Historically Speaking—: The Early Beginnings of Set Theory

1970 ◽  
Vol 63 (8) ◽  
pp. 690-692
Author(s):  
Phillip E. Johnson
Keyword(s):  
Present Article ◽  
Set Theory ◽  
Euclidean Geometry ◽  
Non Euclidean Geometry ◽  
The Creation

Georg Canttor created and largely developed the theory of sets in approximately the year. 1874-1897. In contrast to such developments as the calculus and non-Euclidean geometry, The creation of set theory was, according to all indications, Cantor's alone. AIso, set theory was not preceded by a long evoIutionary period such as is usually the case with big mathematical breakthroughs. The present article will concern itself primarily with the very earliest set-theoretic works of Cantor, namely, his first two papers in this area.1

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 RETROSPECTIVE AND CONTRADICTIONS OF CREATING ARCHITECTURAL PROJECTS IN THE CONTEXT OF DIGITALIZATION

2021 ◽  
Vol 82 (4) ◽  
pp. 63-73
Author(s):  
A.S. Nabiyev ◽  
◽  
S.B. Pomorov ◽  
Keyword(s):  
Euclidean Geometry ◽  
Digital Architecture ◽  
Research Article ◽  
Traditional Design ◽  
Non Euclidean Geometry ◽  
The Creation ◽  
Form Approach

The research article examines the retrospective of the creation of architectural projects, systematizes the experience of architects, reveals contradictions in the development of digital architecture and its relationship with traditional design. At the same time, the problems of the development of digital architecture in the context of the formation of digital civilization are noted. The tendencies of designing objects based on non-Euclidean geometry are revealed, the features of postmodernism and parametrism are systematized, the threats and consequences of the "from figure to form" approach are substantiated.

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

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 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.

scholarly journals MODELLING OF PREVOCATIONAL EDUCATION OF STUDENTS WITH SPECIAL EDUCATIONAL NEEDS: SITUATION AND OPPORTUNITIES

2015 ◽  
Vol 2 ◽  
pp. 150 ◽  
Author(s):  
Ingrida Baranauskienė ◽  
Aistė Valaikienė
Keyword(s):  
Present Article ◽  
School Community ◽  
Educational Needs ◽  
Actual Situation ◽  
Special Educational Needs ◽  
The Creation ◽  
Education Of Students ◽  
Prevocational Education

The aim of the present article – to reveal the directions of prevocational education of students with SEN, actual situation and opportunities. In 2012 in Lithuania the research of the Delphi group was performed where 13 experts having direct pedagogical experience in working with students having SEN participated. In the article the influence of traditions in the country on the success of prevocational education, the importance of the creation of the interaction child-family-school-community have been analyzed, the main aims of prevocational education, actual situation and directions to be improved have been revealed.

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