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REAL NEWS March 10

Posted by Xaniel777 on March 9, 2012

TODAY’S NEWS : March 10, 2012

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TSA Threatens MSM Reporters Over Coverage Of Body Scanner Story

 

From 12160.info

Agency spokesperson “strongly cautioned” journalists to back off

Steve Watson
Infowars.com
March 9, 2012

Two mainstream media reporters have revealed that the TSA has “strongly cautioned” them not to cover the story of an engineer revealing major flaws in the agency’s $1 billion dollar body scanner program.

As we reported earlier this week, Engineer Jon Corbett of the popular blog TSA Out of Our Pants! posted a video that demonstrates how the TSA’s radiation firing scanners can easily be bypassed, when carrying metal objects.

Despite YouTube initially restricting the video for no discernable reason, the story went viral and the TSA was forced to respond, albeit in a way that only made the subject more pressing.

Now Corbett, who was the first person in the country to sue the TSA over the body scanners, says that two mainstream media journalists have contacted him to make it known that the TSA warned them off the story.

“I’ve been on the phone all day for the last 2 days with reporters and journalists of all kinds,” writes Corbett.

“One South Florida reporter told me that he had been “strongly cautioned” by the TSA not to cover this story. Absolutely unbelievable”

Corbett later updated his post to say that another reporter had also been “strongly cautioned” not to cover the story.

The reporters cite a TSA spokeswoman called Sari Koshetz as the person attempting to intimidate them out of covering the issue. They say that Koshetz described Corbett as someone who “clearly has an agenda” that “should not be aided by the mainstream media”.

END

 

America Gone Stupid Over Iran – An Analysis by Dr. Lawrence Davidson

 

From INTIFADA

   Voice of Palestine

March 09, 2012

         Courtesy MCW News

Making The Same Mistake Twice

It is estimated that up to a million people died as a function of George Bush Jr.’s decision to invade Iraq. According to Bush, that decision was made on the basis of “faulty intelligence.” This is the ex-president’s way of passing the blame. The decision was made by Mr. Bush’s insistence that the accurate intelligence he was getting from traditional sources was false, and that the lies he was being told by other parties were true.

Now there is Iran. Over and again the intelligence community has told the powers that be that Iran is not engaged in a nuclear weapons program. And over and again the men and women in Congress and the White House have insisted that these traditional sources of information are wrong and that the stories that are coming from other sources (in this case the Israeli government and its special interest agents in Washington) know better. As in 2003, so it is in 2012. The politicians appear to be out for blood. One wonders how many dead and maimed bodies will satisfy them? Perhaps it will be a million dead Iranians.

The only difference is that today, we have a president who is hesitant to go to war this very momentAs General Martin Dempsey, Chairman of the Joint Chiefs of Staff, has put it, the major difference between the U.S. and Israel on military action against Iran is timing. For President Obama, first comes the “diplomacy” of ultimatums combined with draconian sanctions, and then comes the slaughter. Perhaps it will come in his anticipated second term.

I have written about this more than once before and it is hard to find anything new to say. Yet, given the play of events, what has been said before warrants being said again. Therefore, below your will find a piece originally posted on the 10th of June 2011, but amended where necessary to bring it up to date.

Part I – Is there an Iranian Nuclear Weapons Program?
 

On Friday 3 June 2011 the investigative reporter Seymour Hersh gave an interview to Amy Goodman for the radio program Democracy Now! The topic was Iran and whether or not it is developing nuclear weapons. Hersh answered this question definitively for Goodman as he did shortly thereafter in a comprehensive piece for The New Yorker (6 June 2011 ) entitled “Iran and the Bomb: How Real is the Threat? His answer: there is no Iranian nuclear weapons programThere is no threat. 

This position has been confirmed by two National Intelligence Estimates (NIEs) on the question of Iran and nuclear weapons. These expressed the collective opinion of 16 U.S. intelligence agencies. Their unanimous conclusion has been that “there is no evidence of any weaponization.”

This was reconfirmed in mid February 2012 by an array of top U.S. intelligence chiefs appearing before the Senate Intelligence Committee to give their annual report on “current and future worldwide threats” to national security.

Hersh set his understanding of the issue against the background of the 2003 invasion of Iraq. In that case there was no credible evidence for weapons of mass destruction yet we had high government officials going around talking about the next world war and mushroom clouds over American cities. Both the U.S. Congress and the general population bought into this warmongering.

Hersh is obviously worried about a replay of that scenario. Thus, in his interview, he said “you could argue its 2003 all over again….There’s just no serious evidence inside that Iran is actually doing anything to make nuclear weapons….So, the fact is…that we have a sanctions program that’s designed to prevent the Iranians from building weapons they’re not building.”

In 2003 those kind of sanctions, applied to Iraq, along with the accompanying misinformation campaign, led to a tragic and unnecessary war. Are we now doing it all over again? As Amy Goodman pointed out, “the Obama White House…has repeatedly cited Iran’s nuclear program as a threat to the world.”

President Obama asserted as much in a 22 May 2011 speech before AIPAC and again in his 4 March 2012 talk to the same organization. On the latter occasion Obama told his audience, “I have said that when it comes to preventing Iran from obtaining a nuclear weapon, I will take no options off the table, and I mean what I say.

That includes all elements of American power: a political effort aimed at isolating Iran….an economic effort that imposes crippling sanctions and, yes, a military effort to be prepared for any contingency.” All this for something that is simply not happening.

If this is the case, what in the world was President Barack Obama talking about when addressing AIPAC? And what are the members of Congress talking about when they address this same issue?  

The vast majority of them take the same line not of President Obama, but of Israeli President Benjamin Netanyahu who thinks Obama is weak and naive and that their should be war against Iran now.

In addition, this morbid fantasizing about Iran’s nuclear ambitions has captured the attention of the mainstream press. Amy Goodman asked Hersh about a New York Times report (24 May 2011) stating “the world’s global nuclear inspection agency [IAEA]…revealed for the first time…that it possesses evidence that Tehran has conducted work on a highly sophisticated nuclear triggering technology that experts said could be used for only one purpose: setting off a nuclear weapon.”

Hersh quickly pointed out the that the word “evidence” never appeared in the IAEA report and, it turns out, the type of nuclear trigger the New York Times was referring to is so fraught with technical problems that, according to Hersh, “there is no evidence that anybody in their right mind would want to use that kind of a trigger.” So, what in the world is the New York Times telling us?

Part II – What is Real?

Questions One and Two: The questions about Iran’s nuclear program are not open ended. They have real answers. First, is Iran developing nuclear energy? The answer to this is a definitiveyes. No one, Iranian or otherwise, denies this. Their aim here is energy production and medical applications. This is all legal. Second, is it developing nuclear weapons? According to every reliable expert within the intelligence agencies of both the United States and Europe, the answer is no. These answers describe reality in relation to Iran and its nuclear activities.

Question Three: The really important question. Why do American politicians and military leaders refuse to accept reality as regards this issue? That too must have an answer. And
intelligent people who investigate these matters should be able to figure it out. I consider myself in this crowd, and so I am going to venture forth with my answer.

Answer to question three: It is Politics. However, it is not just U.S. politics. Others have helped write the script. These others can be identified by asking to whom are American officials pledging to pursue the Iranian nuclear weapons fantasy? The president’s pledge has gone to AIPAC and the Israelis. Members of Congress have done the same.

Part III – Other People’s Fears Become America’s Fantasies

Israeli politicians are addicted to the Iran threat. Iran serves, alongside the Palestinians, as the latter day ruthless anti-Semite who would destroy the Jews. Zionists seem to need this kind of “existentialist” enemy. This is the equivalent of the Islamic fundamentalist taking the place of the hateful communist as the great enemy that the United States also seems to need.

And, as it turns out, the Israeli lobby is more influential in formulating U.S. foreign policy toward Iran than all of the nation’s intelligence services put together. Hence our politicians from the President on down, chase shadows. Not just verbally, mind you, but in terms of definable policy (like sanctions against Iran).

U.S. politicians and military leaders can not talk like this and create policy like this without the mainstream press following along. Where there is smoke, there must be fire. Plus, ever since the Iranian hostage crisis (1979-1981), Americans have been told that the Iranians hate us.

So, whether it is Fox TV, whose fanatical conservative backers have always lived in a bi-polar fantasy world of good and evil, or the New York Times, whose quasi-liberal backers empathize with Israel just enough to buy into that country’s paranoia, the message is that the Iranians are crazy people out to destroy the West. And the evidence? Who needs it?

Part IV- The Real Danger is Acting on False Assumptions

What happens when a well armed individual can not tell the difference between reality and unreality? What happens when a well armed individual just knows, in his gut, that the other guy is plotting to destroy him? Chances are something horrible will happen.

And, the American public ought to know that this is so, because collectively we have already lived out this tragedy in 2003. In that year we had leadership who were much more influenced by their guts, by religious imagery, by duplicitous Iraqi con men, by scheming Zionists and ideologically driven neo-cons, than anything vaguely resembling hard evidence. That “something horrible” cost the lives of up to a million human beings.

So let us get this straight. It seems there are two worlds. The real world of facts and evidence and the unreal world of fantasy. Our political leaders and their advisers are, apparently, stuck in the unreal one. Their words, and their policies, are built on the assumptions of this fantasy world. They go to war and kill people based on beliefs that are demonstrably false.

And the rest of us? Most of us are stuck in our own local niches and beyond them we do not know what is real or unreal. So we rely on others to tell us what to believe. Who are the others? They just happen to be our political leaders, their advisers, and follow-the-leader media commentators. Well, that makes a nice little circle. And, a fatal one at that.

ldavidson@wcupa.edu
www.tothepointanalyses.com
www.twitter.com/pointanalyses

*********

DR. LAWRENCE DAVIDSON is professor of Middle East history at West Chester University in West Chester, PA, and the author of America’s Palestine: Popular and Official Perceptions from Balfour to Israeli Statehood (University of Florida Press, 2001), Islamic Fundamentalism (Greenwood Press, 2003), and Foreign Policy, Inc.: Privatizing American National Interest (University of Kentuck Press, 2009).

END

FREE ENERGY ~ The New Wave to The Advancement of Our World

From Coast To Coast A.M. and Wikipedia

On Saturday night ( March 03, 2012 ), John B. Wells was joined by filmmakers Foster & Kimberly Gamble who discussed Thrive, their unconventional documentary that lifts the veil on what’s really going on in our world and how it connects free energy, UFOs, and the global elite.

Foster explained how their research revealed that the energy pattern known as a torus can be found in various “healthy systems” throughout the universe.

It is also depicted in ancient cave drawings, modern crop circles, and in reports from ET contactees, leading the duo to surmise that visitors to Earth are trying to impart the knowledge of this energy pattern to the human race.

According to them, the principals of the torus pattern can be used to create free energy, which has been discovered many times by enterprising inventors.

From Wikipedia : Torus 

Not to be confused with Taurus (disambiguation).

This article is about the surface and mathematical concept of a torus. For other uses, see Torus (disambiguation).

A torus

As the distance to the axis of revolution decreases, the ring torus becomes a spindle torus and then degenerates into a sphere.

In geometry, a torus (pl. tori) is a surface of revolution generated by revolving a circle in three dimensional space about an axis coplanar with the circle. In most contexts it is assumed that the axis does not touch the circle – in this case the surface has a ring shape and is called a ring torus or simply torus if the ring shape is implicit.

Other types of torus include the horn torus, which is generated when the axis is tangent to the circle, and the spindle torus, which is generated when the axis is a chord of the circle. A degenerate case is when the axis is a diameter of the circle, which simply generates the surface of a sphere. The ring torus bounds a solid known as a toroid. The adjective toroidal can be applied to tori, toroids or, more generally, any ring shape as in toroidal inductors and transformers. Real world examples of (approximately) toroidal objects include doughnutsvadaisinner tubes, many lifebuoysO-rings and vortex rings.

In topology, a ring torus is homeomorphic to the Cartesian product of two circlesS1 × S1, and the latter is taken to be the definition in that context. It is a compact 2-manifold of genus 1. The ring torus is one way to embed this space into Euclidean space, but another way to do this is the Cartesian product of the embedding of S1 in the plane. This produces a geometric object called the Clifford torus, surface in 4-space.

The word torus comes from the Latin word meaning cushion.[1]

Geometry

A torus is the product of two circles, in this case the red circle is swept around axis defining the pink circle. R is the radius of the pink circle, r is the radius of the red one.

ring

Ring torus

horn

Horn torus

spindle

Spindle torus

Bottom-halves and cross-sections of the three classes

A diagram depicting the poloidal (\theta) direction, represented by the red arrow, and the toroidal (\zetaor \phi) direction, represented by the blue arrow.

A torus can be defined parametrically by:[2]

x(u, v) =  (R + r \cos{v}) \cos{u} \, y(u, v) =  (R + r \cos{v}) \sin{u} \, z(u, v) =  r \sin{v} \,

where

u,v are in the interval [0, 2π),R (or A) is the distance from the center of the tube to the center of the torus,r (or a) is the radius of the tube.

R and r are also known as the “major radius” and “minor radius”, respectively. The ratio of the two is known as the “aspect ratio“. A doughnut has an aspect ratio of 2 to 3.

An implicit equation in Cartesian coordinates for a torus radially symmetric about the z-axis is

\left(R - \sqrt{x^2 + y^2}\right)^2 + z^2 = r^2, \,\!

or the solution of  f(x,y,z) = 0, where

 f(x,y,z) = \left(R - \sqrt{x^2 + y^2}\right)^2 + z^2 - r^2.\,\!

Algebraically eliminating the square root gives a quartic equation,

 (x^2+y^2+z^2 + R^2 - r^2)^2 = 4R^2(x^2+y^2).  \,\!

The three different classes of standard tori correspond to the three possible relative sizes of r and R. When R > r, the surface will be the familiar ring torus. The case R = r corresponds to the horn torus, which in effect is a torus with no “hole”. The case R < r describes the self-intersecting spindle torus. When R = 0, the torus degenerates to the sphere.

The surface area and interior volume of this torus are easily computed using Pappus’s centroid theorem giving[3]

A = 4 \pi^2 R r = \left( 2\pi r \right) \left(2 \pi R \right) \,

V = 2 \pi^2 R r^2 = \left ( \pi r ^2 \right ) \left( 2 \pi R \right). \,

These formulas are the same as for a cylinder of length 2πR and radius r, created by cutting the tube and unrolling it by straightening out the line running around the center of the tube. The losses in surface area and volume on the inner side of the tube exactly cancel out the gains on the outer side.

As a torus is the product of two circles, a modified version of the spherical coordinate system is sometimes used. In traditional spherical coordinates there are three measures, R, the distance from the center of the coordinate system, and \theta and \phi, angles measured from the center point. As a torus has, effectively, two center points, the centerpoints of the angles are moved; \phi measures the same angle as it does in the spherical system, but is known as the “toroidal” direction. The center point of \theta is moved to the center of r, and is known as the “poloidal” direction. These terms were first used in a discussion of the Earth’s magnetic field, where “poloidal” was used to denote “the direction toward the poles”.[4] In modern use these terms are more commonly used to discuss magnetic confinement fusion devices.

[edit]Topology

Topologically, a torus is a closed surface defined as the product of two circlesS1 × S1. This can be viewed as lying in C2 and is a subset of the 3-sphere S3 of radius √2. This topological torus is also often called the Clifford torus. In fact, S3 is filled out by a family of nested tori in this manner (with two degenerate circles), a fact which is important in the study of S3 as a fiber bundle over S2 (the Hopf bundle).

The surface described above, given the relative topology from R3, is homeomorphic to a topological torus as long as it does not intersect its own axis. A particular homeomorphism is given by stereographically projecting the topological torus into R3 from the north pole of S3.

The torus can also be described as a quotient of the Cartesian plane under the identifications

(x,y) ~ (x+1,y) ~ (x,y+1).

Or, equivalently, as the quotient of the unit square by pasting the opposite edges together, described as a fundamental polygon ABA^{-1}B^{-1}.

Turning a punctured torus inside-out

The fundamental group of the torus is just the direct product of the fundamental group of the circle with itself:

\pi_1(\mathbb{T}^2) = \pi_1(S^1) \times \pi_1(S^1) \cong \mathbb{Z} \times \mathbb{Z}.

Intuitively speaking, this means that a closed path that circles the torus’ “hole” (say, a circle that traces out a particular latitude) and then circles the torus’ “body” (say, a circle that traces out a particular longitude) can be deformed to a path that circles the body and then the hole. So, strictly ‘latitudinal’ and strictly ‘longitudinal’ paths commute. This might be imagined as two shoelaces passing through each other, then unwinding, then rewinding.

If a torus is punctured and turned inside out then another torus results, with lines of latitude and longitude interchanged.

The first homology group of the torus is isomorphic to the fundamental group (this follows from Hurewicz theorem since the fundamental group is abelian).

[edit]Two-sheeted cover

The 2-torus double-covers the 2-sphere, with four ramification points. Every conformal structure on the 2-torus can be represented as a two-sheeted cover of the 2-sphere. The points on the torus corresponding to the ramification points are theWeierstrass points. In fact, the conformal type of the torus is determined by the cross-ratio of the four points.

[edit]n-dimensional torus

The torus has a generalization to higher dimensions, the ndimensional torus, often called the ntorus for short. (This is one of two different meanings of the term “n-torus”.) Recalling that the torus is the product space of two circles, the n-dimensional torus is the product of n circles. That is:

\mathbb{T}^n = \underbrace{S^1 \times S^1 \times \cdots \times S^1}_n.

The torus discussed above is the 2-dimensional torus. The 1-dimensional torus is just the circle. Just as for the 2-torus, the n-torus can be described as a quotient of Rn under integral shifts in any coordinate. That is, the n-torus is Rn modulo the action of the integer lattice Zn (with the action being taken as vector addition). Equivalently, the n-torus is obtained from the n-dimensional hypercube by gluing the opposite faces together.

An n-torus in this sense is an example of an n-dimensional compact manifold. It is also an example of a compact abelian Lie group. This follows from the fact that the unit circle is a compact abelian Lie group (when identified with the unit complex numbers with multiplication). Group multiplication on the torus is then defined by coordinate-wise multiplication.

Toroidal groups play an important part in the theory of compact Lie groups. This is due in part to the fact that in any compact Lie group G one can always find a maximal torus; that is, a closed subgroup which is a torus of the largest possible dimension. Such maximal tori T have a controlling role to play in theory of connected G.

Automorphisms of T are easily constructed from automorphisms of the lattice Zn, which are classified by integral matrices M of size n×n which are invertible with integral inverse; these are just the integral M of determinant +1 or −1. Making M act on Rn in the usual way, one has the typical toral automorphism on the quotient.

The fundamental group of an n-torus is a free abelian group of rank n. The k-th homology group of an n-torus is a free abelian group of rank n choose k. It follows that the Euler characteristic of the n-torus is 0 for all n. The cohomology ring H(Tn,Z) can be identified with the exterior algebra over theZmodule Zn whose generators are the duals of the n nontrivial cycles.

[edit]Configuration space

The configuration space of 2 not necessarily distinct points on the circle is the orbifold quotient of the 2-torus, T^2/S_2, which is theMöbius strip.

As the n-torus is the n-fold product of the circle, the n-torus is the configuration space of n ordered, not necessarily distinct points on the circle. Symbolically, T^n = (S^1)^n. The configuration space of unordered, not necessarily distinct points is accordingly the orbifold T^n/S_n, which is the quotient of the torus by the symmetric group on n letters (by permuting the coordinates).

For n=2, the quotient is the Möbius strip, the edge corresponding to the orbifold points where the two coordinates coincide. For n=3 this quotient may be described as a solid torus with cross-section an equilateral triangle, with a twist; equivalently, as atriangular prism whose top and bottom faces are connected with a ⅓ twist (120°): the 3-dimensional interior corresponds to the points on the 3-torus where all 3 coordinates are distinct, the 2-dimensional face corresponds to points with 2 coordinates equal and the 3rd different, while the 1-dimensional edge corresponds to points with all 3 coordinates identical.

These orbifolds have found significant applications to music theory in the work of Dmitri Tymoczko and collaborators (Felipe Posada and Michael Kolinas, et al.), being used to model musical triads.[5][6]

[edit]Flat torus

The flat torus is a specific embedding of the familiar 2-torus into Euclidean 4-space or higher dimensions. Its surface has zero Gaussian curvature everywhere. Its surface is “flat” in the same sense that the surface of a cylinder is “flat”. In 3 dimensions one can bend a flat sheet of paper into a cylinder without stretching the paper, but you cannot then bend this cylinder into a torus without stretching the paper. In 4 dimensions one can (mathematically).

A simple 4-d Euclidean embedding is as follows: <x,y,z,w> = <R cos uR sin uP cos vP sin v> where R and P are constants determining the aspect ratio. It is diffeomorphic to a regular torus but not isometric. It can not be isometrically embedded into Euclidean 3-space. Mapping it into 3-space requires you to “bend” it, in which case it looks like a regular torus, for example, the following map <x,y,z> = <(R + P sin v)cos u, (R + P sin v)sin uP cos v>.

A flat torus partitions the 3-sphere into two congruent solid tori subsets with the aforsaid flat torus surface as their common boundary.

Clifford-torus.gif

A stereographic projection of a Clifford torusperforming a simple rotation through the xz-plane.

[edit]n-fold torus

In the theory of surfaces the term n-torus has a different meaning. Instead of the product of n circles, they use the phrase to mean the connected sum of n 2-dimensional tori. To form a connected sum of two surfaces, remove from each the interior of a disk and “glue” the surfaces together along the disks’ boundary circles. To form the connected sum of more than two surfaces, sum two of them at a time until they are all connected. In this sense, an n-torus resembles the surface of n doughnuts stuck together side by side, or a 2-dimensional sphere with n handles attached.

An ordinary torus is a 1-torus, a 2-torus is called a double torus, a 3-torus a triple torus, and so on. The n-torus is said to be an “orientable surface” of “genus” n, the genus being the number of handles. The 0-torus is the 2-dimensional sphere.

The classification theorem for surfaces states that every compact connected surface is either a sphere, an n-torus with n > 0, or the connected sum of n projective planes (that is, projective planes over the real numbers) with n > 0.

Double torus illustration.png
double torus
Triple torus illustration.png
triple torus

[edit]Toroidal polyhedra

For more details on this topic, see Toroidal polyhedron.

toroidal polyhedron with 6×4=24 quadrilateral faces.

Polyhedra with the topological type of a torus are called toroidal polyhedra, and satisfy a modified version of the polyhedron formulaE-F-V = 0.

The term “toroidal polydron” is also used for higher genus polyhedra and for immersions of toroidal polyhedra.

[icon]

This section requires expansion.

[edit]Automorphisms

The homeomorphism group (or the subgroup of diffeomorphisms) of the torus is studied in geometric topology. Its mapping class group (the group of connected components) is isomorphic to the group GL(n, Z) of invertible integer matrices, and can be realized as linear maps on the universal covering space \mathbf{R}^n that preserve the standard lattice \mathbf{Z}^n (this corresponds to integer coefficients) and thus descend to the quotient.

At the level of homotopy and homology, the mapping class group can be identified as the action on the first homology (or equivalently, first cohomology, or on the fundamental group, as these are all naturally isomorphic; note also that the first cohomology group generates the cohomology algebra):

\mathrm{MCG}(T^n) = \mathrm{Aut}(\pi_1(X)) = \mathrm{Aut}(\mathbf{Z}^n) = \mathrm{GL}(n,\mathbf{Z}).

Since the torus is an Eilenberg-MacLane space K(G, 1), its homotopy equivalences, up to homotopy, can be identified with automorphisms of the fundamental group); that this agrees with the mapping class group reflects that all homotopy equivalences can be realized by homeomorphisms – every homotopy equivalence is homotopic to a homeomorphism – and that homotopic homeomorphisms are in fact isotopic (connected through homeomorphisms, not just through homotopy equivalences). More tersely, the map \mathrm{Homeo}(T^n) \to \mathrm{SHE}(T^n) is 1-connected (isomorphic on path-components, onto fundamental group). This is a “homeomorphism reduces to homotopy reduces to algebra” result.

Thus the short exact sequence of the mapping class group splits (an identification of the torus as the quotient of \mathbf{R}^n gives a splitting, via the linear maps, as above):

1 \rightarrow {\rm Homeo}_0(T^n) \rightarrow {\rm Homeo}(T^n) \rightarrow {\rm MCG}(T^n) \rightarrow 1,

so the homeomorphism group of the torus is a semidirect product\mathrm{Homeo}(T^n) \cong \mathrm{Homeo}_0(T^n) \rtimes \mathrm{GL}(n,\mathbf{Z}).

The mapping class group of higher genus surfaces is much more complicated, and an area of active research.

[edit]Coloring a torus

If a torus is divided into regions, then it is always possible to color the regions with no more than seven colors so that neighboring regions have different colors. (Contrast with the four color theorem for the plane.)

This construction shows the torus divided into the maximum of seven regions, every one of which touches every other.

[edit]Cutting a torus

standard torus (specifically, a ring torus) can be cut with n planes into at most

 \frac16 (n^3 + 3n^2 + 8n)  parts.[7]

The initial terms of this sequence for n starting from 1 are:

2, 6, 13, 24, 40, … (sequence A003600 in OEIS).

[edit]See also

Portal icon Mathematics portal

[edit]Notes

  1. ^ Harold A. Stein … (2002). Fitting guide for rigid and soft contact lenses : a practical approach. St. Louis: Mosby. p. 16. ISBN 9780323014403.

  2. ^ http://www.geom.uiuc.edu/zoo/toptype/torus/standard/eqns.html

  3. ^ Weisstein, Eric W., “Torus” from MathWorld.

  4. ^ “Oxford English Dictionary Online”poloidal. Oxford University Press. Retrieved 2007-08-10.

  5. ^ Tymoczko, Dmitri (7 July 2006). “The Geometry of Musical Chords”Science 313 (5783): 72–74. doi:10.1126/science.1126287PMID 16825563

  6. ^ Tony Phillips, Tony Phillips’ Take on Math in the Media, American Mathematical Society, October 2006

  7. ^ Weisstein, Eric W., “Torus Cutting” from MathWorld.

[edit]References

External links

END

 

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