**JSMaresca**

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

Is the earth a perfect sphere?

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Rating:

+5

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

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

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.

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 did you think of this review?**

Helpful

3

Thought-Provoking

3

Fun to Read

3

Well-Organized

3

woopak_the_thrill
February 04, 2012

The earth is square or so what they used to say in the old days LOL! Nice review as always!

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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