Home About us Products Services Contact us Bookmark
:: wikimiki.org ::
Vedic

Vedic

Vedic may refer to: Hindu scriptures:
- The Vedas, the oldest preserved Indo-Aryan texts
- Vedic Sanskrit, their language
- Vedic religion
- Vedic civilization Hindu culture:
- Vedic astrology
- the Ayurveda (Vedic medicine) Maharishi Mahesh Yogi:
- Vedic science
- Maharishi Vedic Medicine
- World Centre of Vedic Learning Or:
- Vedic mathematics, developed by Shri Bharati Krishna Tirthaji

Vedas

The Vedas (Sanskrit:- वेद), collectively refers to a corpus of ancient Indo Aryan religious literature that are considered by adherents of Hinduism to be revealed knowledge. The word Veda means Knowledge and is cognate with the word "wit" in English (as well as "vision" through Latin). Many Hindus believe the Vedas existed since the beginning of creation. The texts of the Vedas have several references to specific patterns in the ancient flows of the Ganges River, which coincide with the sites of its ancient (but now dried) tributaries. The newest parts of the Vedas are estimated to date back to around 500 BCE. The oldest text (RigVeda) found is now dated to around 1,500 BCE, but most Indologists agree that a long oral tradition possibly existed before it was written down. They represent the oldest stratum of Indian Literature and according to modern scholars are written in forms of a language which evolved into Sanskrit. They consider the use of Vedic Sanskrit for the language of the texts an anachronism, although it is generally accepted.

Contents

The Vedas consist of several kinds of texts, all of which date back to early times. The core is formed by the Mantras which represent hymns, prayers, incantations, magic and ritual formulas, charms etc. The hymns and prayers are addressed to a pantheon of gods (and a few goddesses), important members of which are Shiva, Varuna, Indra, Agni, etc. The mantras are supplemented by texts regarding the sacrificial rituals in which these mantras are used as well as texts exploring the philosophical aspects of the ritual tradition, narratives etc.

Organization

The Mantras are collected into anthologies called Samhitas. There are four Samhitas, the Rk (= Poetry), Sāman (=Song), Yajus(=Prayer) and Atharvan (=A kind of priest) commonly referred to as the Rig Veda, Yajur Veda, Sama Veda and Atharva Veda. Each Samhita is preserved in a number of versions, the differences among them being minor, except in the case of the Yajur Veda, where there are the "Black" (krishna) and "White" (shukla) versions, with the Black also containing explanatory material apart from the Mantras. The Rig Veda contains the oldest part of the corpus, and consists of 1028 hymns. The Sama Veda is mostly a rearrangement of the Rig Veda for musical rendering. The Yajur Veda gives sacrificial prayers and the Atharva Veda gives charms, incantations, magic formulas etc. Apart from these there are some stray secular material, legends, etc. The next category of texts are the Brahmanas. These are ritual texts that describe in detail the sacrifices in which the Mantras were to be used, as well as commenting on the meaning of the sacrificial ritual. The Brahmanas are associated with one of the Samhitas. The Brahmanas may either form separate texts, or in the case of the Black Yajur Veda, can be partly integrated into the text of the Samhita. The most important of the Brahmanas is the Shatapatha Brahmana of the White Yajur Veda. The Aranyakas and Upanishads are theological and philosophical works. They often form part of the Brahmanas (e.g. the Brhadaranyaka Upanishad). They are the basis of the Vedanta school of Darsana.

Position and compilation

Hindu tradition regards the Vedas as uncreated, eternal and being revealed to sages (Rishis). The hymns of the Rig-Veda Samhita are believed to have been collected and arranged by Paila under the supervision of Vyasa. Others were chanted during religious and social ceremonies and were compiled by Vaishampayana under the title Yajus mantra Samhita (see Yajur-Veda). Jaimini is said to have collected hymns that were set to music and melody — 'Saman' (see Sama-Veda). The fourth collection of hymns and chants known as Atharva Samhita. Philosophies and sects that developed in the Indian subcontinent have taken differing positions on the Vedas. In Buddhism and Jainism, the authority of the Veda is repudiated, and both evolved into separate religions. The sects which did not explicitly reject the Vedas remained followers of the Sanatana Dharma, which is known in modern times as Hinduism. In later Hinduism, the Vedas hold an exalted position. They are regarded as Shruti, i.e. Revelation, and the Brahminical caste based on the Vedas forms an important part of Hindu religious life to this day. Vedanta, Yoga, Tantra and even Bhakti acknowledge the Vedas as revelation.

Study

In the dharmashastras the study of the Vedas was regarded as a religious duty of the three upper varnas (Brahmins, Kshatriyas and Vaishyas). Women and Shudras were neither required nor allowed to study the Veda (this came to happen only in the very Later Vedic or the Sutra Age, because numerous evidences suggest that all humans were equally allowed to study the Vedas, and many Vedic "authors" were women). Elaborate methods for preserving the text (by learning them by heart and not by writing), subsidiary disciplines (Vedanga), exegetical literature, etc., were developed in the Vedic schools. In the fourteenth century Sayana wrote famous commentaries on the Vedic texts. In modern times, Vedic studies are crucial in the understanding of Indo-European linguistics, as well as ancient Indian history. It may be interesting to note that Hinduism encourages the Vedic mantras to be interpreted as liberally and as philosophically as possible unlike the Abrahamic religions (concerning the Tanakh, the Bible and the Koran). Infact, too literal interpretation of the mantras is actually discouraged, and even the three layers of commentaries (Brahmanas, Aranyakas and Upanishads), which form an intergral part of the shruti literature, actually interpret the seemingly polytheistic, ritualistic and highly complex Samhitas in a philosophical and metaphorical way to explain the "hidden" concepts of God (Ishwara), the Supreme Being (Brahman) and the soul or the self (Atman). Also, many Hindus believe that the very sound of the Vedic mantras is purifying for the environment and human mind.

Religious views: Monism, Monotheism, Henotheism and Polytheism

The religion of the Vedic period, particularly at its earliest, was distinct in a number of respects, including reference to females in positions of religious authority (female rishis, or sages), an apparent lack of belief in reincarnation, and a markedly different pantheon, with Indra generally the chief god, and little mention of the later primary gods Vishnu and Shiva, although Brahma does appear quite frequently. While Hinduism is generally monistic or monotheistic admitting emanating deities, the early Rig Veda (undeveloped early Hinduism) was what Max Müller based his views of henotheism on. In the four Vedas, Müller believed, a striving towards One was being aimed at by the worship of different cosmic principles, such as Agni (fire), Vayu (wind), Indra (rain, thunder, the sky; also the King of gods), etc. each of which was variously, by clearly different writers, hailed as supreme in different sections of the books. Indeed, however, what was confusing was an early idea of Rita, or supreme order, that bound all the gods. Other phrases such as ekam sat, vipraha bahudha vadanti (Truth is One though the sages know it as many) lead to understandings that the Vedic people admitted of fundamental oneness. There were attempts at monism by subordinating other gods to singular entities or gods of supreme power, three most notably being Vishvakarma, Indra and Varuna, though Indra was the most eulogized as supreme in his 200 Rig Vedic verses. From this mix of monism, monotheism and naturalist polytheism Max Müller decided to name the early Vedic religion henotheistic. He decided that while polytheism did not fit with views so clearly admitting of fundamental unity, monism in his opinion was not yet fully developed. This, however, is clearly a one-man view. Extremely advanced, indeed unprecedented and thitherto unduplicated ideas of pure monism are to be found in the early Vedas, notwithstanding clearly monist and monotheist movements of Hinduism that developed with the advent of the Upanishads. One such example of early Vedic monotheism is the Nasadiya hymn of the Rig Veda: "That One breathed by itself without breath, other than it there has been nothing." To collectively term the Vedas henotheistic, and thus further leaning towards polytheism, rather than monotheism, is to ignore the bent of the Vedas that laid the foundation for the Upanishads as early as 1000 BCE.

Cosmogony

The Vedic view of the world and cosmogony sees one true divine principle self-projecting as the divine word, Vaak, 'birthing' the cosmos that we know from 'Hiranyagarbha' or Golden Womb, a primordial sun figure that is equivalent to Surya. The varied gods like Vayu, Indra, Rudra (the Destroyer), Agni (Fire, the sacrifical medium) and the goddess Saraswati (the Divine Word, aka Vaak) are just some examples of the myriad aspects of the one underlying nature of the universe.

See also


- Pandit
- Vedic chant

External links


- [http://www.vedmandir.com A great source of information]
- [http://www.stephen-knapp.com/complete_review_of_vedic_literature.htm A Complete Review of Vedic Literature]
- [http://www.comparative-religion.com/hinduism/vedas/ Vedas: Rig, Sama, Yajur, and Artharva]
- [http://www.vedah.com/org/index.asp Excellent site about Vedas (Aurobindo)]
- [http://san.beck.org/EC7-Vedas.html Veda and Upanishads]
- [http://veda.harekrsna.cz/ VEDA - Vedas and Vedic Knowledge Online (Vaishnava and general)]
- [http://sarasvati.tripod.com/veda.htm Vedic Chanting .mp3 audio files]
- [http://www.india-picture.net/vedic_ritual Photos of the performance of Vedic rituals in India]

References


- Winternitz, Moritz : History of Indian Literature, Vol.1 (Calcutta 1926)l.
- Category:Holy scripture Category:Religious texts Category:Sanskrit texts ko:베다 ja:ヴェーダ

Vedic religion

The religion of the Vedic civilization is the predecessor of classical Hinduism, usually included in the term. Its liturgy is reflected in the text of the Vedas. The religion centered on a clergy (the Brahmins) administering sacrificial rites. Texts considered to date to the Vedic period, composed in Vedic Sanskrit, are mainly the four Vedas, but the Brahmanas, and some of the older Upanishads are also considered Vedic. The Vedas record the liturgy connected with the rituals and sacrifices performed by the purohitas. To the rishis, the hymns of the Rigveda and other Vedic hymns divinely revealed and they were rather "hearers", of divine revelation. (shrauta means "what is heard"). The mode of worship was performance of sacrifices and chanting of hymns (see Vedic chant). The priests helped the common man in performing rituals. People prayed for abundance of children, cattle and wealth. The main deities of the Vedic pantheon were Indra, Agni (fire), and Soma. Other deities were Varuna, Surya (the Sun), Mitra, Vayu (the wind). Goddesses included Ushas (the dawn), Prithvi (the Earth) and Aditi. Rivers, especially Sarasvati, were also considered goddesses. Deities were not viewed as all-powerful. The relationship between the devotee and the deity was one of transaction, with Agni (the sacrificial fire) taking the role of messenger between the two. Strong traces of a common Indo-Iranian religion remain visible, especially in the Soma cult and the fire ritual also preserved in Zoroastrianism. The Ashvamedha (horse sacrifice) has parallels in the 2nd millennium BC Andronovo culture, in India allegedly continued until the 4th century AD. Vegetarianism, the practice now thought by many to be so characteristic of Hinduism, arose only in late or post-Vedic times, possibly already at the time of Panini: The root-compound goghan "slaying cattle", in RV 7.56.17 used parallel to nrhan "slaying men" in reference to the referring to the weapon vadha of the Maruts, :17c aaré gohaá nRhaá vadháH vaH astu "far be your cow-slaying, men-slaying weapon!" in Panini is taught to refer to a "receiver of a cow" exclusively; this change occurred parallel to the rise of, and possibly under the influence of, Buddhism, which began as a reform-movement of the Vedic religion. In later texts, the cow is often described as aditi and aghnya (that which should not be killed). Specific rituals and sacrifices of the Vedic religion include:
- The Soma cult described in the Rigveda, descended from a common Indo-Iranian practice.
- Fire rituals, also a common Indo-Iranian practice, cf. Zoroastrianism:
  - The Agnihotra or oblation to Agni
  - The Agnicayana, the sophisticated ritual of piling the fire altar.
  - The Agnistoma or fire sacrifice
- The Ashvamedha or horse sacrifice described in the Yajurveda
- The Purushamedha or human sacrifice, probably very early reduced to a symbolic sacrifice.
- The rituals described in the Atharvaveda concerned with demonology and magic.

Post-Vedic religions

Vedic religion evolved into the Hindu paths of Yoga and Vedanta, a religious path considering itself the 'essence' of the Vedas. The Vedic pantheon was interpreted as a unitary view of the universe with God seen as immanent and transcendent in the forms of Ishvara and Brahman, projected into various deities in the human mind. Religions considered to be related to the Vedic religion include:
- Buddhism
- Hinduism
- Jainism
- Sikhism

See also


- Vedic priesthood
- Vedic civilization Category:Hindu history ja:ヴェーダの宗教

Vedic astrology

Jyotish is an ancient system of astrology that originated in the Vedic civilization of northern Bharat, better known as India. The Sanskrit word is rooted in "jyoti" which means light. Jyotish signifies the "science of light". In western countries, Jyotish is often referred to as Vedic, Indian, or Hindu astrology. Jyotish is often discussed as the instructional element of the Rig Veda, and as such is a Vedanga, or "body part" of the Vedas. Jyotish is called the Eye of the Veda, for its believed ability to view both phenomenal reality and wisdom itself. Part of a larger Vedic curriculum including mathematics, architecture, medical and military applications, it superficially has much in common with ancient and modern Western astrology (and the early traces of the descent of various schools of astrology from the Harappan and Egyptian cultures, Chinese and the Chaldean, through the Arabs, Greeks, and early Romans show complex interweavings that are assessed variously by diverse camps of scholars -- who, however, currently find little common ground as to the exact historical development). Jyotish has many facets, and some of its basics are clearly also cornerstones of Western astrology, such as symbolically endowed signs, houses and planets. But Jyotish has its own sophisticated reference to the noumenal: the planets are "grahas", semi-divine consciousnesses or forces that seize or act upon created beings and influence their actions and fates. Jyotish has historically been part of a continuous "holistic" approach to living and to spiritual practice within the life of Hindus predominant in India.

Foundations

Jyotisha's many lineages or paramparas emphasize that its study is a sadhana or technique of mental and existential development. In modern times it is a chief source of reference for many Hindus and other spiritual practitioners with common ties globally. In addition to sustaining its own lore, commentary and debates on the dilemmas of fate and free will and the philosophy of karma, jyotish maintains a virtual materia medica of remedies for difficulties found in horoscopes. Vedic astrologers will frequently prescribe special stones, or specific therapeutic practices or meditation techniques using mantras to those facing difficult or unclear futures as predicted by means consistent with Jyotish methodology. In past centuries, Brahmins have been the primary practitioners of Jyotish. In the last century, a renaissance of study of Jyotish and other Vedic sciences has emerged in India and the west. Although the subject of much controversy among secularists and skeptics, as of the late 1990s and early 2000s, Indian universities have begun to create courses and curricula in the discipline. The Vedas are replete with references to astrology in that cosmology and divinity are indistinguishable from the movements of Nature and planets and the growth of understanding in man as he lives in harmony with his highest spirituality. Surya, the Sun, is a manifestation of Vishnu, a central aspect of the Supreme, and is also the Atman within man. The term "Vedic astrology" has been recently introduced by American and Western astrologers in the 1980s and 1990s, leading to collaborative organizations such as the now-international [http://www.councilvedicastrology.org/ Council of Vedic Astrology]. Jyotish is still commonly used to aid in important decisions in modern India. In Hindu culture, newborns are traditionally named based on their jyotish charts, and jyotish concepts are pervasive in the organization of the calendar and holidays as well as in many areas of life and science. Astrology is vital to decisions made about marriage, opening a new business, moving into a new home, etc.

Hindu and Western astrologies

The most easily referred to difference between the two lies in the method of measurement of the Zodiac. Vedic astrology uses primarily the sidereal zodiac (in which stars are considered to be the fixed background against which the motion of the planets is measured), whereas most Western astrology uses the tropical zodiac (the motion of the planets is measured against the position of the Sun on the Spring equinox). Of course, the ancient rishis were aware of the tropical, season-based cycles of northern and southern declination paths of the Sun and used them also when appropriate. But in the popular mind, the main difference between the two systems is that Jyotish uses the sidereal zodiac and Western astrology uses the tropical. The most obvious effect of the sidereal/tropical difference is that about 80% of planets in a Western chart will move to the previous sign in a sidereal reading of the same chart. Both Jyotish and Western traditions have existed for millennia. Vedic astrology includes several nuanced sub-systems of interpretation and prediction incorporating unique sacralized elements not found elsewhere, such as its specific system of lunar mansions (called nakshatras, encompassing a pantheon of archetypal deities). The nakshatras are used to pick auspicious times of day or month for every human activity as well as to provide insight into the motivations and guiding characteristics of humans and events coming under their influence. Nakshatra cycles, or dashas, are developing a reputation in contemporary culture for the accuracy with which they time events. A further unique concept in jyotish not seen in Western astrology is the concept of Dashas - a mathematical analyses that breaks down human or the subject's lifetime into various sub-periods based on the location of Moon at birth. Predictions in jyotish incorporate various elements around the birth chart - influences of transits (similar to Western Astrology though more focused on houses or bhavas) as well as Dashas.

Fundamentals of Jyotisha

Jyotish is based on what Western astrologers call the whole house system and recognizes nine grahas (heavenly bodies or "planets"): They also recognize twelve zodiac signs, or Rashis: One's Ascendant, or lagna, the rashi which is rising on the eastern horizon at the time of one's birth, is the most influential and important one. Of lesser importance but still some impact is the Janma Rashi, the rashi in which the moon lay while one was born. There are three different Jyotish chart notations, which are functionally equivalent but quite different in appearance. The following images show the same birth chart in the two main notations - North Indian and South Indian. The third notation is followed in Eastern parts of India.
image:Birth_Chart_(northern_format).png image:Birth_Chart_(southern).png
In the North Indian notation, the house positions are fixed (1st house top middle, with the rest following in counterclockwise order) and the signs of the zodiac are indicated by numbers in the chart (1 for Aries, and so on). Conversely, in the South Indian notation, the signs of the zodiac have fixed positions (Aries always occupies the 2nd box from the left in the top row, with the rest following in clockwise order), and the first house is marked "As" (for ascendant) with the rest following in clockwise order.
The charts are broken into twelve sections, houses or Bhavas, each of which is related to a rashi in an equal house system.

Partial Bibliography


- "27 Celestial Portals", Trivedi, Lotus Press, Twin Lakes, Wisconsin, ISBN 0-940985-84-5
- "Astrology of the Seers", Frawley, Lotus Press, Twin Lakes, Wisconsin, ISBN 0-914955-89-6
- "Fundamentals of Vedic Astrology, Veeic Astrologer's Handbook Vol. 1", Behari, Lotus Press, Twin Lakes, Wisconsin, ISBN 0-940985-52-7
- "Key of Life: Astrology of the Lunar Nodes", Trivedi, Lotus Press, Twin Lakes, Wisconsin, ISBN 0-940985-33-0
- "Light on Life: An Introduction to the Astrology of India", de Fouw and Svoboda, Lotus Press, Twin Lakes, Wisconsin, ISBN 0-940985-69-1
- "Myths and Symbols of Vedic Astrology", Behari, Lotus Press, Twin Lakes, Wisconsin, ISBN 0-940985-51-9
- "Nakshatras: The Lunar Mansions of Vedic Astrology", Harness, Lotus Press, Twin Lakes, Wisconsin, ISBN 0-914955-83-7
- "Planets in the Signs and Houses: Vedic Astrologer's Handbook Vol. 2", Behari, Lotus Press, Twin Lakes, Wisconsin, ISBN 0-940985-53-5

See Also


- Vedas
- Hinduism
- History of India
- Culture of India
- Hindu calendar
- Hindu
- Bhrigu Samhita Category:Hindu astronomy Category:Concepts in Hinduism Category:Astrology by tradition

Vedic science

Vedic science is the term used in modern attempts to systematize ancient scientific thought to be found in early Indian scriptures, especially the Vedas.

Types of Vedic science

Adherents of Maharishi Vedic science describe it as the science of self (atmavidya). Veda means knowledge; and Vedic science asserts that there are two kinds of knowledge: lower or outer, and higher or inner. Further, the Vedic system asserts that one needs traditional modes of reasoning to obtain outer knowledge. But to obtain inner knowledge, special study, discipline and practice is recommended. Vedic science claims that there is a connection between the outer and the inner and this connection manifests itself in our awareness. Vedic science is another name for the science of consciousness. It also claims that such a science cannot be like any standard science, since it deals with the experiencing subject and not objects. Some believe that these writings to anticipate modern science suggesting that many mathematical axioms of modern age have their ancient equivalents in the Vedic chants. Vedic mathematical methods are said to aid in fast and accurate mental multiplication of extremely large numbers using numeric properties as their base. The branch of study of vedic methods in mathematics is commonly referred to as Vedic mathematics.

Criticisms of Vedic science

Critics dencounce these theories as pseudoscience similar to Western Creation science. Some charge that "Vedic science" is promulgated by right-wing Hindutva (Hindu nationalist) politicians as part of their cultural agenda.

See also


- Maharishi Vedic Medicine
- Traditional Chinese medicine
- Ayurveda

External links


- [http://uk.arxiv.org/abs/physics/0303001 Greek and Indian Cosmology: Review of Early History] Comparison between Indian and Greek science.
- "Postmodernism, Hindu nationalism and `Vedic science' " [http://www.frontlineonnet.com/fl2026/stories/20040102000607800.htm Part 1]-[http://www.frontlineonnet.com/fl2101/stories/20040116001408700.htm Part 2] : Criticism of study of Vedic Science and the dangers it poses by Meera Nanda
- [http://www.swaveda.com/articles.php?action=show&id=58 A Rejoinder to Meera Nanda’s Article “Postmodernism, Hindu nationalism and Vedic science”]
- [http://www.hinduonnet.com/thehindu/thscrip/print.pl?file=2004052201691000.htm&date=2004/05/22/&prd=th& "Calling India's freethinkers"]: An opinion piece by Meera Nanda
- [http://www.beliefnet.com/story/146/story_14684_1.html?rnd=46 U.S. Hinduism Studies: A Question of Shoddy Scholarship]: Alleges domination of Hinduism studies by a western, offensive, unsympathetic viewpoint. Category:Concepts in Hinduism Category:Pseudoscience Category:New Age

Maharishi Vedic Medicine

Maharishi Vedic Medicine (or Maharishi's Consciousness-Based Health Care) was founded in the mid 1980s by Maharishi Mahesh Yogi, who is perhaps most famous for bringing the transcendental meditation technique to the entire world. Maharishi revived the ancient ideas of "consciousness as the root of all things" and reintegrated it into healthcare using the ancient treatments of ayurveda. MVM is a preventative system of health care which operates on the most fundamental levels of the physiology. Practitioners detect diseases in early stages, before they've arisen in the gross physiology, and give simple treatments (consisting mainly of dietary adjustments, routine changes, etc.) to elminate the problem before it arises. Maharishi Vedic Medicine is on the forefront of "alternative" medicines and aims at being a complementary system to exist alongside modern, western medicine.

See also


- Vedic science

External links


- http://www.mum.edu/cmvm
- http://www.theraj.com Category:New Age

Vedic mathematics

:Note: Vedic mathematics is not to be confused with Vedic physics or any other Vedic Science, or with Ancient Vedic weights and measures.) Vedic mathematics is a system of mental calculation developed by Shri Bharati Krishna Tirthaji which he claimed he had based on a lost appendix of Atharvaveda, an ancient text of the Indian teachings called Veda. It has some similarities to the Trachtenberg system in that it speeds up some arithmetic calculations. It claims to have applications to more advanced mathematics, such as calculus and linear algebra. The system was first published in the book Vedic Mathematics ISBN 8120801644 in 1965. The system has since been developed further and there have been several other books released. Critics have questioned whether this subject deserves the name Vedic or indeed mathematics. They point to the lack of evidence of any sutras from the Vedic period consistent with the system, the inconsistency between the topics addressed by the system (such as decimal fractions) and the known mathematics of early India, the substantial extrapolations from a few words of a sutra to complex arithmetic, and the restriction of applications to convenient cases. They have also been worried that it deflects attention from genuine achievements of ancient and modern Indian mathematics and mathematicians, and that its promotion by Hindu nationalists may damage mathematics education in India. The system is based upon sixteen formulas and their corollaries, some of which are described below.

All from nine and the last from ten

Corollary 1: Whatever the extent of its deficiency, lessen it still further to that very extent; and also set up the square of that deficiency. For instance, in computing the square of 9 we go through the following steps: #The nearest power of 10 to 9 is 10. Therefore, let us take 10 as our base. #Since 9 is 1 less than 10, decrease it still further to 8. This is the left side of our answer. #On the right hand side put the square of the deficiency, that is 12. Hence the answer is 81. #Similarly, 82 = 64, 72 = 49. #For numbers above 10, instead of looking at the deficit we look at the surplus. For example: :11^2 = (11+1)\cdot 10+1^2 = 121.\, :12^2 = (12+2)\cdot 10+2^2 = 144.\, :14^2 = (14+4)\cdot 10+4^2 = 18\cdot10+16 = 196.\, :and so on. This is based on the identities (a+b)(a-b)=a^2-b^2 and (a+b)^2=a^2+2ab+b^2.

By one more than the one before

The proposition "by" means the operations this formula concerns are either multiplication or division. [ In case of addition/subtraction proposition "to" or "from" is used.] Thus this formula is used for either multiplication or division. It turns out that it is applicable in both operations. An interesting application of this formula is in computing squares of numbers ending in five. Consider: : 35 × 35 = (3 × (3 + 1)),25 = 12,25 The latter portion is multiplied by itself (5 by 5) and the previous portion is multiplied by one more than itself (3 by 4) resulting in the answer 1225. This is a simple application of (a+b)^2=a^2+2ab+b^2 when a=10c and b=5, i.e. :(10c+5)^2=100c^2+100c+25=100c(c+1)+25. It can also be applied in multiplications when the last digit is not 5 but the sum of the last digits is the base (10) and the previous parts are the same. Consider: : 37 × 33 = (3 × 4),7 × 3 = 12,21 : 29 × 21 = (2 × 3),9 × 1 = 6,09 This uses (a+b)(a-b)=a^2-b^2 twice combined with the previous result to produce: :(10c+5+d)(10c+5-d)=(10c+5)^2-d^2=100c(c+1)+25-d^2=100c(c+1)+(5+d)(5-d). We illustrate this formula by its application to conversion of fractions into their equivalent decimal form. Consider fraction 1/19. Using this formula, this can be converted into a decimal form in a single step. This can be done by applying the formula for either a multiplication or division operation, thus yielding two methods.

Method 1: using multiplications

1/19, since 19 is not divisible by 2 or 5, the fractional result is a purely circulating decimal. (If the denominator contains only factors 2 and 5 is a purely non-circulating decimal, else it is a mixture of the two.) So we start with the last digit : 1 Multiply this by "one more", that is, 2 (this is the "key" digit from Ekadhikena) : 21 Multiplying 2 by 2, followed by multiplying 4 by 2 : 421 → 8421 Now, multiplying 8 by 2, sixteen : 68421 : 1 ← carry multiplying 6 by 2 is 12 plus 1 carry gives 13 : 368421 : 1 ← carry Continuing : 7368421 → 47368421 → 947368421 : 1 Now we have 9 digits of the answer. There are a total of 18 digits (= denominator − numerator) in the answer computed by complementing the lower half: : 052631578 : 947368421 Thus the result is .052631578,947368421

Method 2: using divisions

The earlier process can also be done using division instead of multiplication. We divide 1 by 2, answer is 0 with remainder 1 : .0 Next 10 divided by 2 is five : .05 Next 5 divided by 2 is 2 with remainder 1 : .052 next 12 (remainder,2) divided by 2 is 6 : .0526 and so on. As another example, consider 1/7, this same as 7/49 which as last digit of the denominator as 9. The previous digit is 4, by one more is 5. So we multiply (or divide) by 5, that is, ...7 => 57 => 857 => 2857 => 42857 => 142857 => .142,857 (stop after 7 − 1 digits) 3 2 4 1 2

Vertically and crosswise

This formula applies to all cases of multiplication and is very useful in division of one large number by another large number.

Transpose and apply

This formula complements "all from nine and the last from ten", which is useful in divisions by large numbers. This formula is useful in cases where the divisor consists of small digits. This formula can be used to derive the Horner's process of Synthetic Division.

When the samuccaya is the same, that samuccaya is zero

This formula is useful in solution of several special types of equations that can be solved visually. The word samuccaya has various meanings in different applications. For instance, it may mean a term which occurs as a common factor in all the terms concerned. A simple example is equation "12x + 3x = 4x + 5x". Since "x" occurs as a common factor in all the terms, therefore, x = 0 is a solution. Another meaning may be that samuccaya is a product of independent terms. For instance, in (x + 7)(x + 9) = (x + 3)(x + 21), the samuccaya is 7 × 9 = 3 × 21, therefore, x = 0 is a solution. Another meaning is the sum of the denominators of two fractions having the same numerical numerator, for example: 1/(2x − 1) + 1/(3x − 1) = 0 means 5x - 2 = 0. Yet another meaning is "combination" or total. This is commonly used. For instance, if the sum of the numerators and the sum of denominators are the same then that sum is zero. Therefore, :=. Therefore, 4x + 16 = 0 or x = −4. This meaning ("total") can also be applied in solving quadratic equations. The total meaning can not only imply sum but also subtraction. For instance when given N1D1 = N2/D2, if N1 + N2 = D1 + D2 (as shown earlier) then this sum is zero. Mental cross multiplication reveals that the resulting equation is quadratic (the coefficients of x2 are different on the two sides). So, if N1 − D1 = N2 − D2 then that samuccaya is also zero. This yield the other root of a quadratic equation. Yet interpretation of "total" is applied in multi-term RHS and LHS. For instance, consider :+=+. Here D1 + D2 = D3 + D4 = 2x − 16. Thus x = 8. There are several other cases where samuccaya can be applied with great versatility. For instance "apparently cubic" or "biquadratic" equations can be easily solved as shown below: :(x-3)^2+(x-9)^3=2(x-6)^3. Note that x − 3 + x − 9 = 2(x − 6). Therefore (x − 6) = 0 or x = 6. (remark by different author: Note also that:(6-3)^2+(6-9)^3=3^2-3^3=9-27=-18, whereas 2 (6-6)^3=0 Thus: x=6 is NOT a solution!) (Another note. This example does work if one considers all exponents to be cubic, in which case (6-3)^3+(6-9)^3 will give 27-27.) Consider :=. Observe: N1 + D1 = N2 + D2 = 2x + 8. Therefore, x = −4. This formula has been extended further.

If one is in ratio, the other one is zero

This formula is often used to solve simultaneous simple equations which may involve big numbers. But these equations in special cases can be visually solved because of a certain ratio between the coefficients. Consider the following example: :6x + 7y = 8 :19x + 14y = 16 Here the ratio of coefficients of y is same as that of the constant terms. Therefore, the "other" is zero, i.e., x = 0. Hence the solution of the equations is x = 0 and y = 8/7. (alternatively: :19x + 14y = 16 is equivalent to: :(19/2)x +7y = 8. Thus it is obvious that x has to be zero, no ratio needed, just div by2!) This formula is easily applicable to more general cases with any number of variables. For instance :ax + by + cz = a :bx + cy + az = b :cx + ay + bz = c which yields x = 1, y = 0, z = 0. A corollary says By addition and by subtraction. It is applicable in case of simultaneous linear equations where the x- and y-coefficients are interchanged. For instance: :45x − 23y = 113 :23x − 45y = 91 By addition: 68x − 68 y = 204 => 68(x − y) = 204 => x − y = 3. By subtraction: 22x + 22y = 22 => 22(x + y) = 22 => x + y = 1.

External links


- [http://www.magicalmethods.com/ Learn To Calculate 10 Times Faster]
- [http://www.amazon.com/exec/obidos/tg/detail/-/0313232008/104-7253290-5011962?v=glance Trachtenberg Speed System of Basic Mathematics at Amazon.com]
- [http://mathforum.org/dr.math/faq/faq.trachten.html The Math Forum @ Drexel]
- [http://vedicmaths.org/ VedicMaths.Org]
- [http://www.vedicmaths.com/ Vedic Mathematics Books]
- [http://www.bespokewear.com/vm/ The Vedic Mathematics Society]
- [http://mathforum.org/epigone/math-history-list/zhimpjufrer Indian mathematics by Richard Askey]
- [http://www.sacw.net/DC/CommunalismCollection/ArticlesArchive/NoVedic.html Neither Vedic Nor Mathematics]
- [http://www.tifr.res.in/~vahia/dani-vmsm.pdf Myths and reality: on "Vedic Mathematics" by Prof. S. G. Dani]
- [http://www.ourkarnataka.com/vedicm/vedicms.htm Vedic Maths, a Forgotten Science] - with Examples and Quiz Category:Mental-skill games Category:Mathematics

Peter Brown (historien)

Peter Robert Lamont Brown, né en 1935 à Dublin (Irlande), est un historien étudiant le transition entre l'Antiquité et le Moyen Âge : l'Antiquité tardive. Il passe son enfance en Irlande, puis rejoint Oxford pour compléter ses études universitaires. Il reste à Oxford comme professeur d'histoire jusqu'en 1975, enseigne ensuite à Londres (1975-1978) et aux États-Unis à Berkeley puis à Princeton. Parmi ces ouvrages principaux, tous traduits de l'anglais, citons La vie de Saint-Augustin, Paris, Le Seuil, 1971, Genèse de l'Antiquité tardive, Paris, Gallimard, 1983 et L'essor du christianisme occidental (200-1000), Paris, Le Seuil, 1997.

Liens externes


- [http://prelectur.stanford.edu/lecturers/brown/ Article sur Peter Brown / Université de Stanford] Brown, PeterBrown, Peter

Architekci wntrz sprzet warsaw apartments teksty hosting










































:: RELATED NEWS ::


Kuybyshev
:This article is not about Samarra, which is in Iraq. Samara (Russian: Сама́ра), from 1935 to 1991—Kuybyshev (Russian: Ку́йбышев), is a major city situated on the Volga River in the southeastern part of European Russia, P
All Rights Reserved 2005 wikimiki.org