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Line 22f1fa19c3a Affine Sphere Diophantine Geometry Faltings Theory 5g WOW SETI

August 3, 2012

Line 22f1fa19c3a Affine Sphere Diophantine Geometry Faltings Theory 5g WOW SETI

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part 284c3a of 100 videos there are more videos after this one i’ll post all then update the #.

Math Equation Wow Seti 1977 radio signal alien

Wow SETI 1977 radio signal alien


Google 0.0071

Google 11 111 1 1 14

research notes quotes links

Affine sphere

Quotes WIKI
In mathematics, and especially differential geometry, an affine sphere is a hypersurface for which the affine normals all intersect in a single point.[1] The term affine sphere is used because they play an analogous role in affine differential geometry to that of ordinary spheres in Euclidean differential geometry.

An affine sphere is called improper if all of the affine normals are constant.[1] In that case, the intersection point mentioned above lies on the hyperplane at infinity.

Affine spheres have been the subject of much investigation, with many hundreds of research articles devoted to their study.[2]


Diophantine geometry

Quotes WIKI
In mathematics, diophantine geometry is one approach to the theory of Diophantine equations, formulating questions about such equations in terms of algebraic geometry over a ground field K that is not algebraically closed, such as the field of rational numbers or a finite field, or more general commutative ring such as the integers. A single equation defines a hypersurface, and simultaneous

Diophantine equations give rise to a general algebraic variety V over K; the typical question is about the nature of the set V(K) of points on V with co-ordinates in K, and by means of height functions quantitative questions about the “size” of these solutions may be posed, as well as the qualitative issues of whether any points exist, and if so whether there are an infinite number.

Given the geometric approach, the consideration of homogeneous equations and homogeneous co-ordinates is fundamental, for the same reasons that projective geometryis the dominant approach in algebraic geometry.

Rational number solutions therefore are the primary consideration; but integral solutions (i.e. lattice points) can be treated in the same way as an affine variety may be considered inside a projective variety that has extra points at infinity.

The general approach of diophantine geometry is illustrated by Faltings’ theorem (a conjecture of L. J. Mordell) starting that an algebraic curve C of genus g > 1 over the rational numbers has only finitely many rational points. The first result of this kind may have been the theorem of Hilbert and Hurwitz dealing with the case g = 0. The theory consists both of theorems and many conjectures and open questions.

 Faltings’ theorem

Faltings’ theorem
From Wikipedia, the free encyclopedia
In number theory, the Mordell conjecture is the conjecture made by Mordell (1922) that a curve of genus greater than 1 over the field Q of rational numbers has only finitely many rational points.

The conjecture was later generalized by replacing Q by a finite extension. It was proved by Gerd Faltings (1983), and is now known as Faltings’ theorem.

19 July 2012 502 pm edt

My Thoughts..

There’s the Q from the WOW SIGNAL


Q in the equation does it relate?

Looking to see if it does..

I always look for any Key word to see if it means something deeper.

Faltings’ theorem key word is

Let C be a non-singular algebraic curve of genus g over Q. Then the set of rational points on C may be determined as follows:

• Case g = 0: no points or infinitely many; C is handled as a conic section.

• Case g = 1: no points, or C is an elliptic curve and its rational points form a finitely generated abelian group (Mordell’s Theorem, later generalized to the Mordell–Weil theorem).

• MoreoverMazur’s torsion theorem restricts the structure of the torsion subgroup.

• Case g > 1: according to the Mordell conjecture, now Faltings’ Theorem, C has only a finite number of rational points.

19 July 2012 517 pm edt

Key word is conic section googled in next video.


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