In mathematics , a periodic sequence (sometimes called a cycle or orbit ) is a sequence for which the same terms are repeated over and over:
54-668: The Ox ( 牛 ) is the second of the 12-year periodic sequence (cycle) of animals which appear in the Chinese zodiac related to the Chinese calendar , and also appears in related calendar systems. The Chinese term translated here as ox is in Chinese niú ( 牛 ), a word generally referring to cows, bulls, or neutered types of the bovine family, such as common cattle or water buffalo . The zodiacal ox may be construed as male, female, neutered, intersex (formerly referred to as hermaphroditic), and either singular or plural. The Year of
108-424: A day in relation to the sign of the zodiac that included the sun when the person was born. Astrologers refer to this as the "sun sign", but it is often commonly called the "star sign". These predictions are vague or general; so much so that even practicing astrologers consider them of little to no value on their own. Experiments have shown that when people are shown a newspaper horoscope for their own sign along with
162-414: A form of divination based on the construction of a horoscope for an exact moment, such as a person's birth as well as location (since time zones may or may not affect a person's birth chart), in which various cosmic bodies are said to have an influence. Astrology in western popular culture is often reduced to sun sign astrology , which considers only the individual's date of birth (i.e. the "position of
216-419: A newspaper horoscope for a different sign, they judge them to be equally accurate on the average. Other tests have been performed on complete, personalized horoscopes cast by professional astrologers, and have shown no correlation between the horoscope results and the person it was cast for. In modern Western astrology the planets represent basic drives or impulses in the human psyche. These planets differ from
270-513: A particular significance to them. Over time they developed the system of twelve signs of the zodiac, based on twelve of the constellations through which the sun passes throughout the year, those constellations that are "Enlightened by the mind". Most western astrologers use the tropical zodiac beginning with the sign of Aries at the Northern Hemisphere vernal equinox always on or around March 21 of each year. The Western Zodiac
324-565: A pattern of proportion. An early example is Ptolemy, who wrote influential texts on all these topics. Al-Kindi , in the 9th century, developed Ptolemy's ideas in De Aspectibus which explores many points of relevance to astrology and the use of planetary aspects. The zodiac is the belt or band of constellations through which the Sun, Moon, and planets move on their journey across the sky. Astrologers noted these constellations and so attached
378-555: A repeating cycle of five years of the ox/cow (over a sixty-year period), each ox/cow year also being associated with one of the Chinese wǔxíng , also known as the "five elements", or "phases": the "Five Phases" being Fire ( 火 huǒ ), Water ( 水 shuǐ ), Wood ( 木 mù ), Metal ( 金 jīn ), and Earth ( 土 tǔ ). The Year of the Ox follows after the Year of the Rat (the first year of
432-470: A repeating cycle of five years of the ox/cow (over a sixty-year period), each ox/cow year also being associated with one of the Chinese wǔxíng, also known as the "five elements", or "phases": the "Five Phases" being Fire (火 huǒ), Water (水 shuǐ), Wood (木 mù), Metal (金 jīn), and Earth (土 tǔ). The Year of the Ox follows after the Year of the Rat (the first year of the zodiacal cycle) which happened in 2020 and it then
486-458: A single organism , all parts of which are correlated with each other. Cycles of change that are observed in the heavens are therefore reflective (not causative) of similar cycles of change observed on earth and within the individual. This relationship is expressed in the Hermetic maxim "as above, so below; as below, so above", which postulates symmetry between the individual as a microcosm and
540-408: Is p -periodic is called its least period or exact period . Every constant function is 1-periodic. The sequence 1 , 2 , 1 , 2 , 1 , 2 … {\displaystyle 1,2,1,2,1,2\dots } is periodic with least period 2. The sequence of digits in the decimal expansion of 1/7 is periodic with period 6: More generally, the sequence of digits in
594-674: Is a periodic sequence. Here, f n ( x ) {\displaystyle f^{n}(x)} means the n -fold composition of f applied to x . Periodic points are important in the theory of dynamical systems . Every function from a finite set to itself has a periodic point; cycle detection is the algorithmic problem of finding such a point. Any periodic sequence can be constructed by element-wise addition, subtraction, multiplication and division of periodic sequences consisting of zeros and ones. Periodic zero and one sequences can be expressed as sums of trigonometric functions: One standard approach for proving these identities
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#1732790467119648-416: Is called the period ( period ). A (purely) periodic sequence (with period p ), or a p- periodic sequence , is a sequence a 1 , a 2 , a 3 , ... satisfying for all values of n . If a sequence is regarded as a function whose domain is the set of natural numbers , then a periodic sequence is simply a special type of periodic function . The smallest p for which a periodic sequence
702-465: Is drawn based on the Earth's relationship to fixed, designated positions in the sky, and the Earth's seasons. The Sidereal Zodiac is drawn based on the Earth's position in relation to the constellations, and follows their movements in the sky. Due to a phenomenon called precession of the equinoxes (where the Earth's axis slowly rotates like a spinning top in a 25,700-year cycle), there is a slow shift in
756-538: Is followed by the Year of the Tiger which happened in 2022. The term " zodiac " reflects similarities and differences with the Western zodiac . Both similarly have cycles divided into twelve parts, with at least the majority of those parts named for animals, and each is widely associated with an ascription of a person's personality or events in their life to a supposed influence of the person's particular relationship to
810-586: Is the strength of a planet or point's zodiac position, judged only by its position by sign and degree, what the pre-eminent 17th-century astrologer William Lilly called "the strength, fortitude or debility of the Planets [or] significators." In other words, essential dignity seeks to view the strengths of a planet or point as though it were isolated from other factors in the sky of the natal chart . Traditionally, there are five dignities: domicile and detriment, exaltation and fall, triplicity, terms, and face. However,
864-496: Is to apply De Moivre's formula to the corresponding root of unity . Such sequences are foundational in the study of number theory . A sequence is eventually periodic or ultimately periodic if it can be made periodic by dropping some finite number of terms from the beginning. Equivalently, the last condition can be stated as a k + r = a k {\displaystyle a_{k+r}=a_{k}} for some r and sufficiently large k . For example,
918-505: The Arabic parts . Various techniques are used, with different degrees of complexity, to provide what astrologers claim are forecasts or predictive statements about the future, as well as to analyse past and current events. These include transits , progressions , and primary directions . Different branches of astrology, such as horary and electional astrology, have their own specific sets of techniques. There are four primary angles in
972-478: The Twenty-Eight Mansions . Because the moon during its monthly cycle could be observed to appear to move from one mansion (or "camp") into the next each night in turn, they are also known as Lunar Mansions. Traditionally, these mansions were divided into four groups of seven each, and associated with one of four spiritual entities . This is applicable to the Year of the Ox, Chǒu (丑), a sign linked to
1026-526: The moon 's path crosses the ecliptic . The North, or Ascending Node marks the place where the moon crosses from South to North (or ascends), while the South, or Descending Node marks where the moon crosses from North to South (or descends). While Lunar nodes are not considered by Western astrologers to be as important a factor as each of the planets, they are thought to mark sensitive areas that are worth taking into account. In astrology, "essential dignity"
1080-424: The "Year of the Ox", while bearing the following elemental phase sign: In traditional Chinese astrology as well as traditional Chinese astronomy the sky was mapped into various asterisms or what are sometimes referred to as Chinese constellations . This is actually more similar to the zodiac of Western astrology than is the 12 animal cycle. The stars along the plane of the ecliptic divide into groups known as
1134-474: The Chinese zodiac related to the Chinese calendar, and also appears in related calendar systems. The Chinese term translated here as ox is in Chinese niú (牛), a word generally referring to cows, bulls, or native varieties of the bovine family, such as the water buffalo in South-East Asia. The zodiacal ox may be construed as male, female, neutered, hermaphroditic, and either singular or plural. The Year of
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#17327904671191188-547: The Ox is also denoted by the Earthly Branch symbol chǒu ( 丑 ). The term " zodiac " ultimately derives from an Ancient Greek term referring to a "circle of little animals". There are also a yearly month of the ox and a daily hour of the ox ( Chinese double hour , 1:00 a.m. to 3:00 a.m.). Years of the oxen (cows) are cyclically differentiated by correlation to the Heavenly Stems cycle, resulting in
1242-532: The Ox is also denoted by the Earthly Branch symbol chǒu (丑). The term "zodiac" ultimately derives from an Ancient Greek term referring to a "circle of little animals". There are also a yearly month of the ox and a daily hour of the ox (Chinese double hour, 1:00 a.m. to 3:00 a.m.). Years of the oxen (cows) are cyclically differentiated by correlation to the Heavenly Stems cycle, resulting in
1296-497: The Sun" at that date). Astrology is a pseudoscience and has consistently failed experimental and theoretical verification. Astrology was widely considered a respectable academic and scientific field before the Enlightenment , but modern research has found no consistent empirical basis to it. A central principle of astrology is integration within the cosmos. The individual, Earth, and its environment are viewed as
1350-581: The Tropical approach is that when we say the Sun or a planet is in a certain zodiac sign, observation of it in the sky will show that it does not lie within that constellation at all. As the Earth spins on its axis, it "wobbles" like a top, causing the vernal equinox to move gradually backwards against the star background, (a phenomenon known as the Precession of the equinoxes ) at a rate of about 30 degrees (one Zodiacal sign length) every 2,160 years. Thus
1404-408: The ancients. The Sun and Moon, also known as 'the lights', are included as they were thought to act like the astronomical planets. Astrologers call inner planets Mercury, Venus and Mars, the 'personal planets', as they represent the most immediate drives. The 'lights' symbolise respectively the existential and sensitive fundamentals of the individuality. The following table summarizes the rulership by
1458-416: The angular distance along the ecliptic in degrees and minutes of celestial longitude between two points, as viewed from the earth. They indicate focal points in the horoscope where the energies involved are given extra emphasis. The more exact the angle, the more powerful the aspect, although an allowance of a few degrees each side of the aspect called an orb is allowed for interpretation. The following are
1512-401: The ascendant in the west is the descendant , which denotes how a person reacts in their relationships with others. It also show the kind of person we are likely to be attracted to, and our ability to form romantic attachments. In most house systems the descendant lies on the cusp of the 7th house of the horoscope. The opposite point to the midheaven is known as the imum coeli . For astrologers
1566-408: The aspects in order of importance: The majority of professional astrologers rely on performing astrology-based personality tests and making relevant predictions about the remunerator's future. Those who continue to have faith in astrology have been characterised as doing so "in spite of the fact that there is no verified scientific basis for their beliefs, and indeed that there is strong evidence to
1620-437: The celestial environment as a macrocosm. As opposed to Sidereal astrology, Western astrology evaluates a person's birth based on the alignments of the stars and planets from the perspective on earth instead of in space. At the heart of astrology is the metaphysical principle that mathematical relationships express qualities or 'tones' of energy which manifest in numbers, visual angles, shapes and sounds – all connected within
1674-475: The celestial region of the Black Warrior , or Xuánwǔ , linked to the stars of Beta Tauri , in modern astronomy . Main Chinese tradition divided the hours of a day-night period into 12 double-hours . Each of these double-hours corresponds with one of the twelve signs of the Chinese zodiac , with similar symbolic motif and astrological significance. The first of the twelve double hours is midnight (at
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1728-493: The contrary". Astrology has not demonstrated its effectiveness in controlled studies and has no scientific validity, and as such, is regarded as pseudoscience . There is no proposed mechanism of action by which the positions and motions of stars and planets could affect people and events on Earth that does not contradict well understood, basic aspects of biology and physics. Where astrology has made falsifiable predictions, it has been falsified. The most famous test
1782-835: The correspondence between Earth's seasons (and calendar) and the constellations of the zodiac. Thus, the tropical zodiac corresponds with the position of the earth in relation to fixed positions in the sky (Western Astrology), while the sidereal zodiac is drawn based on the position in relation to the constellations (sidereal zodiac). In modern Western astrology the signs of the zodiac are believed to represent twelve basic personality types or characteristic modes of expression. The twelve signs are divided into four elements fire , earth , air and water . Fire and air signs are considered masculine, while water and earth signs are considered feminine. The twelve signs are also divided into three qualities, also called modalities, Cardinal , fixed and mutable . Zodiac sign for an individual depends on
1836-655: The cycle. A major difference between the two is that the animals of the Chinese zodiac are not associated with constellations spanned by the ecliptic plane (that is, the part of the sky through which the Sun appears to move from the perspective of Earth). The Chinese/East Asian 12-part cycle corresponds to years, rather than months. The ox of the Chinese zodiac has a long history. In Chinese mythology, many myths about oxen or ox-like entities include celestial and earthly beings. The myths range from ones which include oxen or composite beings with ox characteristics as major actors to ones which focus on human or divine actors, in which
1890-396: The decimal expansion of any rational number is eventually periodic (see below). The sequence of powers of −1 is periodic with period two: More generally, the sequence of powers of any root of unity is periodic. The same holds true for the powers of any element of finite order in a group . A periodic point for a function f : X → X is a point x whose orbit
1944-473: The definition of a planet in astronomy in that the Sun, Moon, and recently, Pluto are all considered to be planets for the purposes of astrology. Each planet is also said to be the ruler of one or two zodiac signs. The three outer planets (Uranus, Neptune, Pluto) have each been assigned rulership of a zodiac sign by astrologers. Traditionally rulership of the signs was, according to Ptolemy , based on seasonal derivations and astronomical measurement, whereby
1998-412: The fact that the ascendant is specific to a particular time and place, it signifies the individual environment and conditioning that a person receives during their upbringing, and also the circumstances of their childhood. For this reason, the ascendant is also concerned with how a person has learned to present themself to the world, especially in public and in impersonal situations. The opposite point to
2052-450: The heavens from that moment throughout its life. The most common form of horoscope is the natal chart based on the moment of a person's birth; though in theory a horoscope can be drawn up for the beginning of anything, from a business enterprise to the foundation of a nation state. In Western horoscopic astrology the interpretation of a horoscope is governed by: Some astrologers also use the position of various mathematical points, such as
2106-399: The horoscope (though the cusps of the houses are often included as important angles by some astrologers). The ascendant is generally considered the most important and personalized angle in the horoscope by the vast majority of astrologers. It signifies a person's awakening consciousness, in the same way that the Sun's appearance on the eastern horizon signifies the dawn of a new day. Due to
2160-453: The houses in the horoscope or birth chart. However, there is no dispute about their meanings, and the 12 houses Many modern astrologers assume that the houses relate to their corresponding signs, i.e. that the first house has a natural affinity with the first sign, Aries, and so on. The aspects are the angles the planets make to each other in the horoscope, and also to the ascendant, midheaven, descendant and nadir. The aspects are measured by
2214-404: The later two have diminished in usage. A planet's domicile is the zodiac sign over which it has rulership. Western astrology is based mainly upon the construction of a horoscope , which is a map or chart of the heavens at a particular moment. The moment chosen is the beginning of the existence of the subject of the horoscope, as it is believed that the subject will carry with it the pattern of
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2268-420: The luminaries being the brightest planets were given rulership of the brightest months of the year and Saturn the coldest furthest classical planet was given to the coldest months of the year, with the other planets ruling the remaining signs as per astronomical measurement. It is noteworthy that the modern rulerships do not follow the same logic. The astrological 'planets' are the seven heavenly bodies known to
2322-673: The middle of the double-hour), corresponding with 11:00 p.m. to 1:00 a.m.: this is the Hour of the Rat. The second and next double-hour is the Hour of the Ox: 1:00 a.m. to 3:00 a.m.; that is the double-hour chǒu ( 丑 ). In the Vietnamese zodiac , the water buffalo occupies the position of the Ox. In Nepal, the Tamu/ Gurung people celebrate the year of the cow . Periodic sequence The number p of repeated terms
2376-462: The nadir or IC traditionally indicates the circumstances at the beginning and end of a person's life, their parents and the parental home, and their own domestic life. In quadrant house systems it lies on the cusp of the 4th house of the horoscope. The horoscope is divided by astrologers into 12 portions called the houses. The houses of the horoscope are interpreted as being 12 different spheres of life or activity. There are various ways of calculating
2430-446: The namesakes of the twelve-year cycle. The race was run, and swum, the finishing line being across a great river. The Rat and the Ox crossed easily enough, the Ox due to being large, powerful, and adept both on land and in water: the Rat asked the good-natured Ox for a ride on its back, but then ungratefully jumped off at the last minute to cross the finish line first. People born within these date ranges can be said to have been born in
2484-454: The periodic sequence 0, 1, 0, 1, 0, 1, .... Western astrology Western astrology is the system of astrology most popular in Western countries. Western astrology is historically based on Ptolemy 's Tetrabiblos (2nd century CE), which in turn was a continuation of Hellenistic and ultimately Babylonian traditions. Western astrology is largely horoscopic , that is, it is
2538-472: The placement of planets and the ascendant in that sign. If a person has nothing placed in a particular sign, that sign will play no active role in their personality. On the other hand, a person with, for example, both the sun and moon in Cancer, will strongly display the characteristics of that sign in their make up. Newspapers often print astrology columns which purport to provide guidance on what might occur in
2592-457: The role of the oxen are more subsidiary. In some cases, Chinese myths focus on oxen-related subjects, such as plowing and agriculture or ox-powered carriage. Another important role for beef cattle is in the religious capacity of sacrificial offerings. Chinese mythology intersects with the idea of the zodiacal ox. According to some old mythological traditions there was a race held by a great deity to determine which creatures, in which order, would be
2646-459: The sequence of digits in the decimal expansion of 1/56 is eventually periodic: A sequence is asymptotically periodic if its terms approach those of a periodic sequence. That is, the sequence x 1 , x 2 , x 3 , ... is asymptotically periodic if there exists a periodic sequence a 1 , a 2 , a 3 , ... for which For example, the sequence is asymptotically periodic, since its terms approach those of
2700-471: The seven classically known planets of each of the twelve astrological signs, together with their effects on world events, people and the earth itself as understood in the Middle Ages. These are the planets discovered in modern times, which have since been assigned meanings by Western astrologers. There are two camps of thought among western astrologers about the "starting point", 0 degrees Aries, in
2754-476: The two zodiacs would be aligned only once every 26,000 years. They were aligned about 2,000 years ago when the zodiac was originally established. This phenomenon gives us the conceptual basis for the Age of Aquarius , whose "dawning" coincides with the movement of the vernal equinox across the cusp from Pisces to Aquarius in the star background. Also important in astrology are the moon's nodes . The nodes are where
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#17327904671192808-413: The zodiac (with some variations) has been popular for a long time in many East Asian countries, such as Japan, South Korea, Vietnam, Cambodia, and Thailand. The ox symbolizes diligence and patience. The people with this age have progressed steadily and owns persistent strength. They are very determined but stubborn. The Ox (牛) is the second of the 12-year periodic sequence (cycle) of animals which appear in
2862-491: The zodiac. Sidereal astrology uses a fixed starting point in the background of stars, while tropical astrology , used by the majority of Western astrologers, chooses as a starting point the position of the Sun against the background of stars at the Northern hemisphere vernal equinox (i.e. when the Sun position against the heavens crosses over from the southern hemisphere to the northern hemisphere) each year. The consequence of
2916-414: The zodiacal cycle) which happened in 2020 and is then followed by the Year of the Tiger , which happened in 2022. The term "zodiacal" refers to the classification scheme based on the lunar calendar that assigns an animal and its reputed attributes to each year in a repeating 12-year cycle. The 12-year cycle is an approximation to the 11.85-year orbital period of Jupiter. Originating from China, this form of
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