Visualization of Algebraic Properties of special HV -structures

Achilles Dramalidis

Abstract


The paper looks at visualization as it relates to special HV -structures, focusing upon how it can be used to improve the perception and understanding of abstract algebraic concepts. Using position vectors into the plane IR2, abstract algebraic properties of HV -structures are gradually transformed into geometrical shapes.


Keywords


Hyperstructures, HV -structures, Visualization

Full Text:

PDF

References


A.J. Bishop, A review of research on visualization in mathematics education, In: A. Borb´as (Ed.), Proceedings of the 12th PME International Conference, (1988), 170-176.

J.S Bruner,The course of cognitive growth, American psychologist, 19, (1964), 1-15.

P.Corsini, V.Leoreanu, Applications of Hypergroup Theory,Kluwer Academic Publishers, 2003

B.Davvaz, V.Leoreanu, Hyperring Theory and Applications,, International Academic Press, 2007

A. Dramalidis, Dual Hv-rings, Rivista di Matematica Pura ed Applicata, 17,(1996), 55-62.

A. Gutirrez, Visualization in 3-dimensional geometry: In search of a framework, In: Proceedings of the 20th PME International Conference, L. Puig & A. Gutierrez (Eds.), 3-19,(1996), 3-19.

R.Palais, The visualization of Mathematics: Towards a Mathematical Exploratorium, Notices of the AMS, 6,(1999), 647-658.

Prenowitz W., Jantosciak J., Join Geometries. A Theory of Convex Sets and Linear Geometry, Springer, N.Y,1979

N.C Presmeg, Visualization and mathematical giftedness, Educational Studies in Mathematics, 17, (1986), 297-311.

N.C Presmeg, Research on visualization in learning an teaching mathematics,In: Handbook of Research on the Psychology of Mathematics Education: Past, Present and Future. PME 1976-2006, Ed Sense Publishers, (2006),205-235.

T. Vougiouklis, The fundamental relation in hyperrings. The general hyperfield, In: 4th AHA Congress,World Scientific,(1991), 203-211.

T.Vougiouklis, Hyperstructures and their Representations, Monographs in Mathematics, Hadronic Press,1994


Refbacks

  • There are currently no refbacks.


Copyright (c) 2013 Achilles Dramalidis

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Ratio Mathematica - Journal of Mathematics, Statistics, and Applications. ISSN 1592-7415; e-ISSN 2282-8214.