The Teaching of Mathematics in the Elementary and the Secondary School

1909 ◽  
Vol 1 (4) ◽  
pp. 121-122
Author(s):  
Arthur Sullivan Gale
Keyword(s):  
Secondary School ◽  
Experimental Work ◽  
Euclidean Geometry ◽  
Geometric Analysis ◽  
Algebraic Equations ◽  
Algebraic Expressions ◽  
Formal Geometry ◽  
Non Euclidean Geometry ◽  
Teaching Of Mathematics ◽  
Class Room

The chapter on geometry (pp. 257-291) is excellent. lt presents ideas on geometric analysis, concrete and formal geometry, methods for treating problems, modern geometry, and non-Euclidean geometry. Especially important is the discussion of problems which lead to algebraic equations and the construction of simple algebraic expressions. A timely plea is made for experimental work and the usc of models and apparatus. As an example of their value, a Rochester teacher exhibited a sextant before a class one morning. A pupil borrowed it for the noon hour and became so enthusiastic in its use that he “cut” his afternoon classes to do some rough surveying. Contrast the interest which the inc;trument developed with the lack of enthusiasm which causes so many absences from the mathematical class-room! The chapter closes with an analysis of trigonometry and suggestions as to where its various parts should be taught.

A Study on the Application of Algorithmic Modelling in Architectural Space Design

2012 ◽  
Vol 174-177 ◽  
pp. 1743-1747
Author(s):  
Cheng Zhi Yuan ◽  
Zhong Yi
Keyword(s):  
Euclidean Geometry ◽  
Modelling Language ◽  
Architectural Space ◽  
Space Design ◽  
Algebraic Expressions ◽  
Non Euclidean Geometry ◽  
Art Works

The birth of algorithmic modelling has made architecture breaking through the constraints of traditional Euclidean geometry truly into "era of non-Euclidean geometry space". Algorithmic modelling often uses pure numbers, mathematical rules and algebraic expressions for generating architectural art works with different styles. Usually there are two ways for algorithmic modelling: language programming and graphical. This article has discussed the design significance and operation methods of algorithmic modelling in order to inspire architects a little.

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

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.

Sign in / Sign up

Export Citation Format

Share Document