Clifford algebraic calculus for geometric reasoning

1998 ◽  
pp. 115-140 ◽  
Author(s):  
Dongming Wang
Keyword(s):  
Geometric Reasoning

Geometric reasoning with logic and algebra

1988 ◽  
Vol 37 (1-3) ◽  
pp. 37-60 ◽  
Author(s):  
Dennis S. Arnon
Keyword(s):  
Geometric Reasoning ◽  
And Algebra

Developing Students’ Geometric Reasoning about the Derivative of Complex Valued Functions

2017 ◽  
Vol 3 (3) ◽  
pp. 173-205 ◽  
Author(s):  
Jonathan Troup ◽  
Hortensia Soto-Johnson ◽  
Gulden Karakok ◽  
Ricardo Diaz
Keyword(s):  
Geometric Reasoning ◽  
Complex Valued

Geometric Reasoning Based on Graph Grammar Parsing

1994 ◽  
Vol 116 (3) ◽  
pp. 763-769 ◽  
Author(s):  
Z. Fu ◽  
A. de Pennington
Keyword(s):  
Intelligent Design ◽  
Feature Recognition ◽  
Geometric Reasoning ◽  
Geometric Constraints ◽  
Graph Grammar ◽  
Feature Interaction ◽  
Knowledge Based ◽  
Feature Based ◽  
Feature Information ◽  
And Performance

It has been recognized that future intelligent design support environments need to reason about the geometry of products and to evaluate product functionality and performance against given constraints. A first step towards this goal is to provide a more robust information model which directly relates to design functionality or manufacturing characteristics, on which reasoning can be carried out. This has motivated research on feature-based modelling and reasoning. In this paper, an approach is presented to geometric reasoning based on graph grammar parsing. Our approach is presented to geometric reasoning based on graph grammar parsing. Our work combines methodologies from both design by features and feature recognition. A graph grammar is used to represent and manipulate features and geometric constraints. Geometric constraints are used within symbolical definitions of features constraints. Geometric constraints are used within symbolical definitions of features and also to define relative position and orientation of features. The graph grammar parsing is incorporated with knowledge-based inference to derive feature information and propagate constraints. This approach can be used for the transformation of feature information and to deal with feature interaction.

scholarly journals The statistical shape of geometric reasoning

2018 ◽  
Vol 8 (1) ◽  
Author(s):  
Yuval Hart ◽  
Moira R. Dillon ◽  
Andrew Marantan ◽  
Anna L. Cardenas ◽  
Elizabeth Spelke ◽  
...  
Keyword(s):  
Geometric Reasoning ◽  
Statistical Shape

Geometric Reasoning

2014 ◽  
pp. 259-286
Author(s):  
Edwin F. Meyer ◽  
Nickolas Falkner ◽  
Raja Sooriamurthi ◽  
Zbigniew Michalewicz
Keyword(s):  
Geometric Reasoning

scholarly journals ТЕОРИЈE РАЗВОЈA ГЕОМЕТРИЈСКОГ МИШЉЕЊА ПРЕМА ВАН ХИЛУ, ФИШБАЈНУ И УДЕМОН-КУЗНИАКУ

TEME ◽  
2017 ◽  
pp. 623 ◽  
Author(s):  
Оливера Ђокић ◽  
Маријана Зељић
Keyword(s):  
Theoretical Analysis ◽  
Mathematics Curriculum ◽  
Theoretical Framework ◽  
Geometric Object ◽  
Geometric Reasoning ◽  
Theoretical Frameworks ◽  
Teaching Geometry ◽  
Content Domain ◽  
Geometric Objects ◽  
Development Of Students

This research is a pedagogical study of theoretical frameworks of development of students’ geometrical thinking in various forms, particularly students’ geometric reasoning in teaching geometry: 1) model of van Hieles’ levels of understanding of geometry, 2) theory of figural concepts of Fischbein and 3) paradigms of Houdement-Kuzniak development of geometrical thinking. The aim of our research was to analyze the three theoretical framework and explain the reasons for their choice and expose them in terms of finding opportunities to permeate and connect them into one complete theory. The study used a descriptive-analytical and analytical-critical method of theoretical analysis. The results show that from each of the three theoretical frameworks we can clearly notice and distinguish geometric objects, as the students do not see them. They see them blended and structured in a series of procedures, and for that very reason we can say that they are poorly linked. We also opened questions for further research of geometric object as an important element for content domain geometry within mathematics curriculum.

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