deidentified medical data sets of selected patient populations and tracing the reported incidents back to original EHRs. We have developed an ontological framework where EHR sources and target clinical research systems can continue using their own local data models, interfaces, and terminology systems, while structural interoperability and Semantic Interoperability are handled through rule-based reasoning on formal representations of different models and terminology systems maintained in the SALUS Semantic Resource Set. SALUS Common Information Model at the core of this set acts as the common mediator. We demonstrate the capabilities of our framework through one of the SALUS safety analysis tools, namely, the Case Series Characterization Tool, which have been deployed on top of regional EHR Data Warehouse of the Lombardy Region containing about 1 billion records from 16 million patients and validated by several pharmacovigilance researchers with real-life cases. The results confirm significant improvements in signal detection and evaluation compared to traditional methods with the missing background information.

scholarly journals The Non-Euclidean Geometry Inevitable

The Monist ◽  
1894 ◽  
Vol 4 (4) ◽  
pp. 483-493
Author(s):  
George Bruce Halsted ◽  
Keyword(s):  
Euclidean Geometry ◽  
Non Euclidean Geometry

scholarly journals After Non-Euclidean Geometry: Intuition, Truth and the Autonomy of Mathematics

2018 ◽  
Vol 6 (3) ◽  
Author(s):  
Janet Folina
Keyword(s):  
19Th Century ◽  
Euclidean Geometry ◽  
Symbolic Logic ◽  
Non Euclidean Geometry ◽  
The 19Th Century ◽  
Spatial Intuition ◽  
Mathematical Inference

The mathematical developments of the 19th century seemed to undermine Kant’s philosophy. Non-Euclidean geometries challenged Kant’s view that there is a spatial intuition rich enough to yield the truth of Euclidean geometry. Similarly, advancements in algebra challenged the view that temporal intuition provides a foundation for both it and arithmetic. Mathematics seemed increasingly detached from experience as well as its form; moreover, with advances in symbolic logic, mathematical inference also seemed independent of intuition. This paper considers various philosophical responses to these changes, focusing on the idea of modifying Kant’s conception of intuition in order to accommodate the increasing abstractness of mathematics. It is argued that far from clinging to an outdated paradigm, programs based on new conceptions of intuition should be seen as motivated by important philosophical desiderata, such as the truth, apriority, distinctiveness and autonomy of mathematics.

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