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ब्रह्मगुप्त: प्रतिभाशाली गणितज्ञ

ब्रह्मगुप्त: प्रतिभाशाली गणितज्ञ


हमारे देश में जन्मे गणितज्ञों में ब्रह्मगुप्त का स्थान भी अत्यंत महत्वपूर्ण है | गणित के साथ साथ ये खगोल शास्त्र तथा ज्योतिष में भी पारंगत थे |
आचार्य ब्रह्मगुप्त का जन्म राजस्थान राज्य के भीनमाल शहर में ईस्वी सन् 598 में हुआ था।
वे तत्कालीन गुर्जर प्रदेश (भीनमाल) के अन्तर्गत आने वाले प्रख्यात शहर उज्जैन (वर्तमान मध्य प्रदेश) की अन्तरिक्ष प्रयोगशाला के प्रमुख थे और इस दौरान उन्होने दो विशेष ग्रन्थ लिखे:
1. ब्रह्मस्फुटसिद्धान्त (सन ६२८ में) और
2. खण्डखाद्यक या खण्डखाद्यपद्धति (सन् ६६५ ई में)
'ब्रह्मस्फुटसिद्धांत' उनका सबसे पहला ग्रन्थ माना जाता है इसके साढ़े चार अध्याय मूलभूत गणित को समर्पित हैं। जिसमें शून्य का एक अलग अंक के रूप में उल्लेख किया गया है । यही नहीं, बल्कि इस ग्रन्थ में ऋणात्मक (negative) अंकों और शून्य पर गणित करने के सभी नियमों का वर्णन भी किया गया है ।
ब्रह्मगुप्त ने द्विघातीय अनिर्णयास्पद समीकरणों ( Nx2 + 1 = y2 ) के हल की विधि भी खोज निकाली। इनकी विधि का नाम चक्रवाल विधि है। गणित के सिद्धान्तों का ज्योतिष में प्रयोग करने वाले यह प्रथम व्यक्ति थे |
>ब्रह्मगुप्त ने किसी वृत्त के क्षेत्रफल को एक समान क्षेत्रफल वाले वर्ग से स्थानान्तरित करने का भी यत्न किया।
>ब्रह्मगुप्त ने पृथ्वी की परिधि ज्ञात की थी, जो आधुनिक मान के निकट है।
>ब्रह्मगुप्त पाई (pi) (३.१४१५९२६५) का मान १० के वर्गमूल (३.१६२२७७६६) के बराबर माना।
>ब्रह्मगुप्त अनावर्त वितत भिन्नों के सिद्धांत से परिचित थे। इन्होंने एक घातीय अनिर्धार्य समीकरण का पूर्णाकों में व्यापक हल दिया, जो आधुनिक पुस्तकों में इसी रूप में पाया जाता है, और अनिर्धार्य वर्ग समीकरण, K y2 + 1 = x2 , को भी हल करने का प्रयत्न किया।

ब्रह्मगुप्त का सूत्र :


ब्रह्मगुप्त का सबसे महत्वपूर्ण योगदान चक्रीय चतुर्भुज पर है। उन्होने बताया कि चक्रीय चतुर्भुज के विकर्ण परस्पर लम्बवत होते हैं। ब्रह्मगुप्त ने चक्रीय चतुर्भुज के क्षेत्रफल निकालने का सन्निकट सूत्र (approximate formula) तथा यथातथ सूत्र (exact formula) भी दिया है।
चक्रीय चतुर्भुज के क्षेत्रफल का सन्निकट सूत्र:

(\tfrac{p + r}{2}) (\tfrac{q + s}{2})


चक्रीय चतुर्भुज के क्षेत्रफल का यथातथ सूत्र:

\sqrt{(t - p)(t - q)(t - r)(t - s)}.

जहाँ t = चक्रीय चतुर्भुज का अर्धपरिमाप तथा p, q, r, s उसकी भुजाओं की नाप है। 

EXCLUSIVE CLONING in Ancient India 14000+ BC Years ago Proof in Rig Veda & Puranas

(the following content is from a research paper presented by
Dr. Padmakar Vishnu Vartak
M.B.B.S., F.U.W.A.I., Ph.D. (Lit) [Washington DC])

"Vasistha and Agastya were test tube babies produced in a utensil named as Vasatiwara, by Mitra and
Varuna.(RV 7-33-13). Even, Cloning was successfully done by the three brothers, the famous Rubhus. They
produced a horse from another horse and a cow from the skin of a cow. I had told this discovery to in the first
meeting of the Veda Vidnyana Mandal in 1976; but everybody laughed, saying if the modern science can not
do it, how is it possible for the Vedic people ? However after 21 years Cloning was performed in the modern
world in 1997 when a lamb was produced from udder of a sheep, which is a part of skin. Therefore the Vedic
principle of cloning appears correct. It proves that the Vedas have recorded only the principles on which we
have to work hard.
The same Rubhus had divided one ‘Chamasa’ into four. Chamasa was not an ordinary pot of clay or
metal. If it was so it could not have been divided into four. Hence it must have been some special. peculiar pot.
The meaning is present in the name ‘Chamasa’ itself. The root ‘Cham’ means to drink and eat.The root
‘As’means to live. Therefore Chamasa means a pot of life energy. The word ‘Chit Chamasa’ is also used by
the Rigveda, which suggests a Chamasa having Chit or Chetana or Manas. Thus Chit-Chamasa means a living
cell. A fertilised egg can be called as Chit Chamas. It was divided into four by Rubhus. It means Rubhus
evolved four animals from a single zygote or fertilised ovum. Such experiments are done in the modern science
and four animals are produced from a single zygote.
I would say that the Veda contains all knowledge, scientific and eternal. The seers blended everything
in Veda. There was no classification of knowledge in different disciplines, as is done today. All the knowledge
was stored in the Veda, which is a vast ocean of knowledge, full of the seeds of all the varieties of knowledge.
We have to take out those seeds, sow them, raise them carefully so that we will get many trees of knowledge,
which will supply us plenty of fruits of knowledge."

Animal Cloning was done few years ago in modern world but human cloning is still not done successfully and it is also prohibited in almost all countries.
In Ancient India, animal cloning was done to multiply number of cows and horses.
In Rigveda, Rubhus are mentioned as brothers (Rubhu, Vajra and Vibhu) who brought youthfulness to their old parents. They even managed to bring back their lost skills. (They must have used ayurvedic recipes to bring back youthfulness. So much literature about such recipes exist even today but is neglected).
They even cloned a cow and a horse.

Seven different sages Kanva Medhatithi (1-20), Angirasa Kutsa (1-110,111), Deerghatamas (1-161), Vishvamitra (3-60), Vamadeva (4-33), Vasistha Maitravaruni (7-48), and Shrunu Arbhava (10-176) mentioned about Rubhus in their vedic verses.
These 7 sages belong to different generations, so it is known that Rubhus were known for their work over a long period of time.

The first work of Rubhus was to bring back youthfulness to their old parents. This is mentioned in multiple verses of Rig Veda.
1-20-4 – With their exclusive power they made their old parents youthful again.
1-110-8 – They made their old parents full of youth again by their skill.
1-111-1 – Ingenious Rubhus prepared a chariot for Indra, prepared two powerful horses (2nd being cloned from 1st), made their old parents youthful again and gave new mothers to orphaned calves or children.
1-161-7 – Oh Rubhus, with the power of your intelligence you converted your old parents into youthful state.
4-33-3 – Rubhus who made their old parents youthful again may come to our Yajna.
4-34-9 – Rubhus gave a new life to their old parents, to Aswinau, to a cow and a horse.
4-35-5 – Oh, ingenious Rubhus, you made your old parents youthful again.
4-36-3 – Oh, Rubhu, Vaja and Vibhu, your workmanship of making your old parents youthful again was praised by gods.

The second work of Rubhus was on cows and their first step was to produce a cow which yielded copious milk. (RigVeda 1-20-3).
Probably cows in that generation did not yield enough milk and to meet the demand, cloning was done.
They mention about a method where skin from cow’s back in taken and cells are multipled from it to produce a new cow (named Viswaroopa) which looks alike.

Third work of Rubhus brothers was to produce two powerful horses. First they created a horse (named Hari) and presented it to Indra. Then they produced another horse which is a clone of Hari and now both were used to yoked to his chariot (1-161-7, 4-33-10).

Before cloning, Rubhus brothers seem to have worked on living cells and their multiplication.
Sun gave ‘Chamasa‘ with Amruta to Rubhus (1-110-3) and they divided it into four equal parts.
‘Chamasa‘ here can be considered as a cell and amruta (immortal thing) makes it a living cell.
Rig Veda suggests a Chamasa having Chit or Chetana or Manas, so Chit-Chamasa means a living cell.
A fertilised egg can be called as ‘Chit Chamasa‘. It was divided into four by Rubhus, which means Rubhus evolved four animals from a single zygote or fertilised ovum.
This living cell or an embryo is prepared Twashta (God).

During the experiment, eldest brother(Rubu) said, “ we can make two cells from the original one ” (4-33-5). However, the younger(Vajra) brother said, “ We can make three” , because he observed that when one cell was divided into two, there were three cells.
The youngest brother(Vibhu) observed and said , “ We can make four ”, as second cell also can be divided equally like the first.

Next was human cloning, which is mentioned in story of King Vena.
He was a great king but became evil and corrupt. So, Mother Earth (Bhoodevi) decided that she would not provide crops to humans anymore.
A group of Rishis (Sages) killed King Vena out of anger. They removed all the evil from his corpse’s thigh.
Then they created his clone from his arm.
This clone had similar body but however, mind cannot be cloned. So, a new King who was named ‘Prithu’ was created with pure mind. He brought back Mother Earth (Bhoodevi) to her normal state and promised be her eternal guardian. This is why Earth (Bhoodevi is also known as Prithvi.

There are examples of abnormal cloning, like of Nishada in Vishnu Purana.
Nishada, though an abnormal clone, could live long and could produce children. His tribe was known after his name and King Nala (of the famous Nala-Damayanti story in Mahabharata) and Ekalavya were his descendants.

Rubhus had also made a chariot flying in air, so they were automobile engineers too.

There are many more instanced like the demon ‘Rakta Beeja’ or AhiRavana and Mahi-Ravana who produce Rakshasas(demons) who look like them from their blood drops in war. It might be cloning from the white blood corpuscles, which contain nuclei.

Makar Sankranti, a scientific, vedic festival that adores universe,sun.

Our ancient ones (rishis) taught us, at the inner core, the human life is Sat-Chit-Anand (Truth-Consciousness-Bliss) and each and every activity in life is meant to lead the individual to that One goal of existential realization.

Thousands of years ago, the Hindu festivals (utsav) spread throughout the Indian-subcontinent and in the east as far as Cambodia, Thailand, Indonesia and in the west as far as America, as recorded by Mayans in South America. These festivals took on local hues depending on the climate, agricultural environment, evolving cultural landscape and location. Though somewhat modified over the millenia, many still retain their core essence ans spirit.
Hindus celebrate major cosmic changes, such as the transmigration of the sun from one zodiac sign (Rashi) as Sankranti. Of the twelve sankrantis, Makara Sankranti on January 14th,or 15 th(It changes) is the most significant; the sun passes through the winter solstice, from the Tropic of Cancer to the Tropic of Capricorn (Makar). We witness cosmic, astronomical harmony and prayerfully honor this scientific Truth. The six months of northern movement of the sun is followed by six months of southern movement.
This festival, unlike other Hindu festivals, is not dependent on the tithi (position of the moon) but on position of the sun. On this day, the sun enters the zodiac sign of Capricorn. To compensate for the difference that occurs due to the revolution around the sun, sometimes the day of sankrant gets pushed ahead by one day.

Makar Sankranti marks the commencement of the Sun's journey to the Northern Hemisphere (Makara raasi ), signifying the onset of Uttarayana Punyakalam, and is a day of celebration all over the country. The day begins with people taking holy dips in the waters and worshipping the Sun.

Traditionally, this period is considered an auspicious time and the veteran Bhishma of Mahabharata chose to die during this period. Bhishma fell to the arrows of Arjun. With his boon to choose the time of his death, he waited on a bed of arrows to depart from this world only during this period. It is believed that those who die in this period have no rebirth.

The Indo Gangetic plain begins this day with taking dips in the Ganga and offering water to the Sun god. The dip is said to purify the self and bestow punya. Special puja is offered as a thanksgiving for good harvest. According to folklore, girls who take the holy dip get handsome husbands and boys get beautiful brides.

Til and Rice are two important ingredients of this festival. In the rice-eating belt of Bihar and eastern Uttar Pradesh, people have a special rice-centric meal on this day. Also known as Gangasagar Mela, on this day, people come from all over India for a ceremonial cleansing in the river Hooghly, near Calcutta.

Karnataka -men, women and children attired in colourful tunics visit friends and relatives and exchange pieces of sugarcane, a mixture of fried til, molasses, pieces of dry coconut, peanuts and fried gram. The significance of this exchange is that sweetness should prevail in all the dealings. As part of the festival, cows and bulls are given a wash and the horns are painted with bright colours and decorated with garland, and are taken in a procession in the village to the accompaniment of pipes and drums. In the night a bonfire is lit and the animals are made to jump over the fire.

It is a big event for the Tamils and the people of Andhra Pradesh. The Telugus like to call it 'Pedda Panduga' meaning big festival. The whole event lasts for four days, the first day Bhogi, the second day Sankranti, the third day Kanuma and the fourth day, Mukkanuma.

One month preceeding Sankranti is called Dhanurmasam and is also an auspicious period. People wake up early, take bath and go around the streets singing devotional songs. Houses are whitewashed and farmers clean their warehouses. Colorful rangoli (muggulu) are drawn in the front yards of every house during this month. These artistic floral designs are drawn on the floor with rice flour or fine powder from limestone. These patterns are decorated with marigold placed on cowdung balls. Colorfully dressed young girls go round them singing songs.

Makar Sankranti has an astrological significance, as the sun enters the Capricorn (Sanskrit: Makara) zodiac constellation on that day. This date remains almost constant with respect to the Gregorian calendar. However, precession of the Earth's axis (called ayanamsa) causes Makara Sankranti to move over the ages. A thousand years ago, Makara Sankranti was on 31 December and is now on 14 January. According to calculations, from 2050 Makar Sankranti will fall on January 15.
Makara Sankranti is a major harvest festival celebrated in various parts of India. Many Indians also conflate this festival with the Winter Solstice, and believe that the sun ends its southward journey (Sanskrit: Dakshinayana) at the Tropic of Capricorn, and starts moving northward (Sanskrit: Uttarayaana) towards the Tropic of Cancer, in the month of Pausha on this day in mid-January. There is no observance of Winter Solstice in the Hindu religion. 

What is Uttarayan and Dakshinayan of SUN-
Sun rising and setting slightly towards North-East and North-West respecitvely between mid-january to mid-july in every year.
This period is called Uttarayan in vedic terms and it means uttar(north)+ayan(movement) of sun.
The remaining 6 months are termed as dakshinayan which means south movement of sun.

Originally, this was celebrated as Winter Solstice in ancient India but later due to the fact that the solstices are continually precessing at a rate of 50″ / year due to the precession of the equinoxes, winter solstice now occurs at 21st december each year.


Surya Siddhantha bridges this difference by juxtaposing the four solstitial and equinotial points with four of the twelve boundaries of the signs.

This is also the best time to spend in a temple or at a peaceful place and recite Gayatri Mantra in silence.

In vedic religion, God doesn’t have any shape and for us, time is manifestation of God.
Vishnu or Narayana is worshipped through Sun God and this Sun’s equinoxes are celebrated as festivals.

Vedic astrology personifies Sankranti. As per Vedic astrology Sankranti is 60 Yojana (approximately 432 Km) wide and long. Sankranti has figure of a man with one face, long nose, wide lips and nine arms. It moves in forwards direction but keeps watching backwards. It keeps revolving while holding a coconut shell in one hand.

As per Hindu beliefs, the above personification seems inauspicious and hence Sankranti window is prohibited for all auspicious activities. However, the Sankranti duration is considered highly significant for charity, penance and Shradh rituals. People offer alms to needy, take bath in holy rivers and perform Shradh for ancestors during Sankranti.

http://www.astrogle.com/astro-predictions/makar-sankranti-2014-astrological-significance-effects.html

http://www.sanatan.org/en/a/111_makar-sankranti.html 

huffingtonpost

Atomic Particles were discovered by India centuries ago.

                                                      Vaisheshika:

A

Vaisheshik system was developed by rishi Kanād, from whose name the particles got the name “Kan” or “Kana.” His teaching was that liberation can only be achieved or attained by thoroughly understanding the nature and our existence. Vaisheshika accepts the cosmology or the evolution of the Nature or Universe. Prakruti is considered to be the cause of cosmic evolution. Prakruti has three constituent qualities (guna), namely, sattva, rajas, and tamas in equilibrium. That is why it is also known as “trigunātmikā.” According to Vaisheshika, all objects in nature (Prakruti) are made of tiniest, indivisible, invisible, indestructible, and eternal particles that are neither created nor destroyed (meaning they were there at the beginning of the creation and they will be there at the end of dissolution) and are called “paramānu.” They are like elementary particles of modern physics. Paramanus make anu. Two paramanu make one dvyanuka. Two, three, four, and more dvyanuka make one tryanuka, chaturanuka, and so on. These anu possess continuous vibratory motion which can be regarded as the spin or wave function. These paramanus are distinct from the soul. Each atomic substances has individual (vishesha) characteristics which distinguishes them from other non-atomic substances (dravyas), such as time (kāl), three dimensional space (dig, dishā) (directions or dimensions), soul (ātmā or ātman), and mind (manas). Vaisheshika has definitions for, ākāsh, time, and space. They have no lower constituents, meaning they are elementary. (Vaisheshika Sutra: 2.1.27-31) The qualities of akash are: sound, number, dimension, distinctness (individuality or separateness), conjunction, and disjunction. (Vaisheshika Sutra: 7.1.22) Time marks past, present, and future; succession, lateness and earliness. (Vaisheshika Sutra: 2.2.6) Time marks beginning, persistence, and end. (Vaisheshika Sutra: 2.2.9) Space is the cause of directions and dimensions between two objects. Vaisheshika clearly defines and describes the principle of cause (kāran) and effect (kārya).

Time can flow at different rates for different observers. Time and space are not absolute. Space and time are relative. There exist countless universes with their own Brahmā, Vishnu, and Mahesh. The universal is taken to be timeless and ubiquitous. Whatever can be defines with respect to space and time cannot be a universal. The processes that mark the passage of time on an object would thus be relative. It is only the universals which are true for all time and space are absolute or transcendental. The only such universals are Brahm and Parabrahm. These ideas are elaborated in the Purans, Agama Shashtras, and in the books such as Yoga-Vashishtha.

Substances can be grouped according to their actions or activities, common characteristics, specific characteristics, and their relationships with the cause and effect. According to Vaisheshika, there are six basic categories (padārtha) associated with reality: dravya (substance), guna (quality or characteristic), karma (motion or actions), sāmānya (common or general), vishesha (specific), and samavāya (inherent or comparative).

Dravyas include 9 basic realities, namely, Pruthwi (earth or solid), Jal (water or liquid), Tej (light or fire), Vayu (air or gas), Akash (ether or void), Desh or Dishā (place or the three dimensional space), Kal (time), Mana (mind), and Atma (soul or spirit).

Seventeen kinds of gunas (qualities or characteristics) of objects are originally described. They are: Rupa (appearance or form), Rasa (taste), Gandh (smell), Sparsh (feel or touch), Sankyā (number), Parimāna (dimensions, size, or quantity), Pruthakatva (individuality, separateness, or isolation), Samyoga or sanjog (conjugation), Vibhāga (parts, divisions, or disjunctions), Paratva (remoteness, farness or superiority), Aparatva (nearness or inferiority), Buddhi (intelligence or judgment), Sukha (happiness or pleasure), Dukha (unhappiness or pain), Ichchhā (desire), Dvesha (aversion or animosity), Prayatna (effort - easy or hard).
Karma means action, activity, motion, or work done. It has four features: Akash (in space or in vacuum), Kāl (time), Dik or Dishā (direction), and Atman (inherent – size, magnitude, etc).