The seven stars in the upper-left corner of Ursa Major form an called the Big Dipper (or the Plough in Great Britain). This group has been recognized by almost all groups of people who live or lived in places where it can be seen in the sky and it is one of the best-known star patterns. The Big Dipper is helpful in finding the north star because an imaginary line drawn through the two stars on the right side will point directly at the north star. These two stars are called The Pointers and they are very important on navigation by stars.
All of the stars in the Big Dipper except Dubhe and Alkaid are moving toward the same point in the sky through proper motion. This group of stars is known as the Ursa Major Moving Group.
Ursa Minor
Ursa Minor is a constellation in the northern sky. It is often called the Little Bear or the Little Dipper. Just like the related constellation Ursa Major, or the Big Bear or Big Dipper, it seems to have a long handle leading to a cup or ladle. The end of the handle is the North Star, called Polaris.
The ancient astronomer Ptolemy included Ursa Minor in his list of 48 constellations. It is now one of the 88 modern constellations. Ursa Minor is special because it includes the north celestial pole. However, this will change after several hundred years because the Earth will change the direction of its axis. That movement is called precession
Ursa Minor is often called the Little Dipper because its seven brightest stars seem to be in the shape of a dipper (ladle or scoop). The star at the end of the dipper handle is Polaris, the North Star.
Polaris is the brightest star in the constellation. It is a 'yellow-white' supergiant shining at 2.02 apparent magnitude. It belongs to an unusual class of stars called Cepheid variables. The brightness of Polaris can change. The second brightest star is β UMi (Kochab). It is a 2.08 orange giant star.
The four stars in the "bowl" of the little dipper are very useful for star watchers. They are of second, third, fourth and fifth magnitude. These stars are an easy guide to knowing what magnitude stars are visible. This is helpful for people who live in cities where light can make dim stars hard to see. It is also a way of testing your eyesight.
There is one dwarf galaxy in the area of the constellation. It is called Ursa Minor Dwarf.
Drawings of Ursa Minor often show it as a baby bear with an unusually long tail. In some stories, the tail is so long because the baby bear was held by the tail and spun around the pole.
Greek mythology connected Ursa Minor and Ursa Major to the story of Callisto and Arcas. However, one older version of the story has Boötes in place of Arcas. In that story Ursa Minor was a dog. This earlier tradition explains both the length of the tail and an older name for Polaris. The North Star used to be called "Cynosura" which means the dog's tail.
In another story from early Greek mythology, the seven stars of the Little Dipper were seven sisters. They were Atlas' daughters, the Hesperides. They were part of a story with the nearby constellations Boötes, Ursa Major, and Draco.
Polaris (star)
Polaris (Alpha Ursae Minoris) is the Pole Star or North Star.
It is the brightest star in the constellation Ursa Minor. It is almost straight above Earth's North Pole. Because of this, when it is seen from Earth, it looks like it always stays in the same place in the sky. For centuries, sailors in the northern hemisphere used Polaris to help them figure out where they were on the ocean and what way they were moving.
Polaris is part of a triple star system. It has a very close dwarf binary, and a larger star, Polaris B, which orbits 2,400 AU away.
The main star, Polaris A, is a giant with 4.5 times the mass of the Sun and a diameter of 45 million kilometers. It is a classic Cepheid variable, the closest to us in the whole Milky Way. Polaris B can be seen even with a modest telescope. It was found by William Herschel in 1780 using one of the most powerful telescopes of the time: his own reflecting telescope. The nearby dwarf star, Ab, was predicted in 1929, but only seen quite recently. The dwarf orbits as close to A as Uranus is to our sun.
Even though Polaris is the North Star today, this has not always been the case. The place in the sky that the Earth's north pole points at changes slowly over time. This movement is called stellar precession. In 3000 BC, a faint star called Thuban in the constellation of Draco was the North Star. Polaris did not become the North Star until about AD 500. It will get closer to straight above the Earth's north pole until sometime in 2102. Then it will move away again. It will be the closest star to the pole until about AD 3000.
Surprisingly, considering its relative nearness, its distance is not yet known for certain. Many recent papers calculate the distance to Polaris at about 434 light-years (133 parsecs). However, some suggest it may be as much as 30% closer. If correct, this would be especially notable because Polaris is the closest Cepheid variable to Earth. Its physical parameters are critical to the whole astronomical distance scale.
There is no star in the southern hemisphere which plays a similar role to Polaris.
Hypercube
In geometry, a hypercube is an "n"-dimensional analogue of a square () and a cube (). It is a closed, compact, convex figure whose 1-skeleton consists of groups of opposite parallel line segments aligned in each of the space's dimensions, perpendicular to each other and of the same length. A unit hypercube's longest diagonal in "n" dimension is equal to formula_1.
An "n"-dimensional hypercube is also called an n"-cube or an n"-dimensional cube. The term "measure polytope" is also used, notably in the work of H. S. M. Coxeter (originally from Elte, 1912), but it has now been superseded.
The hypercube is the special case of a hyperrectangle (also called an "n-orthotope").
A unit hypercube is a hypercube whose side has length one unit. Often, the hypercube whose corners (or "vertices") are the 2 points in R with each coordinate equal to 0 or 1 is called "the" unit hypercube.
A hypercube can be defined by increasing the numbers of dimensions of a shape:
This can be generalized to any number of dimensions. This process of sweeping out volumes can be formalized mathematically as a Minkowski sum: the "d"-dimensional hypercube is the Minkowski sum of "d" mutually perpendicular unit-length line segments, and is therefore an example of a zonotope.
The 1-skeleton of a hypercube is a hypercube graph.
Iron Man 2
Iron Man 2 is a 2010 American superhero film. It is based on the Marvel Comics character Iron Man. It is the sequel to the 2008 film "Iron Man" and the third film for the Marvel Cinematic Universe.
It was directed by Jon Favreau and written by Justin Theroux. It stars Robert Downey, Jr., Gwyneth Paltrow, Don Cheadle, Scarlett Johansson, Sam Rockwell and Mickey Rourke. The story is set six months after the events of "Iron Man". Tony Stark has revealed his identity as Iron Man. He is resisting calls by the United States government to hand over the technology. Ivan Vanko, meanwhile, has developed the same technology and built weapons of his own.
After the successful release of "Iron Man", Marvel Studios announced and immediately set to work on producing a sequel. In July of that same same year, Theroux was hired to write the script. Favreau was signed to return and direct. Downey and Paltrow were to repeat their roles from "Iron Man". Cheadle was brought in to replace Terrence Howard in the role of James Rhodes. In early 2009, Rourke, Rockwell and Johansson completed the supporting cast. The movie went into production that summer. Like its predecessor, the movie was shot mostly in California, except for a key sequence in Monaco.
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