Pencil

However costly the pencil is, it needs a hand to write!

What is inside is more important than the color of the pencil!

The pencil will be sharpened now and often!!

Whatever the pencil writes the rubber has the capacity to rub it!

Implement these 4 in your life replacing pencils, to make living life easy!

My Thoughts.......... 59

 1) Love is all about giving and not demanding, it knows the joy of giving!

2) All attachments are illusions, nothing, and no one can suffer or enjoy your karmas, but you!

3) Maturity does not come easy. It takes a toll on experiences of hot and cold, ups and downs, acceptance and rejection, love and hate, fall and rise, but in the end, it makes you a worthy person with wisdom of life!

4) More than the disease, the perceived disease kills a person each minute!

5) Without Darkness you can't see the stars, without sorrow, you can't value happiness!

6) Remember, formless has all the forms in it and all forms come out of formless!

7) Remember, attachment and aversion are the cause of sorrow!

8) If you're travelling in the wrong direction turn in the right direction immediately, the longer the distance in the wrong direction, the more expensive it will be to turn back!!

9) Remember, it takes 2 years to learn to talk and 60 to learn to remain silent!  

10) Don't be a perfectionist; it is a pain. Be carefree & Enjoy the world!

The Rani of Jhansi

 

Lakshmibai, The Rani of Jhansi 19 November 1835 – 17 June 1858 known as Jhansi Ki Rani, was the queen of the Maratha-ruled princely state of Jhansi, was one of the leading figures of the Indian Rebellion of 1857, and a symbol of resistance to British rule in India. She has gone down in Indian history as a legendary figure, as India's "Joan of Arc. she was called by the name Manikarnika. Affectionately, her family members called her Manu. At a tender age of four, she lost her mother. As a result, the responsibility of raising her fell upon her father. While pursuing studies, she also took formal training in martial arts, which included horse riding, shooting and fencing .

Originally named Manikarnika at birth nicknamed Manu , she was born on 19 November 1835 at Kashi Varanasi to a Maharashtrian Karhade Brahmin family from Dwadashi, District Satara. She lost her mother at the age of four. She was educated at home. Her father Moropant Tambey worked at the court of Peshwa Baji Rao II at Bithur and then travelled to the court of Raja Gangadhar Rao Newalkar, the Maharaja of Jhansi, when Manu was thirteen years old. She was married to Gangadhar Rao, the Raja of Jhansi, at the age of 14.
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During that period, Lord Dalhousie was the Governor General of British India. The adopted child was named Damodar Rao. As per the Hindu tradition, he was their legal heir. However, the British rulers refused to accept him as the legal heir. As per the Doctrine of Lapse, Lord Dalhousie decided to seize the state of Jhansi. Rani Lakshmibai went to a British lawyer and consulted him. Thereafter, she filed an appeal for the hearing of her case in London. But, her plea was rejected. The British authorities confiscated the state jewels. Also, an order was passed asking the Rani to leave Jhansi fort and move to the Rani Mahal in Jhansi. Laxmibai was firm about protecting the state of Jhansi.

After her marriage, she was given the name Lakshmi Bai. Because of her father's influence at court, Rani Lakshmi Bai had more independence than most women, who were normally restricted to the zenana: she studied self-defense, horsemanship, archery, and even formed her own army out of her female friends at court.

Rani Lakshmi Bai gave birth to a son in 1851, however, this child died when he was about four months old. After the death of their son, the Raja and Rani of Jhansi adopted Damodar Rao. However, it is said that her husband the Raja never recovered from his son's death, and he died on 21 November 1853 of a broken heart.

Because Damodar Rao was adopted and not biologically related to the Raja, the East India Company, under Governor-General Lord Dalhousie, was able to install the Doctrine of Lapse, rejecting Rao's rightful claim to the throne. Dalhousie then annexed Jhansi, saying that the throne had become "lapsed" and thus put Jhansi under his "protection". In March 1854, the Rani was given a pension of 60,000 rupees and ordered to leave the palace at the Jhansi fort.

Rani Jhansi was determined not to give up Jhansi. She strengthened its defences and assembled a volunteer army. Women were also given military training. Rani's forces were joined by warriors including Gulam Gaus Khan, Dost Khan, Khuda Baksh, Lala Bhau Bakshi, Moti Bai, Sunder-Mundar, Kashi Bai, Deewan Raghunath Singh and Deewan Jawahar Singh.

While this was happening in Jhansi, on May 10, 1857 the Sepoy (soldier) Mutiny of India started in Meerut. This would become the starting point for the rebellion against the British. It began after rumours were put about that the new bullet casings for their Enfield rifles were coated with pork/beef fat, pigs being taboo to Muslims and cows sacred to Hindus and thus forbidden to eat. British commanders insisted on their use and started to discipline anyone who disobeyed. During this rebellion many British civilians, including women, and children were killed by the sepoys. The British wanted to end the rebellion quickly.

Meanwhile, unrest began to spread throughout India and in May of 1857, the First War of Indian Independence erupted in numerous pockets across the northern subcontinent. During this chaotic time, the British were forced to focus their attentions elsewhere, and Lakshmi Bai was essentially left to rule Jhansi alone. During this time, her qualities were repeatedly demonstrated as she was able swiftly and efficiently to lead her troops against skirmishes breaking out in Jhansi. Through this leadership Lakshmi Bai was able to keep Jhansi relatively calm and peaceful in the midst of the Empire’s unrest.

Up to this point, she had been hesitant to rebel against the British, and there is still some controversy over her role in the massacre of the British HEIC officials and their wives and children on the 8th June 1857 at Jokhan Bagh. Her hesitation finally ended when British troops arrived under Sir Hugh Rose and laid siege to Jhansi on 23rd March 1858. Rani Jhansi with her faithful warriors decided not to surrender. The fighting continued for about two weeks. Shelling on Jhansi was very fierce. In the Jhansi army women were also carrying ammunition and were supplying food to the soldiers. Rani Lakshmi Bai was very active. She herself was inspecting the defense of the city. She rallied her troops around her and fought fiercely against the British. An army of 20,000, headed by the rebel leader Tatya Tope, was sent to relieve Jhansi and to take Lakshmi Bai to freedom. However, the British, though numbering only 1,540 in the field so as not to break the siege, were better trained and disciplined than the “raw recruits,” and these inexperienced soldiers turned and fled shortly after the British began to attack on the 31st March. Lakshmi Bai’s forces could not hold out and three days later the British were able to breach the city walls and capture the city. Yet Lakshmi Bai escaped over the wall at night and fled from her city, surrounded by her guards, many of whom were from her women’s military.

Along with the young Damodar Rao, the Rani decamped to Kalpi along with her forces where she joined other rebel forces, including those of Tatya Tope. The Rani and Tatya Tope moved on to Gwalior, where the combined rebel forces defeated the army of the Maharaja of Gwalior after his armies deserted to the rebel forces. They then occupied the strategic fort at Gwalior. However on the second day of fighting, on 18 June 1858, the Rani died.
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She died on 18 June, 1858 during the battle for Gwalior with 8th Hussars that took place in Kotah-Ki-Serai near Phool Bagh area of Gwalior. She donned warrior's clothes and rode into battle to save Gwalior Fort, about 120 miles west of Lucknow in what is now the state of Uttar Pradesh. The British captured Gwalior three days later. In the report of the battle for Gwalior, General Sir Hugh Rose commented that the rani "remarkable for her beauty, cleverness and perseverance" had been "the most dangerous of all the rebel leaders".
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However, the lack of a corpse to be convincingly identified as the Rani convinced Captain Rheese of the so called "bravest" regiment that she had not actually perished in the battle for Gwalior, stating publicly that:" Queen of Jhansi is alive!". It is believed her funeral was arranged on same day near the spot where she was wounded. One of the her maidservants helped with the arrangement of quick funeral.

Because of her bravery, courage, and wisdom, and her progressive views on women's empowerment in 19th century India, and due to her sacrifices, she became an icon of Indian independence movement. The Rani was memorialized in bronze statues at both Jhansi and Gwalior, both of which portray her on horseback.

Her father, Moropant Tambey, was captured and hanged a few days after the fall of Jhansi. Her adopted son, Damodar Rao, was given a pension by the British Raj and cared for, although he never received his inheritance.

Rani Lakshmi Bai became a national heroine and was seen as the epitome of female bravery in India. When the Indian National Army created its first female unit, it was named after her.

Indian poetess Subhadra Kumari Chauhan wrote a poem in the Veer Ras style about her, which is still recited by children in schools of contemporary India.

In a prophetic statement in the 1878 book The History of the Indian Mutiny, Colonel Malleson said "...her countrymen will always believe that she was driven by ill-treatment into rebellion; that her cause was a righteous cause; ..... To them she will always be a heroine !!

Konark Sun Temple

 

Konark Sun Temple

It's a 13th-century Sun Temple at Konark, in Odisha, India.

It was supposedly built by King Narasimhadeva I of Eastern Ganga Dynasty around 1250.It has been built in the shape of a gigantic chariot with elaborately carved stone wheels, pillars and walls. A major part of the structure is now in ruins

The name Konark derives from the combination of the Sanskrit words, Kona (corner) and Arka (sun), in reference to the temple which was dedicated to the Sun god Surya.

The monument was also called the Black Pagoda by European sailors. In contrast, the Jagannath Temple in Puri was called the White Pagoda. Both temples served as important landmarks for the sailors.

The temple was originally built at the mouth of the river Chandrabhaga, but the waterline has receded since then. The temple has been built in the form of a giant ornamented chariot of the Sun god, Surya. It has twelve pairs of elaborately carved stone wheels some of which are 3 meters wide and is pulled by seven pairs of horses. The temple follows the traditional style of Kalinga architecture. It is carefully oriented towards the east, so that the first rays of sunrise strike the principal entrance. The temple is built from Khondalite rocks.

The original temple had a main Sanctum Sanctorum (vimana), which was supposedly 229 feet (70 m) tall. Due to the weight of the superstructure (70m tall) and weak soil of the area the main vimana fell in 1837. The audience hall (Jagamohana), which is about 128 feet (30 m) tall, still stands and is the principal structure in the surviving ruins. Among the structures, which have survived to the current day, are the dance hall (Nata mandira) and dining hall (Bhoga mandapa). The Konark temple is also known for its erotic sculptures of maithunas.

Two smaller ruined temples have been discovered nearby. One of them is called the Mayadevi Temple and is located southwest from the entrance of the main temple. It is presumed to have been dedicated to Mayadevi, one of the Sun god's wives. It has been dated to the late 11th century, earlier than the main temple. The other one belongs to some unknown Vaishnava deity. Sculptures of Balarama, Varaha and Trivikrama have been found at the site, indicating it to be a Vaishnavite temple. Both temples have their primary idols missing.

A collection of fallen sculptures can be viewed at the Konark Archaeological Museum which is maintained by the Archaeological Survey of India.

According to Bhavishya Purana and Samba Purana, there may have been a sun temple in the region earlier than current one, dating to the 9th century or earlier. The books mention three sun temples at Mundira (possibly Konark), Kalapriya (Mathura), and Multan.

According to the scriptures, Samba, the son of Krishna, was cursed with leprosy. He was advised by the sage, Kataka, to worship the sun god to cure his ailment. Samba underwent penance for 12 years in Mitravana near the shores of Chandrabhaga. Both the original Konark temple and the Multan temple have been attributed to Samba.

The Periplus of the Erythraean Sea (1st Century CE) mentions a port called Kainapara, which has been identified as current day Konark.

According to the Madala Panji, there was another temple in the region. It was built by one Pundara Kesari. He may have been Puranjaya, the 7th century ruler, of the Somavasmi Dynasty dynasty.

Narasimhadeva I

The current temple is attributed to Narasimhadeva I of the Eastern Ganga Dynasty. His reign spanned from 1238 to 1264 CE. The temple may have been a monument to his victory against Tughral Tughan Khan.

Dharmapada's Tale

According to local folklore, Narasimhadeva I had hired a chief architect called Bisu Maharana to build the temple. After a period of twelve years, a workforce of twelve thousand almost finished the construction. But, they failed to mount the crown stone. The impatient king ordered the temple to be finished in three days or the artisans be put to death. At the time, Bisu Maharana's twelve year old son, Dharmapada arrived at the site. Bisu Maharana had never seen his son, as he had left his village when his wife was still pregnant. Dharmapada successfully proposed a solution to mount the crown stone. But, the artisans were still apprehensive that the king will be displeased to learn that a boy succeeded where his best artisans failed. Dharmapada climbed onto the temple and leapt into the water to save his father and his co-workers.

Collapse

There have been several proposed theories for the collapse of the main sanctum. The date of the collapse is also not certain.

The Kenduli copper plates of Narasimha IV (Saka 1305 or 1384 CE) states the temple to be in a perfect state.

In the 16th century Ain-i-Akbari, Abul Fazl also mentions Konark being in a proper state. The account also mentions the cost of construction being 12 years of revenue.

The cause of collapse is also placed on Kalapahad who invaded Odisha in 1568.

In 1627, the then Raja of Khurda had removed the sun idol from Konark and moved it to the Jagannath temple in Puri.

James Fergusson (1808–1886) had the opinion that marshy foundation had caused the collapse. But, the structure has shown no sign of sinking into its foundation. Fergusson, who visited the temple in 1837, recorded a corner of the main sanctum still standing. It also fell down in 1848 due to a strong gale.

According to Percy Brown (1872–1955), the temple was not properly completed and so it collapsed. This contradicts earlier recorded accounts of the temple being in a proper state.

In 1929, an analysis of a moss covered rock estimated the date of abandonment at around 1573.

Other proposed causes include lighting and earthquake.

Aruna Stambha

In the last quarter of the 18th century, when worship had ceased in the temple, the Aruna stambha (Aruna pillar) was removed from the entrance of Konark temple and placed at the Singha-dwara (Lion's Gate) of the Jagannath temple in Puri by a Maratha Brahmachari called Goswain (or Goswami). The pillar is made of monolithic chlorite and is 33 feet 8 inches (10.26 m) tall . It is dedicated to Aruna, the charioteer of the Sun god.

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VIDUR

 

Is it true that Vidur was himself the Yamraj (god of death) who was suffering a curse over Earth in the epic of Mahabharata?

• Vidur : Vidura also known as Kshatri, plays a key role in the Hindu epic Mahabharata. He is described as the prime minister of the Kuru kingdom and is the paternal uncle of both the Pandavas and the Kauravas.

• Yes ,it's true Yamraj get punishment from one Saint. Vidur was himself the yamraj who was suffering a curse over earth in the epic Mahabhart.

here is story …

Sage Maitreya told Vidura that he was not an ordinary man, but was infact an incarnation of YAMRAJ (the Lord of Death). Maitreya further told Vidura that it was because of Curse of sage Manduka that Yamraja had to take birth in human form as Vidura. The complete story has been narrated in Mahabharata regarding birth of Yamraj in human form as Vidura

• O Vidura, in the past time, there was a king, whose jewelry had been stolen. The thieves were looking for a safe place to hide the stolen Jewelry. They concealed the stolen Jewelry at the hermitage of Sage Manduka, who was meditating at the Bank of River and practicing the silence. Soldiers of the King came near the hermitage of Sage Manduka and asked him about the thieves.

• But as Sage Manduka was practicing the oath of Silence, so he did not respond. Later the soldiers discovered the stolen Jewelry in the hermitage of Manduka. The soldiers of king arrested all the thieves and Manduka Muni. When King asked Sage Manduka about the stolen Jewelry, he did not utter even a single word as he had taken the oath of silence. Hence King punished the sage Manduka to death by being pierced with a lance. Later the King discovered that he was great Sage so he sought pardon from Manduka.

• Sage Manduka pardoned the king but he went to Yamloka and inquired with Yama about the sin committed by him for which he was made to suffer impalement on a stake? Sage Manduka further questioned Yamraja that he did not remember any such act done by him in his life time which invited such punishment.

• Then Yamraja replied that in his childhood , Manduka pierced an ant with a sharpened straw, and for that reason he had to face the consequences. Manduka replied that as a child, he was not having guilty mind to commit a crime. He was wrongly punished by Yamraja for his innocence. He further cursed Yamraja to take the birth in human form and to undergo the suffering. This was the reasons for suffering of Vidura.

• Manduka further reminded Yamraja that he committed mistake in not considering the laws narrated in the Scriptures as scriptures did not not consider the act of a child as sinful up to the age of twelve. Manduka further declared a law that a child till the age of fourteen, shall not be punished for any of his act as till this time, a child does not have guilty mind. After hearing this story, Vidura relieved from the suffering he was undergoing throughout his life

Brihadeshwara Temple, Thanjavur.

 

Brihadeshwara Temple, Thanjavur.

When people think of India they think of the Taj Mahal, Shāh Jahān’s Eternal memorial dedicated to his wife Mumtāz Mahal.

But there is a more ancient and secret India hidden deep in its tropical jungles with one of the greatest building efforts in the Human History produced Thousands of strange and mysterious temples, today they are lost and forgotten. This is India's Deep South the land of emerald green Rice fields and Immense Palm Forests where every few miles temples sour towards the heavens in the country side.

Here over a thousand year ago, 985 AD to be exact Rajaraja Cholan became King of the Chola Dynasty, His Original name was Arunmozhivarman and his title was Rajakesari Varman or Mummudi-Sola-Deva, he was the second son of the Parantaka Cholan II.

His capital was the city of Thanjavur. Thanjavur was the royal city of the Cholas, Nayaks and the Mahrattas. Thanjavur derives its name from Tanjan-an asura (giant), who according to local legend devastated the neighborhood and was killed by Sri Anandavalli Amman and the God Vishnu.

He was one of the greatest kings of India and in the south, he embarked on one of the largest building plans in the history of Mankind that still continues till this day, He and his successor have moved more Stone than the great pyramid of Giza.

This temple is so large that over 200 Taj Mahal’s can fit into its Temple Grounds.

It's one of the most amazing buildings in India, its 10 times taller than anything builds before it and not only it's huge but its made of Granite, one of the hardest stones in the world. The inner shrine under the large tower contains a large stone Lingam, 12ft in height and 5ft in diameter. The original name of the deity was Rajarajeshwar. It was the Marathas who gave it the name Brihadeeshwara or the Great Ishwara. The statue of Nandi at the entrance of the temple is carved out of a single stone. The image of Nandi faces the Sanctum and constructed with such great precision that it reflects the rays of the Sun on to the Sanctum.

A unique stone named Chandrakanta is laid on the Sanctum which is said to regulate the temperature inside the shrine. The walls and ceilings of the shrine are replete with magnificent sculptures and bear silent testimony to the creativity of the craftsmen. Several other shrines dedicated to various Gods are located within the temple premises, along with the images of Navagrahas, the nine planetary deities. Numerous bronze statues depicting Chola art prevalent in the 11th century are also found within the temple complex.

To build Temple's like this, required Huge Amounts of Money, and the way to get it is by attacking your weaker neighbors and Rajaraja began his career with the conquest of the Chera country. He defeated Chera King Bhaskara Ravivarman, whose fleet he destroyed in the port of Kandalur. He also seized Pandya Amara Bhujanga and captured the port of Vilinam. By his campaign against the Singhalees, he annexed northern Ceylon (Modern Day Sri Lanka), building a number of a stone temple in the Ceylonese capital Polonnaruva, of which one now stands to Shiva. It was at about the 14th year of his reign (AD 998-999) that most of his triumphs were achieved. Having already overcome the Chera, Rajaraja assumed the title "Mummudi Cholan".Through his son Rajendra Cholan. Chola also simultaneously directed his arms against Ceylon. Rajaraja moved the capital from Anuradhapura to Polonnaruwa. With Rajaraja, the Chola culture and Shiva religion permeated the whole of Ceylon (Sri Lanka).

Rajarajan having thus realized his cherished military glories, in or about 1003 AD has sheathed his sword, and turned his thoughts towards a life of peace. It was about this time, that the Chidambaram temple authorities bestowed on him the title of "Sri Rajarajan".

After Rajaraja secured a good supply of money he started construction on his Temple of Bragatheeswarar. The quarry that supplied the granite, one of the hardest stones in the world, was over 50 miles away from the temple site. Most of the Stones were moved over Boats but some much heavier ones like the Capstones which summit the top of the tower weight 40 ton's each, were moved with the combination of a Ramp and Elephants.

The main temple is entirely built of granite. More than 1,30,000 tons of granite is said to have been used to build it. The original Ramp's remains still exist today after over a 1000 years and its calculated to be at a Gentle 6-degree slope pointing towards the Temple Top and is situated 1 mile from the temple. After calculations, a Ramp with a 6 degree slope and 1 mile away would intersect the tower's top exactly 216ft in the air which is also the height of the temple tower known as Dakshin Meru or Southern Meru is topped by a dome structure which rests on a single 7.7 m square granite block weighing around 80 tons.

To Move the Stones from the Quarry to the Ramp and up on the Ramp, Elephants were used by using wooden Rollers beneath the Stones so they could be rolled into place much like how the Ancient Egyptians made the Pyramid. The entire rectangular complex measures approximately 140 x 75 meters and is surrounded by a wall with regular interior niches. Inside the compound are various secondary shrines and a monumental double gateway entrance. The building has a front entrance porch (mandapa) with 36 columns, and there are two additional entrances at the base of the tower on each side.

All three entrances are decorated with guardian figure sculptures, some double life-size, and are approached by a richly carved monumental flight of stairs. The hundreds of niches of the exterior are decorated with sculpture of divine figures (murti) – especially Shiva and Devi, lion heads (kirttimukha), and fan shapes.

You’d think Rajaraja was crazy going to so much trouble to make just a Temple, but Rajaraja was a very religious man and he was caught between a Rock and a hard place, on one hand, His Religion Forbade him to kill, and on the other hand to be a successful king he had to make war on his neighbors for his people's sake otherwise his kingdom would be weak and easily overrun and so he was responsible for the deaths of Hundred’s of Thousands of his enemy's.

He firmly believed as do all Hindus today in Rebirth & Reincarnation, that your actions in this life will determine your Lot in the next one, given the blood on Rajaraja's hand he might come back as a worm or something even worse. So he spent fabulous amounts of money on his temple's for example it is written in an inscription that it took 4000 cows, 7000 Goats, and 30 buffalos just to supply the butter required for the Lamps that were lit in the temple & temple grounds, all this to light just 1 temple and Rajaraja provided for 100's of temples that he created just to insure that he kept his karma in good standing because of the generosity he hoped that gods would overlook his transgressions and be persuaded to reincarnate him as something better than a worm.

Indian Religion during Rajaraja's time also spread across other lands, that’s why in the steaming jungles of Cambodia the Temples of Angkor wat don’t depict Cambodian Gods but the Gods of India. Not only did religion spread Art also spread when Europe was languishing in the Dark Age the Artist’s in the Chola Empire were making bronze statues like the famous Nataraja.

Shiva who appears as Nataraja the Lord of the dance simultaneously crushes the dwarf of ignorance under his foot, beating the drum of creation, unleashing the fires of destruction, and finally raising 1 hand in assurance telling us to fear not.

The temple was laid out on a precise plan of 16 x 16 squares, a design known as Padmagarbha mandala in the Dravida architecture of southern India. The interior contains the typical passageway for worshippers to perform circumambulation, in this case on two levels. There is a snapana platform, too, for the ritual bathing of the god located within a portico (ardhamandapa). Murals decorate the interior walls, and, once hidden by later Nayaka period paintings, these include fine images of Rajaraja I, his spiritual advisor or guru, and his three queens. Other subjects include a Nataraja (Shiva as Lord of the Dance) who was the clan deity of the Cholas (kuladevata).

When Rajaraja died in 1014 he left behind him a shining legacy that made him one of the greatest patrons of art and religion in India.

The Chola Dynasty ended with King Rajendra Chola III the last Chola King. The last recorded date of Rajendra III is 1279 A.D. There is no evidence that Rajendra was followed immediately by another Chola prince. The Chola empire was completely overshadowed by the Pandyan empire, though many small chieftains continued to claim the title "Chola" well into the fifteenth century C.E.

The temple has a portrait of Raja Raja Cholan paying obeisance to Lord Natarajar. This is undoubtedly, the first ever instance of a royal portrait.

Inscriptions in the temple point towards Kunjara Mallan Raja Raja Perunthachan as the chief architect of the temple. His successors survive to this day and practice the art of Vastu or Vastu Shastra.

Depictions of nartakis or dancers showing eighty-one of hundred and eight karanas (synchronized movements of hands and feet) in Bharata Natyam are carved here. These karanas are a part of karanas mentioned in the Natya Shastra of Bharata Muni or Sage Bharata. There is also evidence that the temple was a platform for talented dancers to showcase their talent. These depictions are first of their kind.

The inscriptions also mention the different kinds of jewels used in the period. Each of these jewels are mentioned in detail. A total of twenty-three different types of pearls, eleven varieties of diamonds and rubies are mentioned in these inscriptions.

What astounds historians is that there was not a single granite quarry in about 100 km radius of the temple. This means that transporting these stones would have been a herculean task. But Raja Raja Cholan insisted on the use of these stones. All of these features make this Chola temple of Tanjore, a magnum opus of the Chola reign.

Significance of Gujarati New Year

 

Significance of Gujarati New Year ::

The Gujarati New Year is celebrated the day after the festival of Diwali (which occurs in mid-fall – either October or November, depending on the Lunar calendar). The Gujarati New Year is synonymous with sud ekam i.e. first day of Shukla paksha of the Kartik month -, which is taken as the first day of the first month of Gujarati lunar calendar.

Bestu Varas is New Year in Gujarati and Varsha-pratipada or Padwa are other names of the same. According to the legends, Lord Krishna once performed Govardhan Pooja along with the people of Vraja for their protection from heavy rains. Since then, it became a tradition to worship Govardhan Parvat and celebrate this day as a New Year.

Bestu Varas Celebrations

Tradtional customs and rituals are performed to welcome the New Year and bid farewell to the by gone time. It's a day of blooming desires and zest. Bestu Varas is the time to reitre all the pains, sufferings and memories of past year.

New Year in Gujarat is the time to make merry. Since these celebrations are escalated at the time of Diwali, it marks a mirthful experience for all the gujjus. Almost all Gujarati houses are lighted colorfully and decorated with flowers. On this day, people dress up nicely and visit temples with flowers and mithai. Everyone wish each other New Year whilst offering prayers to God. Some temples in Gujarat also conduct a grand Govardhan Pooja.

A lavish meal at the end of the day credits the festival spirit. Most of the Gujaratis indulge in heavy eating this day. Thus, New Year in Gujarat reflects the true spirit of Indian tradition. The essence of Gujarati culture and religion can be felt in the New Year celebrations. Love, unity and togetherness are the intangible assets of these celebrations.

My Thoughts ...................... 58

 1) Why be in competition with anybody, accept yourself as you are, you are perfect, the masterpiece!!

2) Fame is foolish, it is pointless, meaningless. Even if the whole world knows you, how does it matter, when you don't know your real self!

3) What goes on within the mind comes invariably on the tongue. The tongue never slips – remember this always.

4) Do not make Death the source of fear, make Death the source of Life, and live life with love, care, and compassion for all!

5) Never allow anybody to interfere in your life & Don't interfere in anybody´s life

6) Victim-orientated people, quite often don’t like the truth very much..

7) Trust is personal, and Belief is social. That's the difference!

8) Don't fall in love, grow together in love, falling is easy, growing needs effort!

9) You feel sorrow as your mind is in captivity!

10) Nothing is good, nothing is bad, everything is your perception and need and aversion

My Thoughts ...................... 57

 1) Acceptance is bliss, wanting to change is a problem!

2) Major reason for health issues today is stress because love, sacrifice, and togetherness are missing from our life, we have become more self-centered!

3) Stop worrying about whether life exists after death. The real question is whether you are alive before death.

4) Remember, In love the other is important; in lust you are important

5) Love is the goal, life is the journey.

6) When you love a person, you love him in toto, he comes with a few defects too, do not try to change him, and regret losing the original one!

7) The desire to possess possesses you and you become a slave to the possessiveness!

8) Life is a celebration. Nature has given us flowers, plants, mountains, rivers, forests, food, etc., but we choose to be unhappy by becoming slaves to our wants and egos!

9) Love & compassion are enough to do good, you need the power to do something harmful!

10) Silence, when alone is easy, maintaining in chaos and provocation is bliss!

DASA MAHAVIDHYA : 10 KAMALA MAHA VIDHYA

 

Goddess Kamala

Kamala is the tenth of the ten Mahavidya Goddesses. Goddess Kamala is considered the most supreme form of the goddess who is in the fullness of Her graceful aspect. She is not only compared with Goddess Lakshmi but also considered to be Goddess Lakshmi. She is also known as Tantric Lakshmi. The goddess in the form of Kamala bestows prosperity and wealth, fertility and crops, and good luck. Hence She is Devi of both Dhan and Dhanya i.e. wealth and grains.

Kamala Origin

Goddess Kamala is same as Goddess Lakshmi. According to Hindu calendar, Kamala Jayanti is celebrated on Amavasya Tithi of Ashwina month (Purnimanta Kartika month).

Kamala Iconography

Goddess Kamala is portrayed in red dress and lavishly adorned with golden jewelry. She has golden complexion. She is depicted with four arms. In two arms, She holds lotus flowers and with remaining two arms She makes boon-giving and being-fearless gestures which are known as Varada and Abhaya Mudra respectively.

She is flanked by four elephants who are shown giving Abhishekam to Goddess Kamala who is sitting in the midst of the ocean on a lotus flower.

Kamala Sadhana

Goddess Kamala Sadhana is performed to gain wealth and prosperity.

Kamala Mool Mantra
ॐ ह्रीं अष्ट महालक्ष्म्यै नमः॥

Om Hreem Ashta Mahalakshmyai Namah॥

The Lost Glory of Bharatha Varsha : Part 8

Amazing Science, Cosmology and Psychology, Medicine (Ayurveda),

Part 8

Plastic Surgery In India 2600 Years Old

Sushruta, known as the father of surgery, practiced his skill as early as 600 BCE. He used cheek skin to perform plastic surgery to restore or reshape the nose, ears, and lips with incredible results. Modern plastic surgery acknowledges his contributions by calling this method of rhinoplasty the Indian method.

125 Types Of Surgical Instruments

"The Hindus (Indians) were so advanced in surgery that their instruments could cut a hair longitudinally".
~MRS Plunket

Sushruta worked with 125 kinds of surgical instruments, which included scalpels, lancets, needles, catheters, rectal speculums, mostly conceived from the jaws of animals and birds to obtain the necessary grips. He also defined various methods of stitching: the use of horse’s hair, fine thread, fibers of bark, goat’s guts, and ant’s heads.

300 Different Operations

Sushruta describes the details of more than 300 operations and 42 surgical processes. In his compendium Sushruta Samhita he minutely classifies surgery into 8 types:

Aharyam = extracting solid bodies

Bhedyam = excision

Chhedyam = incision

Aeshyam = probing

Lekhyam = scarification

Vedhyam = puncturing

Visraavyam = evacuating fluids

Sivyam = suturing

The ancient Indians were also the first to perform an amputation, cesarean surgery, and cranial surgery. For rhinoplasty, Shushruta first measured the damaged nose, skillfully sliced off the skin from the cheek, and sutured the nose. He then placed medicated cotton pads to heal the operation.

India’s Contributions Acknowledged

Contributors:

"It is true that even across the Himalayan barrier India has sent to the west, such gifts as grammar and logic, philosophy and fables, hypnotism and chess, and above all numerals and the decimal system."

Will Durant (American Historian, 1885-1981)

Language

"The Sanskrit language, whatever be its antiquity, is of wonderful structure, more perfect than the Greek, more copious than the Latin and more exquisitely refined than either".

Sir William Jones (British Orientalist, 1746-1794)

Philosophy

~If I were asked under what sky the human mind has most fully developed some of its choicest gifts, has most deeply pondered on the greatest problems of life and has found solutions, I should point out to India".

Max Muller (German Scholar, 1823-1900

Religion

"There can no longer be any real doubt that both Islam and Christianity owe the foundations of both their mystical and their scientific achievements to Indian initiatives".

-Philip Rawson (British Orientalist)

Atomic Physics

"After the conversations about Indian philosophy, some of the ideas of Quantum Physics that had seemed so crazy suddenly made much more sense".

W. Heisenberg (German Physicist, 1901-1976)

Surgery

"The surgery of the ancient Indian physicians was bold and skillful. A special branch of surgery was devoted to rhinoplasty or operations for improving deformed ears, noses and forming new ones, which European surgeons have now borrowed".

Sir W.Hunter (British Surgeon, 1718-1783)

Literature

"In the great books of India, an empire spoke to us, nothing small or unworthy, but large, serene, consistent, the voice of an old intelligence which in another age and climate had pondered and thus disposed of the questions that exercise us".

- R.W.Emerson (American Essayist, 1803-1882)

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The Lost Glory of Bharatha Varsha : Part 7

 

Amazing Science, Cosmology and Psychology, Medicine (Ayurveda)

Part 7

The Indian Numeral System

Although the Chinese were also using a decimal-based counting system, the Chinese lacked a formal notational system that had the abstraction and elegance of the Indian notational system, and it was the Indian notational system that reached the Western world through the Arabs and has now been accepted as universal. Several factors contributed to this development whose significance is perhaps best stated by French mathematician, Laplace: "The ingenious method of expressing every possible number using a set of ten symbols (each symbol having a place value and an absolute value) emerged in India. The idea seems so simple nowadays that its significance and profound importance is no longer appreciated. Its simplicity lies in the way it facilitated calculation and placed arithmetic foremost amongst useful inventions."

Brilliant as it was, this invention was no accident. In the Western world, the cumbersome Roman numeral system posed as a major obstacle, and in China the pictorial script posed as a hindrance. But in India, almost everything was in place to favor such a development. There was already a long and established history in the use of decimal numbers, and philosophical and cosmological constructs encouraged a creative and expansive approach to number theory. Panini's studies in linguistic theory and formal language and the powerful role of symbolism and representational abstraction in art and architecture may have also provided an impetus, as might have the rationalist doctrines and the exacting epistemology of the Nyaya Sutras, and the innovative abstractions of the Syadavada and Buddhist schools of learning.

Influence of Trade and Commerce, Importance of Astronomy

The growth of trade and commerce, particularly lending and borrowing demanded an understanding of both simple and compound interest which probably stimulated the interest in arithmetic and geometric series. Brahmagupta's description of negative numbers as debts and positive numbers as fortunes points to a link between trade and mathematical study. Knowledge of astronomy - particularly knowledge of the tides and the stars was of great importance to trading communities who crossed oceans or deserts at night. This is borne out by numerous references in the Jataka tales and several other folktales. The young person who wished to embark on a commercial venture was inevitably required to first gain some grounding in astronomy. This led to a proliferation of teachers of astronomy, who in turn received training at universities such as at Kusumpura (Bihar) or Ujjain (Central India) or at smaller local colleges or Gurukuls. This also led to the exchange of texts on astronomy and mathematics amongst scholars and the transmission of knowledge from one part of India to another. Virtually every Indian state produced great mathematicians who wrote commentaries on the works of other mathematicians (who may have lived and worked in a different part of India many centuries earlier). Sanskrit served as the common medium of scientific communication.

The science of astronomy was also spurred by the need to have accurate calendars and a better understanding of climate and rainfall patterns for timely sowing and choice of crops. At the same time, religion and astrology also played a role in creating an interest in astronomy and the negative fallout of this irrational influence was the rejection of scientific theories that were far ahead of their time. One of the greatest scientists of the Gupta period - Aryabhatta (born in 476 AD, Kusumpura, Bihar) provided a systematic treatment of the position of the planets in space. He correctly posited the axial rotation of the earth and inferred correctly that the orbits of the planets were ellipses. He also correctly deduced that the moon and the planets shined by reflected sunlight and provided a valid explanation for the solar and lunar eclipses rejecting the superstitions and mythical belief systems surrounding the phenomenon. Although Bhaskar I (born Saurashtra, 6th C, and follower of the Asmaka school of science, Nizamabad, Andhra ) recognized his genius and the tremendous value of his scientific contributions, some later astronomers continued to believe in static earth and rejected his rational explanations of the eclipses. But in spite of such setbacks, Aryabhatta had a profound influence on the astronomers and mathematicians who followed him, particularly on those from the Asmaka school.

Mathematics played a vital role in Aryabhatta's revolutionary understanding of the solar system. His calculations on pi, the circumference of the earth (62832 miles) and the length of the solar year (within about 13 minutes of the modern calculation) were remarkably close approximations. In making such calculations, Aryabhatta had to solve several mathematical problems that had not been addressed before, including problems in algebra (beej-ganit) and trigonometry (trikonmiti).

Bhaskar I continued where Aryabhatta left off and discussed in further detail topics such as the longitudes of the planets; conjunctions of the planets with each other and with bright stars; risings and settings of the planets; and the lunar crescent. Again, these studies required still more advanced mathematics and Bhaskar I expanded on the trigonometric equations provided by Aryabhatta, and like Aryabhatta correctly assessed pi to be an irrational number. Amongst his most important contributions was his formula for calculating the sine function which was 99% accurate. He also did pioneering work on indeterminate equations and considered for the first time quadrilaterals with all the four sides unequal and none of the opposite sides parallel.

Another important astronomer/mathematician was Varahamira (6th C, Ujjain) who compiled previously written texts on astronomy and made important additions to Aryabhatta's trigonometric formulas. His works on permutations and combinations complemented what had been previously achieved by Jain mathematicians and provided a method of calculation of nCr that closely resembles the much more recent Pascal's Triangle. In the 7th century, Brahmagupta did important work in enumerating the basic principles of algebra. In addition to listing the algebraic properties of zero, he also listed the algebraic properties of negative numbers. His work on solutions to quadratic indeterminate equations anticipated the work of Euler and Lagrange.

Emergence of Calculus

In the course of developing a precise mapping of the lunar eclipse, Aryabhatta was obliged to introduce the concept of infinitesimals - i.e. tatkalika gati to designate the infinitesimal, or near-instantaneous motion of the moon, and express it in the form of a basic differential equation. Aryabhatta's equations were elaborated on by Manjula (10th C) and Bhaskaracharya (12th C) who derived the differential of the sine function. Later mathematicians used their intuitive understanding of integration in deriving the areas of curved surfaces and the volumes enclosed by them.

Applied Mathematics, Solutions to Practical Problems

Developments also took place in applied mathematics such as in the creation of trigonometric tables and measurement units. Yativrsabha's work Tiloyapannatti (6th C) gives various units for measuring distances and time and also describes the system of infinite time measures.

In the 9th C, Mahaviracharya ( Mysore) wrote Ganit Saar Sangraha where he described the currently used method of calculating the Least Common Multiple (LCM) of given numbers. He also derived formulae to calculate the area of an ellipse and a quadrilateral inscribed within a circle (something that had also been looked at by Brahmagupta) The solution of indeterminate equations also drew considerable interest in the 9th century, and several mathematicians contributed approximations and solutions to different types of indeterminate equations.

In the late 9th C, Sridhara (probably Bengal) provided mathematical formulae for a variety of practical problems involving ratios, barter, simple interest, mixtures, purchase and sale, rates of travel, wages, and filling of cisterns. Some of these examples involved fairly complicated solutions and his Patiganita is considered an advanced mathematical work. Sections of the book were also devoted to arithmetic and geometric progressions, including progressions with fractional numbers or terms, and formulas for the sum of certain finite series are provided.

A Mathematical investigation continued into the 10th C. Vijayanandi (of Benares, whose Karanatilaka was translated by Al-Beruni into Arabic) and Sripati of Maharashtra are amongst the prominent mathematicians of the century.

The leading light of 12th C Indian mathematics was Bhaskaracharya who came from a long-line of mathematicians and was head of the astronomical observatory at Ujjain. He left several important mathematical texts, including the Lilavati and Bijaganita and the Siddhanta Shiromani, an astronomical text. He was the first to recognize that certain types of quadratic equations could have two solutions. His Chakrawaat method of solving indeterminate solutions preceded European solutions by several centuries, and in his Siddhanta Shiromani, he postulated that the earth had a gravitational force, and broached the fields of infinitesimal calculation and integration. In the second part of this treatise, there are several chapters relating to the study of the sphere and its properties and applications to geography, planetary mean motion, an eccentric epicyclical model of the planets, first visibilities of the planets, the seasons, the lunar crescent, etc. He also discussed astronomical instruments and spherical trigonometry. Of particular interest are his trigonometric equations: sin(a + b) = sin a cos b + cos a sin b; sin(a - b) = sin a cos b - cos a sin b;

The Spread of Indian Mathematics

The study of mathematics appears to slow down after the onslaught of the Islamic invasions and the conversion of colleges and universities to Madarsas. But this was also the time when Indian mathematical texts were increasingly being translated into Arabic and Persian. Although Arab scholars relied on a variety of sources, including Babylonian, Syrian, Greek, and some Chinese texts, Indian mathematical texts played a particularly important role. Scholars such as Ibn Tariq and Al-Fazari (8th C, Baghdad), Al-Kindi (9th C, Basra), Al-Khwarizmi (9th C. Khiva), Al-Qayarawani (9th C, Maghreb, author of Kitab fi al-hisab al-Hindi), Al-Uqlidisi (10th C, Damascus, author of The book of Chapters in Indian Arithmetic), Ibn-Sina (Avicenna), Ibn al-Samh (Granada, 11th C, Spain), Al-Nasawi (Khurasan, 11th C, Persia), Al-Beruni (11th C, born Khiva, died Afghanistan), Al-Razi (Teheran), and Ibn-Al-Saffar (11th C, Cordoba) were amongst the many who based their own scientific texts on translations of Indian treaties. Records of the Indian origin of many proofs, concepts and formulations were obscured in the later centuries, but the enormous contributions of Indian mathematics were generously acknowledged by several important Arabic and Persian scholars, especially in Spain. Abbasid scholar Al-Gaheth wrote: " India is the source of knowledge, thought and insight”. Al-Maoudi (956 AD) who traveled in Western India also wrote about the greatness of Indian science. Said Al-Andalusi, an 11th C Spanish scholar and court historian was amongst the most enthusiastic in his praise of Indian civilization and specially remarked on Indian achievements in the sciences and in mathematics. Of course, eventually, Indian algebra and trigonometry reached Europe through a cycle of translations, traveling from the Arab world to Spain and Sicily, and eventually penetrating all of Europe. At the same time, Arabic and Persian translations of Greek and Egyptian scientific texts became more readily available in India

The Kerala School

Although it appears that original work in mathematics ceased in much of Northern India after the Islamic conquests, Benaras survived as a center for mathematical study, and an important school of mathematics blossomed in Kerala. Madhava (14th C, Kochi) made important mathematical discoveries that would not be identified by European mathematicians until at least two centuries later. His series expansion of the cos and sine functions anticipated Newton by almost three centuries. Historians of mathematics, Rajagopal, Rangachari, and Joseph considered his contributions instrumental in taking mathematics to the next stage, that of modern classical analysis. Nilkantha (15th C, Tirur, Kerala) extended and elaborated upon the results of Madhava while Jyesthadeva (16th C, Kerala) provided detailed proofs of the theorems and derivations of the rules contained in the works of Madhava and Nilkantha. It is also notable that Jyesthadeva's Yuktibhasa which contained commentaries on Nilkantha's Tantrasamgraha included elaborations on planetary theory later adopted by Tycho Brahe, and mathematics that anticipated work by later Europeans. Chitrabhanu (16th C, Kerala) gave integer solutions to twenty-one types of systems of two algebraic equations, using both algebraic and geometric methods in developing his results. Important discoveries by the Kerala mathematicians included the Newton-Gauss interpolation formula, the formula for the sum of an infinite series, and a series notation for pi. Charles Whish (1835, published in the Transactions of the Royal Asiatic Society of Great Britain and Ireland) was one of the first Westerners to recognize that the Kerala school had anticipated by almost 300 years many European developments in the field.

Yet, few modern compendiums on the history of mathematics have paid adequate attention to the often pioneering and revolutionary contributions of Indian mathematicians. But as this essay amply demonstrates, a significant body of mathematical works was produced in the Indian subcontinent. The science of mathematics played a pivotal role not only in the industrial revolution but in the scientific developments that have occurred since. No other branch of science is complete without mathematics. Not only did India provide the financial capital for the industrial revolution (see the essay on colonization) India also provided vital elements of the scientific foundation without which humanity could not have entered this modern age of science and high technology.

Notes: Mathematics and Music: Pingala (3rd C AD), author of Chandasutra explored the relationship between combinatorics and musical theory anticipating Mersenne (1588-1648) author of a classic on musical theory.

Mathematics and Architecture: Interest in arithmetic and geometric series may have also been stimulated by (and influenced) Indian architectural designs - (as in temple shikaras, gopurams, and corbelled temple ceilings). Of course, the relationship between geometry and architectural decoration was developed to its greatest heights by Central Asian, Persian, Turkish, Arab and Indian architects in a variety of monuments commissioned by the Islamic rulers.

Transmission of the Indian Numeral System: Evidence for the transmission of the Indian Numeral System to the West is provided by Joseph (Crest of the Peacock):-

· Quotes Severus Sebokht (662) in a Syriac text describing the "subtle discoveries" of Indian astronomers as being "more ingenious than those of the Greeks and the Babylonians" and "their valuable methods of computation which surpass description" and then goes on to mention the use of nine numerals.

Quotes from Liber abaci (Book of the Abacus) by Fibonacci (1170-1250): The nine Indian numerals are ...with these nine and with the sign 0 which in Arabic is sifr, any desired number can be written. (Fibonacci learned about Indian numerals from his Arab teachers in North Africa)

Influence of the Kerala School: Joseph (Crest of the Peacock) suggests that Indian mathematical manuscripts may have been brought to Europe by Jesuit priests such as Matteo Ricci, who spent two years in Kochi (Cochin) after being ordained in Goa in 1580. Kochi is only 70km from Thrissur (Trichur) which was then the largest repository of astronomical documents. Wish and Hyne - two European mathematicians obtained their copies of works by the Kerala mathematicians from Thrissur, and it is not inconceivable that Jesuit monks may have also taken copies to Pisa (where Galileo, Cavalieri, and Wallis spent time), or Padua (where James Gregory studied) or Paris (where Mersenne who was in touch with Fermat and Pascal, acted as agent for the transmission of mathematical ideas).

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The Lost Glory of Bharatha Varsha : Part 6

Amazing Science, Cosmology and Psychology, Medicine (Ayurveda)

Part 6

Science and Mathematics in India

History of Mathematics in India

Why one might ask, did Europe take over a thousand years to attain the level of abstract mathematics achieved by Indians such as Aaryabhatta?
The answer appears to be that Europeans were trapped in the relatively simplistic and concrete geometrical mathematics developed by the Greeks.
It was not until they had, via the Arabs, received, assimilated and accepted the place-value system of enumeration developed in India that they were able to free their minds from the concrete and develop more abstract systems of thought. This development, thus, triggered the scientific and information technology revolutions which swept Europe and, later, the world.

The role played by India in the development is no mere footnote, easily and inconsequentially swept under the rug of Eurocentric bias. To do so is to distort history, and to deny India one of its greatest contributions to world civilization.

Science and Mathematics in India

In all early civilizations, the first expression of mathematical understanding appears in the form of counting systems. Numbers in very early societies were typically represented by groups of lines, though later different numbers came to be assigned specific numeral names and symbols (as in India) or were designated by alphabetic letters (such as in Rome). Although today, we take our decimal system for granted, not all ancient civilizations based their numbers on a ten-base system. In ancient Babylon, a sexagesimal (base 60) system was in use.

The Decimal System in Harappa

In India, a decimal system was already in place during the Harappan period, as indicated by an analysis of Harappan weights and measures. Weights corresponding to ratios of 0.05, 0.1, 0.2, 0.5, 1, 2, 5, 10, 20, 50, 100, 200, and 500 have been identified, as have scales with decimal divisions. A particularly notable characteristic of Harappan weights and measures is their remarkable accuracy. A bronze rod marked in units of 0.367 inches points to the degree of precision demanded in those times. Such scales were particularly important in ensuring proper implementation of town planning rules that required roads of fixed widths to run at right angles to each other, for drains to be constructed of precise measurements, and for homes to be constructed according to specified guidelines. The existence of a gradated system of accurately marked weights points to the development of trade and commerce in Harappan society.

Mathematical Activity in the Vedic Period

In the Vedic period, records of mathematical activity are mostly to be found in Vedic texts associated with ritual activities. However, as in many other early agricultural civilizations, the study of arithmetic and geometry was also impelled by secular considerations. Thus, to some extent, early mathematical developments in India mirrored the developments in Egypt, Babylon, and China.

The system of land grants and agricultural tax assessments required accurate measurement of cultivated areas. As land was redistributed or consolidated, problems of mensuration came up that required solutions. In order to ensure that all cultivators had equivalent amounts of irrigated and non-irrigated lands and tracts of equivalent fertility - individual farmers in a village often had their holdings broken up in several pieces to ensure fairness. Since plots could not all be of the same shape - local administrators were required to convert rectangular plots or triangular plots to squares of equivalent sizes and so on.

Tax assessments were based on fixed proportions of annual or seasonal crop incomes but could be adjusted upwards or downwards based on a variety of factors. This meant that an understanding of geometry and arithmetic was virtually essential for revenue administrators. Mathematics was thus brought into the service of both the secular and the ritual domains.

Arithmetic operations (Ganit) such as addition, subtraction, multiplication, fractions, squares, cubes, and roots are enumerated in the Narad Vishnu Purana attributed to Ved Vyas (pre-1000 BC). Examples of geometric knowledge (Rekha-ganit) are to be found in the Sulva-Sutras of Baudhayana (800 BC) and Apasthmaba (600 BC) which describe techniques for the construction of ritual altars in use during the Vedic era.

It is likely that these texts tapped the geometric knowledge that may have been acquired much earlier, possibly in the Harappan period. Baudhayana's Sutra displays an understanding of basic geometric shapes and techniques of converting one geometric shape (such as a rectangle) to another of equivalent (or multiple, or fractional) areas (such as a square). While some of the formulations are approximations, others are accurate and reveal a certain degree of practical ingenuity as well as some theoretical understanding of basic geometric principles.
Modern methods of multiplication and addition probably emerged from the techniques described in the Sulva-Sutras.

Pythagoras - the Greek mathematician and philosopher who lived in the 6th C B.C was familiar with the Upanishads and learned his basic geometry from the Sulva Sutras. An early statement of what is commonly known as the Pythagoras theorem is to be found in Baudhayana's Sutra: The chord which is stretched across the diagonal of a square produces an area of double the size. A similar observation pertaining to oblongs is also noted. His Sutra also contains geometric solutions of a linear equation in a single unknown. Examples of quadratic equations also appear. Apasthamba's sutra (an expansion of Baudhayana's with several original contributions) provides a value for the square root of 2 that is accurate to the fifth decimal place. Apasthamba also looked at the problems of squaring a circle, dividing a segment into seven equal parts, and a solution to the general linear equation. The Jain texts from the 6th C BC such as the Surya Pragyapti describe ellipses.

Modern-day commentators are divided on how some of the results were generated. Some believe that these results came about through hit and trial - as rules of thumb, or as generalizations of observed examples. Others believe that once the scientific method came to be formalized in the Nyaya-Sutras - proofs for such results must have been provided, but these have either been lost or destroyed, or else were transmitted orally through the Gurukul system, and only the final results were tabulated in the texts. In any case, the study of Ganit i.e mathematics was given considerable importance in the Vedic period. The Vedang Jyotish (1000 BC) includes the statement: "Just as the feathers of a peacock and the jewel-stone of a snake are placed at the highest point of the body (at the forehead), similarly, the position of Ganit is the highest amongst all branches of the Vedas and the Shastras."

(Many centuries later, Jain mathematician from Mysore, Mahaviracharya further emphasized the importance of mathematics: "Whatever object exists in this moving and non-moving world, cannot be understood without the base of Ganit (i.e. mathematics)".)

Panini and Formal Scientific Notation

A particularly important development in the history of Indian science that was to have a profound impact on all mathematical treatises that followed was the pioneering work by Panini (6th C BC) in the field of Sanskrit grammar and linguistics. Besides expounding a comprehensive and scientific theory of phonetics, phonology, and morphology, Panini provided formal production rules and definitions describing Sanskrit grammar in his treatise called Asthadhyayi. Basic elements such as vowels and consonants, parts of speech such as nouns and verbs were placed in classes. The construction of compound words and sentences was elaborated through ordered rules operating on underlying structures in a manner similar to formal language theory.

Today, Panini's constructions can also be seen as comparable to modern definitions of a mathematical function. G G Joseph, in The crest of the peacock, argues that the algebraic nature of Indian mathematics arises as a consequence of the structure of the Sanskrit language. Ingerman in his paper titled Panini-Backus form finds Panini's notation to be equivalent in its power to that of Backus - inventor of the Backus Normal Form used to describe the syntax of modern computer languages. Thus Panini's work provided an example of a scientific notational model that could have propelled later mathematicians to use abstract notations in characterizing algebraic equations and presenting algebraic theorems and results in a scientific format.

Philosophy and Mathematics

Philosophical doctrines also had a profound influence on the development of mathematical concepts and formulations. Like the Upanishadic world view, space and time were considered limitless in Jain cosmology. This led to a deep interest in very large numbers and definitions of infinite numbers. Infinite numbers were created through recursive formulae, as in the Anuyoga Dwara Sutra. Jain mathematicians recognized five different types of infinities: infinite in one direction, in two directions, in area, infinite everywhere and perpetually infinite. Permutations and combinations are listed in the Bhagvati Sutras (3rd C BC) and Sathananga Sutra (2nd C BC).

Jain set theory probably arose in parallel with the Syadvada system of Jain epistemology in which reality was described in terms of pairs of truth conditions and state changes. The Anuyoga Dwara Sutra demonstrates an understanding of the law of indices and uses it to develop the notion of logarithms. Terms like Ardh Aached, Trik Aached, and Chatur Aached are used to denote log base 2, log base 3 and log base 4 respectively. In Satkhandagama various sets are operated upon by logarithmic functions to base two, by squaring and extracting square roots, and by raising to finite or infinite powers. The operations are repeated to produce new sets. In other works, the relation of the number of combinations to the coefficients occurring in the binomial expansion is noted.

Since Jain epistemology allowed for a degree of indeterminacy in describing reality, it probably helped in grappling with indeterminate equations and finding numerical approximations to irrational numbers.

Buddhist literature also demonstrates an awareness of indeterminate and infinite numbers. Buddhist mathematics was classified either as Garna (Simple Mathematics) or Sankhyan (Higher Mathematics). Numbers were deemed to be of three types: Sankheya (countable), Asankheya (uncountable) and Anant (infinite).

Philosophical formulations concerning Shunya - i.e. emptiness or the void may have facilitated the introduction of the concept of zero. While the zero (Bindu) as an empty place holder in the place-value numeral system appears much earlier, algebraic definitions of the zero and it's a relationship to mathematical functions appear in the mathematical treatises of Brahmagupta in the 7th C AD. Although scholars are divided about how early the symbol for zero came to be used in numeric notation in India, (Ifrah arguing that the use of zero is already implied in Aryabhatta) tangible evidence for the use of the zero begins to proliferate towards the end of the Gupta period. Between the 7th C and the 11th C, Indian numerals developed into their modern form, and along with the symbols denoting various mathematical functions (such as plus, minus, square root etc) eventually became the foundation stones of modern mathematical notation.