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parallel postulate of Euclid

, in its modern reformulation there is a line and a point not on the line, one line through the point parallel to the line drawn on a map may contain . Gerolamo Saccheri (1667-1733) brilliant attempt to prove an argument reductio ad absurdum. There were two ways of contradicting the assumption could have a place), no parallel lines (straight lines in a plane is always right, if extended far enough), or 2) on several parallel lines through a given point to a given line in the plan. These axioms are non-Euclidean. Saccheri convince his reductio reached for the first option, with the innocent assumption that straight lines are infinite [CF. Jeremy Gray, Ideas of Space Euclidean, Non-Euclidean and Relativistic, Oxford, 1989 p. 64]. Later, David Hilbert (1862-1953) noted that the evidence reductio even assuming that the delay could be achieved by only three points on a line can be between two Hilbert [David and S. Cohn-Vossen Geometry and the imagination are (descriptive geometry - geometry intuitively better translated)] Chelsea Publishing Co., 1952, p. 240. For the second option, however, has not reached Saccheri good evidence. And it only as an axiom, that the first full non-Euclidean geometries of Bolyai (1802-1860) and Lobachevskii ‘s (1792-1856 have been achieved).
If by “flat” understand that we mean a level line as Euclid, then right non-Euclidean manifold (ie, areas, volumes, space, time, etc.) which are contrary to the well Euclid, who was on fair -Talk should be flat. They could not be folded. Straight lines are Euclidean straight line, but given the characteristics of non-Euclidean axioms are satisfied. However, since Bernhard Riemann (1826-1866), non-Euclidean manifolds are considered “folded” and that space is Euclidean himself as “flat”. Contradiction # 1 top producing “positive” curved space (“spherical” or “elliptic” geometry, first described by Riemann himself), and the contradiction # 2 “negatively” curved space (hyperbolic or Lobachevskian geometry). Euclid, it certainly seems his point: to prove the axiom on parallel straight lines, curves produced with only non-Euclidean geometry honest. “Curvature” in this regard but it is used in an unusual sense. Euclidean geodesic “right” line and generalized “geodesic”. “Flat” spaces over three dimensions can be designated as “Euclidean” because of their lack of curvature, but it is an extension of geometry which would have been very strong new Euclid, and I want to keep the historical link between the “Euclidean” and Euclid]. What is “bending” would have meant to Euclid, is now “extrinsic” curvature that for a line or a plane or a room in “folded” There must be a higher-dimensional space, i. e. occupying a curve in a line-up of a curved plane, results in a volume, a volume curve requires some fourth dimension, etc. Now, the “intrinsic” curvature has nothing to do with a higher dimension. But how could this happen? Why “curvature” to come to this unusual sense? Why should we say that we confuse “intrinsic” line, the surveyors in curvature of the non-Euclidean space? Indeed, non-Euclidean planes that extrinsically curved surfaces in Euclidean space can be modeled. Thus, the surface of a sphere is the classic two-dimensional curved Riemannian space is positive, but while the great circle line (surveying) on the intrinsic properties of the surface, one sees the surface, as in third dimension curves of Euclidean space. A ball is a good representation of a surface non-Euclidean and spherical geometry has been developed as well as he is now a little surprising that it does not show the basis of the first non-Euclidean geometry [see Gray , ibid. Page 171]. However, as mentioned, such a geometry is incompatible with other axioms of geometry, which can be adjusted easily. Accept spaces of positive curvature means that these axioms must be rejected. In addition, more importantly, these models in Euclidean space are not always successful. with space Lobachevskian. A saddle-shaped surface is a room Lobachevskian in the middle of the saddle, but a real place Lobachevskian has no center. Other models Lobachevskian distort shapes and sizes. There is no representation of a surface Lobachevskian the virtues of having a hand ball no center, no singularities (ie points which are not part of the room), and is moving at low closely at the figures without distorting shape or size. Three-dimensional non-Euclidean spaces are obviously not at all modeled by a Euclidean space.
This raises two questions: 1) What can we visualize spatially? (A question of psychology) and 2) that can exist in reality? (A question of ontology). We can not see the real Lobachevskian spaces or spaces non-Euclidean in general, with more than two dimensions – or any space at all with more than three dimensions. In addition, we can visualize the surface one positive curvature, if it is not integrated in a volume with an Euclidean extrinsic curvature explicitly. “Curve” is a natural expression of intrinsic properties, because there was always extrinsic curvature for each model that could be visualized. Why are there limits to this, we can visualize what? Why should our visual imagination limited to three-dimensional Euclidean? It is common now to say that the graphics are drilling restrictions, but these references are always projections of non-Euclidean spaces and multi-dimensional on the computer screen in two dimensions. These projections may be too difficult, well before the computer, but they have never done and do not produce more, such as drawings flat Euclidean curves. If these images are to be expected, our spirit that we change to see things differently, it is not a prediction or a hope, not a fact. And when you consider that non-Euclidean geometries for nearly two centuries, the transformation of our imagination conceived seems a little late, but many computers can now help to. Mathematicians do not care about these issues in visualization, visualization, because it is not necessary for the analytical formulas that describe the rooms. The formulas have been significant in the non-Euclidean geometry that common sense has never been.
Euclidean nature of our imagination leads Kant to say that although the negation of Euclid’s axioms can be thought without contradiction, our intuition is at the limit imposed by the shape of the space of our own thoughts about the world. It is not uncommon for applications to determine the existence of non-Euclidean geometry refuted Kant’s theory, not as to reflect the meaning of the term “synthetic”, meaning that a consolidated proposal may be denied without contradiction. Leonard Nelson clear that Kant’s theory is a prediction of non-Euclidean geometry, not a denial of fact necessary, and that the existence of non-Euclidean geometry in Kant justifies the assertion that the axioms of geometry are synthetic products. The clarity of the non-Euclidean geometry in Kant’s theory is neither psychological nor an ontological question, but simply a logical – with the criterion of the possibility that Hume logically conceivable. Kant does not tell the non-Euclidean geometry is logically impossible, but it’s not just because he does not argue that each geometry is logically true, in his view is the synthetic geometry, analytic. And the belief of Kant that Euclidean geometry is true, because our intuitions tell us, it seems to be either unintelligible or false.
If we are unable to visualize non-Euclidean geometries, without lines curved outward, but the intelligibility of Kant’s theory is not difficult to find. The meaning of the truth of Euclidean geometry, for Kant, neither more nor less than the confidence that the centuries had supported the land in the parallel postulate, a real confidence in our spatial imagination. If the argument of Kant is “incomprehensible,” said Gray had not thought about why everyone in the story that the 19th Century believed that the parallel postulate is true. This is the psychological question, not logical or ontological. The meaning of the ancient faith can still be had today, simply by trying the non-Euclidean geometry for students who have never heard him explain. Arguably, attempts to demonstrate this assumption proved wrong about a bit, but the general expectation was that the premise was really a theorem, and nobody in their discomfort by trying to geometry with a denial of the cashed-build . Saccheri denied, but only because it builds evidence reductio ad absurdum. The non-Euclidean geometry does not change our perception of space, only proved what Kant had already implicitly: the synthetic and the axiomatically independent character of the first principles of geometry. It may well be the case that Kant is right and we would never be able to change the appearance of multi-dimensional non-Euclidean spaces or Lobachevskian or she can be without external curve model, but we also understand the analytical equations. It’s just a matter of psychology, not logic, mathematics, physics or ontology. The mathematicians are free to ignore the limits of our imagination, even if they run the risk of wandering away from common sense that the limits of mathematics will never be complete, people knowledgeable about general knowledge. In addition, since Kant believed that space was a form of forced our heads in the world he did not believe that the room actually exist outside of our experience. This brings us to the ontological question: what can exist in reality? The non-Euclidean geometry is nothing more than a mathematical curiosity, she turned to the physics of Einstein. Now it all seems much deeper and more complex than the time of Kant, or Riemann. If our imagination is necessarily Euclidean, hard wired in the brain, as can now think the analogy with the computer, but Einstein has found a way to non-Euclidean geometry, applied to the world, then we may think piece has a reality and a real structure in the world, but we are able to present visually.
In light of the distinction between inner and outer curvature, we have taken into account, covering all types of ontological axioms that can describe all possible fields of Euclidean geometry and non-Euclidean geometry. If the restrictions currently imposed on us by our imagination with the characteristics of real space, we should say that the inner curvature, although analytically independent of the curve on the outside, only in connection with the outer bow, and then there is a embedding in higher dimensions. This could be called the axiom of ortho-curvature, which is actually not a real non-Euclidean geometry to non-Euclidean geodesic necessarily extrinsic curvature and is never straight lines, we need to contradict the former assumption of Euclid. The geometry of a spherical surface would be at the ortho-curvature, because the interior of straight lines, great circles, to simultaneously visualize and understand, curved lines in three-dimensional Euclidean space. On the other hand, there may be intrinsically curved spaces can actually exist without external curvature is incorporated so easily into a higher dimension. This could be called the axiom of hetero-curvature, and this would be true non-Euclidean geometry as possible, because the lines do not do with non-Euclidean relations with each other just to be heard in the usual sense of the word Euclid and Kant.
Another ontological distinction can be made. Even if the axiom is true ortho-curvature, a functionally non-Euclidean geometry could be possible if a higher dimension that allows outside curvature exists but is hidden. We need only consider whether the three dimensions of space or if there are extra dimensions that we are not in some way, but experience can an inner curve, not their physical properties can be viewed or controlled by us imagination to create. Thus we must distinguish between an axiom ortho closed curve, so that the three-dimensional space is all there, and an axiom of open ortho-curvature, so that higher dimensions exist then. This gives us three options:
Closing with the axiom of ortho-curvature, there is no real non-Euclidean geometries (and not more than three spatial dimensions), but only />
Related to the axiom of open ortho-curvature, there is no real non-Euclidean geometries, but we can with a non-Euclidean geometry functional in Euclidean space whose outer curve is with us in dimensions (to be confronted more than covered the best known three-dimensional space) not available for our inspection - it is an apparent right elbow;
And, with the axiom of the hetero-curvature, there are real non-Euclidean geometries, their intrinsic properties are not ontologically assumes higher (if there are more than three spatial dimensions).
It is necessary to note that these axioms answers to questions about the reality that the application of physics and metaphysics is logically separate and completely over the condition of the geometry of logic or mathematics or our psychic powers of visual imagination . The second axiom leaves open the question of whether “hidden” hidden dimensions just our perception or reality separate from our own existence dimensional. With this alternative ontological mind, we can now use the philosophical implications of Einstein’s use of the non-Euclidean geometry.

§ 3 Geometry
Einstein Theory of Relativity
Einstein’s theory of general relativity indicates that the “force of gravity is in fact an intrinsic curvature of spacetime, not the exchange-Newtonian action at a distance or from a quantum virtual particles. If we project explained Einstein’s philosophical response to Kant’s antinomy of space View – How many rows can be in the room at the end, but without time limits – suggests the introduction of time considered a fourth dimension we have the inside curvature of space-time curvature separated on the basis of the relationship between space and time: We can Einstein’s theory as one, think that satisfies the axiom of ortho-curvature open, with the particularity that it is indeed time, instead of a higher dimensional space, which is set beyond our familiar three spatial dimensions. This is an elegant theory metaphysics, as we give the mathematical usage of a higher dimension without the need to postulate a real spatial dimension beyond our experience and existence. Time is a dimension that is present to us only one slice at a time space, as the third dimension is only one (radial cut) developed by the curved surface of a sphere in the previous model of a space of positive curvature.
Our spherical model of the space-time non-Euclidean, but it is not quite right, because if the analogy, the intrinsic lines in space, geodesics, and so appear to us directly. You must show the curve in terms of higher dimension, like the great circles appear on the ball from our point of view three-dimensional curves. This is not the form of astronomical space, where the lines are in freefall in the organs of gravity set course true imagination folded into three dimensions, even if they fall, surveyors, and only in their form in the higher dimension of space-time. This is exactly the opposite is true in the model: Free Falling paths (world lines) are geodesics in space-time, but extrinsically curved lines in space, while the model in circles outline extrinsic fixed in space (corresponding to the space-time), but are geodesic curves placed on the plane (corresponding area).
explain the internal curvature, which was introduced by Riemann in straight lines with the properties could not bend curve associated in the usual sense of the term is now used to explain how something that is obviously bent, for example, the orbit a planet is really right. Something has turned itself around. If the curvature of space-time is obvious to us in the extrinsically curved lines in three dimensional space, then the shape of the analogy requires us to “high” or extrinsic dimension, curves, straight lines, as space, not one time. If this is not a three-dimensional space is curved outward in the period following the axiom of open ortho-curvature, then it is time that the curves are extrinsically in the dimensions of space. In the model, where the surface before the ball was similar to fixed, now, the surface similar to two dimensions of space and time, with the third dimension of space as the space-geodetic time curves are extrinsically. Changing the role of time suddenly makes the model is not very intuitive, but it is the function of the model that the geodesic is forced to the surface of the ball. It does not help the philosophical question, to eject the complications of the axiom of open ortho-curvature, just take the four dimensions of space-time as the fulfillment of hetero-curvature for those losing sight Kant’s antinomy of space, we hope to answer and the fact that even in the dimension of the relativity of time is not exactly the same as the dimensions of the room. This is intuitively obvious in the “separation” formula: S2 = t2 – (x2 + y2 + z2) / C2. The formula of Pythagoras for change in spatial location, the speed of light squared, divided by the change in time to square off against the space-time “separation” in units of time. Thus, time is not simply as another spatial dimension treated. We must therefore examine the differences between space and time, and the axiom of open ortho-curvature may be alone on this.
The result of the allocation to other extrinsic curvature by the specificity of the proposed to explain “curved space” only to gravity, as is often in museums and textbooks around the world, for the curved space evokes images of mountains and valleys, through moving objects trajectories describe curves. However, these images and the social movement and the movement is exactly what needs to be explained. Gravity not only a direct motion, it is the cause. An object passing through the earth to the earth more quickly and thus has a velocity along a vector, where it was previously not speed at all. An object at rest relative resting on the ground without a muzzle velocity in all directions will be accelerated to a speed towards the Earth. If there are no forces “in the body act as Einstein said, so the only change that occurs is the body’s movement along the time axis, and if the body is in the room moved, it must be moved by the movement axis. The time axis can be bent if the axle itself can move, so that the curvature of spacetime in a gravitational field on the curvature of the time, not space. The external dimension of ortho-curvature, the curve right, is a dimension of ordinary Euclidean space. This can be illustrated intuitively, not so much in our non-Euclidean models, but simply a graph of time (t) against one dimension of space (r). An acceleration of the body to describe a curved line that is in the r axis as in the T-coordinate axis changes changed. If the acceleration comes from the space-time itself, then the coordinate grid itself will curve: the T-axis shift lines curve, not against the r-axis (spatial location), while the line graph of the r axis. The curvature of time itself is hidden from us because we actually cut into a single point on the timeline. So we know how our accelerated by gravity? In free fall we moved to the hall itself, and if we spend our frame of reference and the whole is not able to recognize the local level. In fact, we can not. It was Einstein’s own “equivalence” principle of general relativity that we can not distinguish between free fall in a gravitational field and float in the absence of a gravitational field. The movement is induced in us by the curvature of time because clearly we can see distant objects not covered by our local acceleration. If we are not in free fall, for example, standing on the surface of the earth, we feel the weight, as under the principle of equivalence, if we are a force (eg a motor speed of rocket) in the absence of a gravitational field. They are, in fact, because in all cases, we are moving relative to make room for our own frame of reference is. If we accelerated by a rocket, we say that we are moving in a reference to the stopping of the outdoor space, but if we are fast on the surface of the earth, it is space itself that moves (by time) compared to us. Either we move in the room or space is moving through us. Such is the experience of weight.
A question remains as to the global nature of space-time. gravitational fields are locally positive curves, but Einstein and his philosophical followers apparently expected that curves space-time would be positive in its entirety as a finite but unbounded universe is aesthetically more satisfying – and he said antinomy Kant space. But now is the geometry of the rule of space-time cosmological dynamics to the fate of the expanding universe bound. Open the growing universe, or even that under Lobachevskian geometry and only closed universe, created for the ultimate collapse, considered positive Riemannian curvature. The empirical evidence is currently an open universe inflationary “,” models even have reason to prefer a Euclidean geometry on a Lobachevskian. These possibilities, however, present significant challenges for Euclidean spaces and Lobachevskian both are infinite, and it is to tell a very different statement that starts an infinitely dense Big Bang singularity finite space in which a finite positive curves can be packed, to say that the universe infinite, homogeneous and isotropic, the infinite must be started from an infinitely dense Big Bang. An infinitely dense singularity, a finite mass, but an infinite density range, even in a small finite region of space can not.
In a recent article in Scientific American cosmology, “Textures and cosmic structure” (March 1992), authors, Spergel, Turok, speaking of the universe (do not tell them the “observable universe”), based an “infinitely small point,” or the universe is both the size of a grapefruit, “as if the true model for all the world. The infinite universe is not even considered, then the questions on density can be ignored. The problem here, because there are actually two infinities in competition with one another: It is the infinite amount of space together, and it is the removal or compaction infinite, the singularity represented by big Bang. How you reduce an infinite space, it is always infinite. On the other hand, any finite region may, in infinite space, no matter how much gets compressed into a single point after the Big Bang. He ‘ there is no conflict between the two infinities so long to give you only what it is that you speak.
The problem is not in the display, the hard truth is logical that an infinite space is infinite and that the Big Bang endless for an area, even if it can be described as a benchmark in terms of area finite space can be a finite singularity.
Even Einstein introduced the cosmological constant to obtain a static universe before the detection of Hubble redshift. He seems to have thought that the positive overall geometry of space-time curve for not necessarily linked to a dynamic evolution of the universe. It’s always a possibility. three-dimensional space can still outside as a hetero-intrinsic curvature of the fate of the universe gravity considered: non-Euclidean, without the need for time or something like a fourth dimension to be extrinsically curved in the reference memory. This provides a finished Big Bang, whatever the fate of the dynamic universe, where fate is linked to the effects of the curvature of the time locally, but globally positive Lobachevskian curves may or Euclidean. But a theory of hetero overall curvature is then the mathematical theory of relativistic gravity separation and a metaphysical theory of cosmology more than a theory of physical cosmology.
A positive universe right curve that reaches the most commonly used cosmological model suit everyone: the inflation of the balloon, where the movement of the spherical model of the non-Euclidean geometry added. The surface of the balloon remains spherical regardless of whether the ball is getting blown or if she can eventually deflate. As a model of the ball which is actually put in five dimensions, with the surface, the three dimensions of space, time and the fourth, but fifth is the third spatial dimension, in the curved surface, whereby the surface moves in time. A positive universe curved lines, but not necessary that the fifth dimension. Would non-Euclidean space without higher dimensions, although along a schedule that moves local ortho-folded in a space-time seems right curve, due to the curvature of the time. The ball model can represent a different kind of theory, as expected, but very suggestive, where the overall structure of the universe homogeneous and isotropic we allow an infinite Big Bang is independent to avoid the fate of the dynamic world and realize the hope of the philosopher Kant, Einstein replied antinomy of space.
§ 4 Conclusion
Just because the calculation does not work, we understand what happens in nature. Any physical theory is a mathematical component, and a conceptual component, but these two are often confused. Many speak as if the component provides an understanding of mathematics, they are even after decades of the beautiful mathematics of quantum mechanics apparently little understanding. The mathematical theory of gravitation Newton were beautiful and well over two centuries, but they do not convey the understanding of what was the force of gravity. Now we even have two contradictory ways of understanding the gravity, or by the geometric method of Einstein or by the interaction of virtual particles in quantum mechanics.
However, there is often a kind of voluntary Know Nothing-ism that mathematics is the explanation. It is not. Instead, contains all the theory that assigns a conceptual interpretation of the meaning of mathematical expressions.

Why?

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MISS UNIVERSE 2007

By Alejandro Guevara Onofre

MISS UNIVERSE 2000

SITE: Nicosia, Cyprus.

HISTORY. Representatives from 79 countries, territories and dependencies attended the Miss Universe contest. Certainly, India became the most powerful country in the Beauty World. Miss India, Lara Dutta, has all the qualities to be a Miss Universe-intelligence, beauty, personality, charisma and determination. Finally, Ms. Dutta was the new Miss Universe. It was one of her lifelong dreams to become Miss Universe. Few misses have had careers as long and varied as Lara Dutta.

In a career of more than seven years, she has been professional model, ambassador and actress. Lara once said, “Winning the Miss Universe title is the culmination of a dream”.

Like Miss Universe 2000, she went to Saint Marteen, Puerto Rico, USA, Colombia, Thailand, Malaysia, Japan, Switzerland, Venezuela, Mexico, Indonesia and the United Arab Emirates. Ms. Dutta became well-known to millions as a women’s rights activist in India. Lara Dutta was one of the best known misses of the 21st century.

MISS UNIVERSE 2001

SITE: Bayamon, Puerto Rico.

HISTORY. Representatives from 77 countries and dependencies attended the Miss Universe. Osmel Sousa, president of Miss Venezuela Organization, wanted to win the Miss Universe title. People who have worked with him say he’s a perfectionist preparing carefully for each project. He is a very private man, who rarely gives interviews.

At the onset, Venezuela’s Eva Monica Ekvall Johnson was the favorite by experts and journalists. Miss Venezuela reached the finals, but surprisingly, she only came in fourth place. Many people felt that the decision was unfair.

A Puerto Rican won the Miss Universe contest again. Like Margarita Moran (Miss Philippines and Miss Universe 1973) and Janelle Penny Commissiong (Miss Trinidad Tobago and Miss Universe), Miss Puerto Rico, Denisse Quiñones, was crowned also Miss Photogenic Universe.Denisse’s ambition was to become a professional singer.

MISS UNIVERSE 2002

SITE: San Juan de Puerto Rico.

HISTORY. San Juan de Puerto Rico hosted the pageant.

The favorites were Colombia (Vanesa Alexandra Mendoza Bustos), India (Neha Dhupia), Panama (Justine Paseak), China (Zhuo Ling), and Russia (Oksana Federova).All made the semi-finalists except for Colombia. Ms.Mendoza became the first black woman to be named Miss Colombia. Miss Colombia will always be remembered as the first black woman representing her country in this contest.

For the first time since 1990, communist bloc sent a Miss China to compete in the Miss Universe. Ironically, Miss Cuba pageant has been forbidden since 1960 by Cuban dictatorship.

At the onset, China’s Zhuo Ling was one of the most popular delegates. Finally, Miss China was the 1st runner-up.

Russia´s Oxana Federova was elected Miss Universe. However, she was obligated to give back the title of Miss Universe. Ms. Federova was a controversial woman. Certainly, her popularity declined in her own country.

During the next months in New York City, Miss Panama, Justine Lissette Pasek Patiño, was crowned Miss Universe 2002. Ms. Pasek was long considered one of the most intelligent women in the Miss Universe history. Panama’s Justine Paseak was born in Kharkov, Ukrania. She had a very happy childhood there with her parents. Next years, her family moved to Panama City. Justine had several years experience as professional model.

MISS UNIVERSE 2003

SITE: Panama City, Panama.

HISTORY. For the second time, Panama City hosted the pageant. One of the most enthusiastic fans was Panamanian president Mireya Elisa Moscoso Rodriguez. On September1, 1999, Mireya Moscoso became Panama’s first female head of state.

The favorites were Miss Dominican Republic (Amelia Vega), Miss Japan (Miyako Miyazaki), Miss Brazil (Gislaine Rodrigues Ferreira) and the Miss USA (Susie Castillo Cintrom). Ms. Castillo has Puerto Rican descent. Miss Japan was undoubtedly one of the great beauties of the 2000s.

Under the leadership of two Venezuelans, Miss Dominican Republic became Miss Universe. Amelia Vega became Dominican Republic’s first Miss Universe. For the first time since 1992, Miss India did not qualify for the semi-finals.

Like Miss Universe 2003, she went to Indonesia, Puerto Rico, Mexico, Ecuador, Thailand, Vietnam, Guyana, USA, India, Saint Maarten and the People’s Republic of China.

MISS UNIVERSE 2004

SITE: Quito, Ecuador.

HISTORY. Ecuadorian newspapers reported that misses Ukraine (Okelsandra Nikolayenko), Venezuela (Ana Karina Añez Delgado), Australia (Jennifer Hawkins), USA (Shandi Ren Finnessey), Paraguay (Yanina Alicia Gonzalez Jorgge), and Ecuador(Susana Rivadeneira Simbal) were the most favored to win the contest.

Surprisingly, Miss Ukraine did not enter the semi-finals. Before she went to Ecuador, Okelsandra Nikolayenko competed in Miss World 2001, where she was semi-finalist. Venezuela’s Ana Añez admired Mahatma Gandhi. “Mahatma Gandhi has been a big influence in my life thanks to his political and religious influence he gave to the world”, she said.

For the first time since 1982, Miss Venezuela did not qualify for the semi-finals. It was sadness for Venezuela’s Osmel Sousa. He once said: “If Venezuela does not make it in the finals, I will have a heart attack!”

Miss Australia was elected Miss Universe. She became Australia’s second Miss Universe. The next day her photo was see all over the world and from that moment the name Jennifer Hawkins was known everywhere. Ms. Hawkins is perhaps the most beautiful woman in Miss Australia history.

The judges were Petra Nemcova (Czech fashion model), Monique Menniken (German fashion model), Elsa Benitez (Mexican super-model), Bo Derek (American actress), Bill Rancic (American entrepreneur), Anne Martin (vice-president of Global Cosmetics and Marketing of Proctor & Gamble Cosmetics), Emilio Estefan (music producer), Jon Tutolo (president of Trump Model Management), and Jefferson Perez ( 1996 Ecuadorian Olympic gold medalist).

MISS UNIVERSE 2005

SITE: Bangkok, Thailand.

HISTORY. Among the most popular delegates in the pageant were Canada’s Natalie Glebova, Dominican Republic´s Renata de Jesus Soñe Savery, Mexico’s Laura Elizondo Erhard, Venezuela’s Monica Spear, India’s Amrita Thapar, South Africa´s Claudia Henkel, and Switzerland’s Fiona Hefti.

A naturalized Canadian citizen who was born in Russia and came to Canada, Natalie Glebova was elected Miss Canada and Miss Universe 2005.Her beauty was loved by millions of people. She became well-known to millions as an anti-AIDS activist in the Third World.

The judges were Carson Kressley(American designer), Cassie Lewis (American model), Bryan Dattilo (American actor), Jean Georges Vongerichten (French chef), Okelsandra Nikolayenko (actress and former Miss Ukraine), Porntip “Bui” Nakhirunkanok (former Miss Thailand and Miss Universe 1988), Mario Cimarro (Mexican actor), Anne Martin (vice-president of Global Cosmetics and Marketing of Proctor & Gamble Cosmetics) Kevin S. Bright (American television executive producer), Heidi Albertsen (Danish model), and Khun Rom Pakdi (Thai actor).

Like Miss Universe 2005, she went to Greece, Canada, India, USA, Thailand, Indonesia, Singapore, Ecuador and Brazil.

MISS UNIVERSE 2006

SITE: Los Angeles, California (USA).

HISTORY. At the onset, Japan’s Kurara Chibana was the favorite. Like Miss Japan 2003, Miyako Miyazaki, she was a beautiful exotic girl from Okinawa, the birthplace of the karate. Certainly, Miss Japan had several fans. However, Miss Puerto Rico,Zuleyka Rivera, made history by becoming the fifth Puerto Rican winner of the contest. She was one of the most famous models in her country. During the Miss Universe, Miss Puerto Rico was bilingual in English and Spanish.

Miss Universe 2006 was dominated by Latin America: Puerto Rico, Paraguay, Bolivia, Colombia, Mexico and Trinidad-Tobago.

The judges were Amelia Vega (former Miss Dominican Republic and Miss Universe), Marc Cherry (American writer), Claudia Jordan (Miss Rhode Island 1997), Tom Green (Canadian sock comic), Emmitt Smith (former American football player), James Lesure (American actor), Maria Celeste Arrras (Puerto Rican journalist), Patrick McMullan (American designer), Santino Rice (American fashion designer), Bridgette Wilson-Sampras (actress and former Miss Teen USA) and Sean Yazbeck (British actor).

MISS UNIVERSE 2007

SITE: Mexico City, Mexico

HISTORY: Representatives from 77 countries attended the Miss Universe pageant.

The favorites are Venezuela´s Ly Jonaites, Tanzania´s Flavia Matata, South Korea’s Honey Lee, Japan’s Riyo Mori, and Philippines’s Ana Therese Licaros.

Miss Venezuela is a fashion model. She has gorgeous brown hair, kind brown eyes and beautiful smile which lights up her whole face. Furthermore, she speaks three languages. She admires Princess Diana Spencer. Her dream is to become fashion designer. She once said, “I plan to be a fashion designer and have my own boutique expressing my personality through my art”. Certainly, Ly Jonaites is one of the best delegates in the Miss Universe history.

The judges are Nave Navarro (singer/American-Mexican), Tony Romo (Professional football player/American-Mexican), James Kyson Lee (actor/American-Korean), Justine Pasek (former Miss Panama and Miss Universe), Adel Chabbi (stylist/French-Tunisie), Dimitris Margetas (American-Greek/ charge of Consumer Marketing for Proctor & Gamble´s Prestige Products Inc), Marc Bouwer (American fashion designer), Dayanara Torrres (former Miss Puerto Rico and Miss Universe), Fred Howard (American-African fashion designer), Thuy Than (American-Vietnamese fashion photographer), Michelle Kwan (American-Chinese sportswoman), Nina Garcia (American-Colombian journalist), Leigh Rossini (American publicist) and Lindsay Clubine (American fashion model).