Home #1 Mathematics A Study Guide for Topology by Giovanni A. Orlando
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Tuesday, 20 September 2011 23:00

The Möbius strip

 

Greetings in the day of Healing,

   ... And you need to Love to teach, you need to love to heal and strength the mind of others.

   Mathematics is not an exception.

  In fact the study of Topology is not well understood ... in the useful sense ... for daily use and neither his applications to Physics, by the way.

  The Möbius strip was discovered like a non-orientable two dimensional surface (because its 2D) with only one side when embedded in three-dimensional Euclidean space, by August Ferdinand Möbius. This Mathematician is also responsible for the μ function, Möbius function in Number Theory.

   This is just a jewel in Topology.

   We have also the Theorem regarding to cover a Sphere, like may be the head. Why not a Redhead?

  

    The boy's head at left illustrates one of topology's basic theorems: a sphere cannot be covered wjth radiating lines (or red hair) without at least one fixed point.

    This explains why each one of us ... has a point ... from where all the hair begin ...

    Topology is one of the most arcane and fascinating branches of math. It is also called: the study of the transformation of surfaces.

    Most images available here comes from Mathematics by David Bergamini (Life Science Library)

    Another fact, may be the procedure to take off your jacket ... keeping one arm inside in turn!

    Well, after this friendly Introduction ... I will submit some books ... that shall let you increase your knowledge of Topology.

  1. From Geometry to Topology by Graham Flegg
  2. General Topology by John Kelly.

   Because Mathematicians loves to induct as well deduct ... very Masters ... Polish Mathematician Kazimierz Kuratowski offer an alternative path very complete with new (different) definitions.

[   ] K. Kuratowski - Topology, Vol I.pdf 18-Mar-2010 12:16 21M  
[   ] K. Kuratowski - Topology, Vol II.pdf 19-Mar-2010 10:52 22M  

    I, Giovanni prefer you read both versions and see the difference.

    I propose also the Kuratowski book, Introduction to set theory and topology (International series of monographs on pure and applied mathematics)

    (If you permit a comment, I purchase that book for Bs 130.00. Actually Bs 130 are US$ 0.03, but you can find the book on the Web for not less than US$ 50.00. This draw you an idea about the Venezuelan Economy).

    The Modern Concepts of Topology were designed from scratch in the beginning of last Century by a group of French Mathematicians, under the pseudonymous of Nicholas Bourbaki, and that was previously generated by the ideas of German Mathematician George Cantor.

    In fact, I used in University the Bourbaki Volumes ... but they are absolutely offensive ... like a First Course on Topology, also at University Level, without the proper introduction.

    You can read it ... here:

[   ] Nicholas Bourbaki - Theorie des ensembles (Elements de Mathematique).pdf 19-Mar-2010 10:22 17M  
[   ] Nicholas Bourbaki - Topologie Generale Chapitres 1-4 (Elements de Mathematique).pdf 19-Mar-2010 10:14 18M  

   I will go still further ... proposing still a new book, from the Russian School ... but in French,

Rohlin V. Fuchs D.

Premier Cours De Topologie - Chapitres géométriques

 

Thanks,

Giovanni A. Orlando.

 

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Last Updated on Thursday, 22 September 2011 09:44