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Poincare Conjecture- A Search for a Shape of the Universe

1 rating: 5.0
Is the earth a perfect sphere?
1 review about Poincare Conjecture- A Search for a Shape...

What is the shape of the earth and the universe itself?

  • Jan 11, 2012
Rating:
+5
Poincare Conjecture-A Search for the Shape of the Universe by O'Shea is
an excellent rendition on the classical theories of shape for the planet
earth and the universe itself utilizing Pythagoras, Euclidean Geometry,
Einstein and modern mathematicians. Fractal geometry is another
possible application because the earth's spherical presentation is
non-linear in many places.

A basic assumption is that we do not know the shape of earth for sure.
In fact, the shape of the planet is not constant. Instead, there are finite and
not so finite changes in topography due to volcano activity, earthquakes
and other significant disturbances that literally change the face of the
planet on a continuing basis.

Continuous space has infinite dimensions. The essence of the Poincare Conjecture
is that there is no boundary for earth in the classic sense of a beginning and an end.
Every loop on a sphere shrinks to a point. In addition, there are no two parallel lines
on a sphere because any two lines intersect at some point.

The Poincare Conjecture also asserts that 3 compact manifolds on which
a closed path shrinks to a point is the exact topology as its 3- sphere.
An equivalent form of the conjecture involves a  homotopy equivalence.
In mathematical topology, two continuous functions from one topological
space to another are called homotopic when one can be "continuously deformed"
into the other. If a 3-manifold is homotopy equivalent to the 3-sphere, then it is
homeomorphic to it. A homeomorphism or topological isomorphism or bicontinuous
function is a continuous function between topological spaces that have a continuous
inverse function.

Grigori Perelman proved the full geometrization conjecture in 2003 employing
the Ricci flow . In differential geometry, the Ricci flow is an intrinsic geometric
flow. It is a process that deforms the metric of a Riemann manifold by
smoothing out irregularities . A Riemann metric opens the possibility to
define various geometric notions on a Riemann manifold, such as angles, lengths of
curves and areas.

Poincare Conjecture-A Search for the Shape of the Universe is a perfect
acquisition for physicists, mathematicians, logicians and an audience of
professionals in the allied areas of mathematics and computer science.
O'Shea's presentation is strong in some spots and difficult to understand
in others.

Credits: First Published on Blogcritics
What is the shape of the earth and the universe itself?

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February 04, 2012
The earth is square or so what they used to say in the old days LOL! Nice review as always!
February 04, 2012
Thank you very much. I wish more people would take a look at these reviews. The public should get more involved with what's happening in math/science these days.
 
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