The ecliptic, or the apparent path of the Sun, is defined by the circular path of the Sun across the sky, as seen from Earth. In other words, the Sun appears to pass through these constellations over the course of a year. The passage of the Sun through the zodiac is a cycle that was used by ancient cultures to determine the time of year.Pronosoft pmg du mali
Most of the planets in the solar system have orbits that take them near the ecliptic plane, within about 8 degrees above or below. The 12 constellations in the zodiac family can all be seen along the ecliptic. The Sun also passes through Ophiuchus and Cetusbut these constellations are not part of the zodiac, but belong to the Hercules and Perseus families respectively.
The northern zodiac constellations — PiscesAriesTaurusGeminiCancer and Leo — are located in the eastern celestial hemisphere, while the southern — VirgoLibraScorpiusSagittariusCapricornus and Aquarius — are found in the west.
Today, the term zodiac is mostly associated with astrology, with the 12 signs of the western zodiac corresponding to the 12 constellations seen along the ecliptic. The so-called cardinal signs AriesCancerLibra and Capricorn mark the beginning of the four seasons, i. The constellations represent the astrological signs of the zodiac.
The image was taken from the Atlas Coelestis. The largest of the 12 zodiac constellations is Virgowhich covers Virgo is also the second largest of all 88 constellations, only slightly smaller than Hydra. Covering an area of Also located in the southern celestial hemisphere, Aquarius represents Ganymede, the cup bearer to the Olympian gods in Greek mythology. Leothe third largest zodiac constellation, occupies an area of It represents the Nemean lion, a mythical monster killed by Heracles as part of his 12 labours.
Pisces comes in 4th with Libra In terms of brightness, several of the 12 constellations contain some of the brightest stars in the sky. Aldebaranthe brightest star in Taurusis the 14th brightest of all stars, followed by Spicathe brightest star in Virgo and 15th brightest star in the sky, Antaresthe bright red supergiant in Scorpius and 16th brightest star, Pollux in Geminithe 17th brightest of all stars, and Regulus in Leowhich comes in 21st overall.
Today, zodiac constellations are most commonly brought up in the context of western astrology, as the 12 constellations correspond to the 12 signs of the zodiac. They are groups of stars that appear to be close to each other, arbitrarily named after different objects, animals, or figures from mythology by human observers at some point in history.
Constellations make a two-dimensional map of the sky used for orientation, to make it easier for astronomers to find objects and explain their location and for navigators to use stars to determine their position. While even Carl Gustav Jung said that astrology holds some value as a theory of the personality, and it can use the scientific approach, it is in itself not based on any kind of science.
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We investigate arithmetical properties of a class of semigroups that includesthose appearing as Weierstrass semigroups at totally ramified points of coveringof curves. Semigroup Forum — Springer Journals. Enjoy affordable access to over 18 million articles from more than 15, peer-reviewed journals.
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Not necessarily. Each constellation is a collection of stars that are distributed in space in three dimensions — the stars are all different distances from Earth. The stars in a constellation appear to be in the same plane because we are viewing them from very, very, far away. Stars vary greatly in size, distance from Earth, and temperature. Dimmer stars may be smaller, farther away, or cooler than brighter stars.
By the same token, the brightest stars are not necessarily the closest. Of the stars in Cygnus, the swan, the faintest star is the closest and the brightest star is the farthest!Super Stars (Constellations): Crash Course Kids #31.1
How are constellations named? Most of the constellation names we know came from the ancient Middle Eastern, Greek, and Roman cultures. They identified clusters of stars as gods, goddesses, animals, and objects of their stories. It is important to understand that these were not the only cultures populating the night sky with characters important to their lives.
Cultures all over the world and throughout time — Native American, Asian, and African — have made pictures with those same stars. In some cases the constellations may have had ceremonial or religious significance. In other cases, the star groupings helped to mark the passage of time between planting and harvesting.
There are 38 modern constellations. In the International Astronomical Union officially listed 88 modern and ancient constellations one of the ancient constellations was divided into 3 parts and drew a boundary around each.
The boundary edges meet, dividing the imaginary sphere — the celestial sphere — surrounding Earth into 88 pieces. Astronomers consider any star within a constellation boundary to be part of that constellation, even if it is not part of the actual picture.
All stars, however, fall within the boundaries of one of the 88 constellation regions. You can see some of these stars by observing the sky on a dark night. If you look at the sky with binoculars, you will see even more stars. If you have a telescope, you will see even more!
How are stars and other objects in the sky named and located? Hundreds of the brightest stars, those visible with the unaided eye, were given names in ancient times. Many of these stars have multiple names, having been observed by different cultures. Today stars are named by their coordinates on the celestial sphere.
This is an imaginary sphere surrounding Earth. Polaris marks the intersection of the extended north pole and the sphere. All stars and objects in space, such as constellations, can be mapped relative to the poles and equator of the celestial sphere. There are numerous catalogs of stars, each with a different scheme for annotating position; this means that each star has even more names!
Another catalog, the Smithsonian Astrophysical Observatory SAO catalog, integrated 10 catalogs to include the positions of overstars. The Hubble Space Telescope has allowed astronomers to see even more stars!In mathematicsthe Weierstrass function is an example of a real-valued function that is continuous everywhere but differentiable nowhere.
It is an example of a fractal curve. It is named after its discoverer Karl Weierstrass. The Weierstrass function has historically served the role of a pathological function, being the first published example specifically concocted to challenge the notion that every continuous function is differentiable except on a set of isolated points. The functions were impossible to visualize until the arrival of computers in the next century, so the proof of the result relied entirely on technically demanding theoretical steps.
The results did not gain wide acceptance until practical applications such as models of Brownian motion necessitated infinitely jagged functions nowadays known as fractal curves. In Weierstrass's original paper, the function was defined as a Fourier series :.
Since each partial sum is continuous, by the uniform limit theoremit follows that f is continuous. Additionally, since each partial sum is uniformly continuousit follows that f is also uniformly continuous.
On the constellations of Weierstrass points
It might be expected that a continuous function must have a derivative, or that the set of points where it is not differentiable should be "small" in some sense.
According to Weierstrass in his paper, earlier mathematicians including Gauss had often assumed that this was true. This might be because it is difficult to draw or visualise a continuous function whose set of nondifferentiable points is something other than a countable set of points. Analogous results for better behaved classes of continuous functions do exist, for example the Lipschitz functionswhose set of non-differentiability points must be a Lebesgue null set Rademacher's theorem.
When we try to draw a general continuous function, we usually draw the graph of a function which is Lipschitz or otherwise well-behaved. The Weierstrass function was one of the first fractals studied, although this term was not used until much later.
The function has detail at every level, so zooming in on a piece of the curve does not show it getting progressively closer and closer to a straight line. Rather between any two points no matter how close, the function will not be monotone. The term Weierstrass function is often used in real analysis to refer to any function with similar properties and construction to Weierstrass's original example. For example, the cosine function can be replaced in the infinite series by a piecewise linear "zigzag" function.Coca cola customer complaints
It turns out that the Weierstrass function is far from being an isolated example: although it is "pathological", it is also "typical" of continuous functions:. The derivative of a function of a real variable measures the sensitivity to change of the function value with respect to a change in its argument.
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