Anoter Day with Abel ... Day 5: Abel's Theorem on the Lemniscate by Dr. Giovanni A. Orlando PDF Print E-mail
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Monday, 09 April 2018 04:50


Greetings in the Moon-day of Christ ... The Crystal Ray of the Master of Masters ... Happy, Loyal, Royal, Friendly and King ...

       And today Oslo ... gain the name Christiania to honor King Christian IV of Denmark. In the days of Abel ... it was called Christiania ... from 1877 until 1925.

       Now, Abel explains in his Letters ... that today become Biographies ... how he enter in the Leminscate ideas ...

       The idea was to divide the Leminscate like we today divide the Circle ... and because xm-1=0 ... give us the roots of unity and the relative expression in sin and cosine ... He, Abel following a comment of Gauss in Section VII of is Famous Disquisitiones Arithmeticae.

         This is the title of Section (like a Chapter) in Gauss's book.

         Equations defining Sections of a Circle

          Abel because Gauss comment ... and we can read in the Disquisitiones Arithmeticae. (by Springer 1966)

I reter to the theory of trigonometric functions corresponding to arcs that are commensurable with the circumference, i.e., the theory of regular polygons. Only a small part of this theory has been developed so far, as the present section will make clear. The reader might be surprised to find a discussion of this subject in the present work which deals with a discipline apparently so unrelated; but the treatment itself will make abundantly clear that there is an intimate connection between this subject and higher Arithmetic.

The principles of the theory which we are going to explain actually extend much farther than we will indicate. For they can be applied not only to circular functions but just as well to other transcendental functions, e.g. to those which depend on the integral √(1 - x4) dx and also to various types of congruences. Since, however, we are preparing a large work on those transcendental functions and since we will treat congruences at length in the continuation of these Disquisittones, we have decided to consider only circular functions here.

     This is the Book from where we take the quote:

     Gauss wrote that book at the age of 21 ... Unfortunately today Young people at the age of 21 ... have other things in Mind ... Great Mathematicians has not become a Model ... in most cases are insulted by fools ... Absurd ... like a type of Mathematical Theorems.


      Now ... I, Giovanni prefer (and you live the Illusion United States have Mathematics ... Nay, United States have Money ... not Mathematics ... Tesla did the Physics ... Einstein got the Applauses and the rest is just Advertising ... However, United States invent the Computer ... You know ... Italians invent the Food ... Mon Die ... What invent the French? ... Casual Sex? ... C'est la vie ...

        I, Giovanni ... after a necessary Irony to take off the Pressure on a Monday morning ... 

       ... Will give you under the Illusion ... a Wonderful article published by AMS (American Mathematical Society) ... that resume and expose well the complete Panorama.

       Yes ... I disagree the Mental Plans applied to Europe and Europeans ... tailored by some ... that have no idea what they are doing, what they do ... and still what they will do ... but got everything ...

       Leminscate, Leminscate, Leminscate ... ∞

Dr. Giovanni A. Orlando.

       You can also download all pages here:  Michael_Rosen_Abel_Theorem_on_the_Lemniscate (PDF)



  PS. How these Words can help us to understand Einstein Theory and his Mistakes or benevolent proposals? ... Well ... We are in 3D ... Linear Space and Time ... now Study 2D and his Geometry is fundamental to understand ... Minimal Mind ... like Tri-angles ... Tri-gonometry. However, the Game began with Solid Polyhedron ... or Pacioli ... which are no other than Plato Solids.

... Modern Mathematics is yet a Baby that do not find yet the Biberon of Edenic Math ...

Last Updated on Monday, 09 April 2018 07:11