Monday, July 27, 2015

Botanical and zoology in ancient science

Reproduction, Sex and Heredity of plants

Ancient Indian literature also deals with sex, genetics, and reproduction of plants by fruits, seeds, roots, cuttings, graftings, plant apices and leaves. Buddha Ghosa, in his Sumangala-vilasini, a commentary on the Digha Nikaya, describes some of these methods under such terms as mula-vija (root seed), khandabija (cuttings), phaluvija (joints), agravija (budding) and bija-bija (seed).

 Atharvaveda and Arthasastra describe the propagation by seed (bija-bija or vijaruha) and bulbous roots (kandavija), respectively. The method of cutting (skandhavija) is described in the Arthasastra, Brhatsamhita and Sumangala-vilasini in the case of sugar cane, jackfruit, blackberry, pomegranate, vine, lemon tree, asvattha (Ficus religiosa), nyagrodha (Ficus bengalensis), udumbara (Ficus glomerata) and several others. 

Some ideas related to sexuality in plants are noticeable in the Harita and Charak Samhitas. Charak recognized male and female individuals in the plant called Kutaja (Hollerhina antidysenterica), and the male categories of plants bearing white flowers, large fruit and tender leaves and the female categories characterized by yellow flowers, small fruits, short stalk, etc. 

The Rajanighantu mentions the existence of male and female plants in the plant Ketaki (Pandanus odoratissimus). The male plant is called sitaketaki, and the female is called svarna ketaki. Regarding heredity, Charaka and Susruta mention that the fertilized ovum contains in miniature all the organs of the plants, for example the bamboo seed containing in miniature the entire structure of the bamboo tree, and further that the male sperm cell have minute elements derived form each of its organs and tissues. 

http://www.infinityfoundation.com/mandala/t_es/t_es_tiwar_botany_frameset.htm

Reproduction, Sex and Heredity of plants Ancient Indian literature also deals with sex, genetics, and reproduction of plants by fruits, seeds, roots, cuttings, graftings, plant apices and leaves. Buddha Ghosa, in his Sumangala-vilasini, a commentary on the Digha Nikaya, describes some of these methods under such terms as mula-vija (root seed), khandabija (cuttings), phaluvija (joints), agravija (budding) and bija-bija (seed). Atharvaveda and Arthasastra describe the propagation by seed (bija-bija or vijaruha) and bulbous roots (kandavija), respectively. The method of cutting (skandhavija) is described in the Arthasastra, Brhatsamhita and Sumangala-vilasini in the case of sugar cane, jackfruit, blackberry, pomegranate, vine, lemon tree, asvattha (Ficus religiosa), nyagrodha (Ficus bengalensis), udumbara (Ficus glomerata) and several others. Some ideas related to sexuality in plants are noticeable in the Harita and Charak Samhitas. Charak recognized male and female individuals in the plant called Kutaja (Hollerhina antidysenterica), and the male categories of plants bearing white flowers, large fruit and tender leaves and the female categories characterized by yellow flowers, small fruits, short stalk, etc. The Rajanighantu mentions the existence of male and female plants in the plant Ketaki (Pandanus odoratissimus). The male plant is called sitaketaki, and the female is called svarna ketaki. Regarding heredity, Charaka and Susruta mention that the fertilized ovum contains in miniature all the organs of the plants, for example the bamboo seed containing in miniature the entire structure of the bamboo tree, and further that the male sperm cell have minute elements derived form each of its organs and tissues. http://www.infinityfoundation.com/mandala/t_es/t_es_tiwar_botany_frameset.htm

Iran's Hindu past

Baku Ateshgah or “Fire Temple” is an ancient Hindu religious temple dedicated to Jwala Ji in Surakhani, a suburb of greater Baku, Azerbaijan.

It was initially thought to be a Zoroastrian fire worship place as “Atash” is the Persian word for fire.Four holy elements of local people belief were: ateshi (fire), badi (air), abi (water), and heki (earth).

A pentagonal complex, which has a courtyard surrounded by cells for monks and a tetrapillar-altar in the middle, was built during the 17th and 18th centuries but temple ceased to be worshiped after 1883 with the installation of petroleum plants (industry) at Surakhany. The complex was turned into a museum in 1975.

Fire is considered sacred in both Indo-Iranian branches of Hinduism and Zoroastrianism (as Agni and Atar respectively),and there has been debate on whether the Atashgah was originally a Hindu structure or a Zoroastrian one. The trident mounted atop the structure is usually a distinctly Hindu sacred symbol (as the Trishul, which is commonly mounted on temples) and has been cited by Zoroastrian scholars as a specific reason for considering the Atashgah as a Hindu site.

There are several inscriptions on the Ateshgah. They are all in either Sanskrit or Punjabi, with the exception of one Persian inscription that occurs below an accompanying Sanskrit invocation to Lord Ganesha and Jwala Ji. Although the Persian inscription contains grammatical errors, both the inscriptions contain the same year date of 1745 Common Era (Samvat/संवत 1802/१८०२ and Hijri 1158/١١٥٨).

Taken as a set, the dates on the inscriptions range from Samvat 1725 to Samvat 1873, which corresponds to the period from 1668 CE to 1816 CE.

One press report asserts that local records exist that state that the structure was built by the Baku Hindu traders community around the time of the fall of the Shirvanshah dynasty and annexation by the Russian Empire following the Russo-Persian War (1722–1723).

The inscriptions in the temple in Sanskrit (in Nagari Devanagari script) and Punjabi (in Gurmukhi script) identify the site as a place of Hindu and Sikh worship,and state it was built and consecrated for Jwala Ji, the modern Hindu fire deity. Jwala (जवाला/ज्वाला) means flame in Sanskrit .

In his Travels Outside Bombay, Modi observed that “not just me but any Parsee who is a little familiar with our Hindu brethren’s religion, their temples and their customs, after examining this building with its inscriptions, architecture, etc., would conclude that this is not a [Zoroastrian] Atash Kadeh but is a Hindu Temple, whose Brahmins (priests) used to worship fire (Sanskrit: Agni).”

There is a famed shrine to Jwala Ji in the Himalayas, in the settlement of Jawalamukhi, in the Kangra district of Himachal Pradesh, India to which the Atashgah bears strong resemblance and few scholars have stated that some Jwala Ji devotees used to refer to the Kangra shrine as the ‘smaller Jwala Ji‘ and the Baku shrine as the ‘greater Jwala Ji‘.

In 1876, James Bryce visited the region and found that “the most remarkable mineral product is naphtha, which bursts forth in many places, but most profusely near Baku, on the coast of the Caspian, in strong springs, some of which are said to always be burning.”
Without referencing the Atashgah by name, he mentioned of the Zoroastrians that “after they were extirpated from Persia by the Mohammedans, who hate them bitterly, some few occasionally slunk here on pilgrimage” and that “under the more tolerant sway of the Czar, a solitary priest of fire is maintained by the Parsee community of Bombay, who inhabits a small temple built over one of the springs“.

The fire was once fed by a vent from a subterranean natural gas field located directly beneath the complex, but heavy exploitation of the natural gas reserves in the area during Soviet rule resulted in the flame going out in 1969. Today, the museum’s fire is fed by mains gas piped in from Baku city.


Baku Ateshgah or “Fire Temple” is an ancient Hindu religious temple dedicated to Jwala Ji in Surakhani, a suburb of greater Baku, Azerbaijan. It was initially thought to be a Zoroastrian fire worship place as “Atash” is the Persian word for fire.Four holy elements of local people belief were: ateshi (fire), badi (air), abi (water), and heki (earth). A pentagonal complex, which has a courtyard surrounded by cells for monks and a tetrapillar-altar in the middle, was built during the 17th and 18th centuries but temple ceased to be worshiped after 1883 with the installation of petroleum plants (industry) at Surakhany. The complex was turned into a museum in 1975. Fire is considered sacred in both Indo-Iranian branches of Hinduism and Zoroastrianism (as Agni and Atar respectively),and there has been debate on whether the Atashgah was originally a Hindu structure or a Zoroastrian one. The trident mounted atop the structure is usually a distinctly Hindu sacred symbol (as the Trishul, which is commonly mounted on temples) and has been cited by Zoroastrian scholars as a specific reason for considering the Atashgah as a Hindu site. There are several inscriptions on the Ateshgah. They are all in either Sanskrit or Punjabi, with the exception of one Persian inscription that occurs below an accompanying Sanskrit invocation to Lord Ganesha and Jwala Ji. Although the Persian inscription contains grammatical errors, both the inscriptions contain the same year date of 1745 Common Era (Samvat/संवत 1802/१८०२ and Hijri 1158/١١٥٨). Taken as a set, the dates on the inscriptions range from Samvat 1725 to Samvat 1873, which corresponds to the period from 1668 CE to 1816 CE. One press report asserts that local records exist that state that the structure was built by the Baku Hindu traders community around the time of the fall of the Shirvanshah dynasty and annexation by the Russian Empire following the Russo-Persian War (1722–1723). The inscriptions in the temple in Sanskrit (in Nagari Devanagari script) and Punjabi (in Gurmukhi script) identify the site as a place of Hindu and Sikh worship,and state it was built and consecrated for Jwala Ji, the modern Hindu fire deity. Jwala (जवाला/ज्वाला) means flame in Sanskrit . In his Travels Outside Bombay, Modi observed that “not just me but any Parsee who is a little familiar with our Hindu brethren’s religion, their temples and their customs, after examining this building with its inscriptions, architecture, etc., would conclude that this is not a [Zoroastrian] Atash Kadeh but is a Hindu Temple, whose Brahmins (priests) used to worship fire (Sanskrit: Agni).” There is a famed shrine to Jwala Ji in the Himalayas, in the settlement of Jawalamukhi, in the Kangra district of Himachal Pradesh, India to which the Atashgah bears strong resemblance and few scholars have stated that some Jwala Ji devotees used to refer to the Kangra shrine as the ‘smaller Jwala Ji‘ and the Baku shrine as the ‘greater Jwala Ji‘. In 1876, James Bryce visited the region and found that “the most remarkable mineral product is naphtha, which bursts forth in many places, but most profusely near Baku, on the coast of the Caspian, in strong springs, some of which are said to always be burning.” Without referencing the Atashgah by name, he mentioned of the Zoroastrians that “after they were extirpated from Persia by the Mohammedans, who hate them bitterly, some few occasionally slunk here on pilgrimage” and that “under the more tolerant sway of the Czar, a solitary priest of fire is maintained by the Parsee community of Bombay, who inhabits a small temple built over one of the springs“. The fire was once fed by a vent from a subterranean natural gas field located directly beneath the complex, but heavy exploitation of the natural gas reserves in the area during Soviet rule resulted in the flame going out in 1969. Today, the museum’s fire is fed by mains gas piped in from Baku city.

Untouchability was not in Vedas

Veda Vyasa & the question of untouchability
**********************************************************
Veda Vyasa is a legendary Hindu sage, whose very name is synonymous to Hindus with knowledge. According to traditional Hindu accounts, he lived at the end of the Dwapara Yuga and early Kali Yuga (the date for the beginning of the Kali Yuga is 3102BC).

Veda Vyasa is accredited with compiling the Vedas and writing the Brahma Sutras, which are one of the three great authoritative Hindu philosophical texts. He was also the recorder/writer of the earliest form of the Mahabharata (which was originally called the ‘Jaya’). The followers of Veda Vyasa (the Vyasas or ‘compilers’) carried out the compilation of the Puranas.

His birthday is celebrated as ‘Guru Purnima’ – one of the most sacred days in the Hindu calendar, which is the day when teachers are honored. A popular saying about Veda Vyasa goes: ‘Vyasocchishtasam jagat sarvam’ meaning that so great was the learning of Rishi Veda Vyasa, that even his voluminous writings represent only the periphery of his knowledge. Virtually every Hindu sampradaya (order) traces their lineage to him, and wherever knowledge is propagated and respected is called a Vyaspeeth – Vyasa’s throne.

Yet had Veda Vyasa, the compiler of the Vedas, lived in the later degenerate and perverted age of Hindu society, he may well have been considered an untouchable and not even allowed to touch the Vedas!

His mother (Satyavati) used to sell fish to make a living, and in many parts of Hindu society in its later period of caste insanity this would have made him an untouchable. Yet Vyasa is considered by all Hindus to be the very epitome of wisdom!

This is just one of many examples (another being Valmiki – author of the Ramayana) that shows that the terrible caste rigidity of Hindu society that we have seen at some points in our past, and which still persists today in some parts, was definitely not originally the state of things, and certainly does not represent the true spirit of Hinduism.

Veda Vyasa & the question of untouchability *********************************************Veda Vyasa is a legendary Hindu sage, whose very name is synonymous to Hindus with knowledge. According to traditional Hindu accounts, he lived at the end of the Dwapara Yuga and early Kali Yuga (the date for the beginning of the Kali Yuga is 3102BC). Veda Vyasa is accredited with compiling the Vedas and writing the Brahma Sutras, which are one of the three great authoritative Hindu philosophical texts. He was also the recorder/writer of the earliest form of the Mahabharata (which was originally called the ‘Jaya’). The followers of Veda Vyasa (the Vyasas or ‘compilers’) carried out the compilation of the Puranas. His birthday is celebrated as ‘Guru Purnima’ – one of the most sacred days in the Hindu calendar, which is the day when teachers are honored. A popular saying about Veda Vyasa goes: ‘Vyasocchishtasam jagat sarvam’ meaning that so great was the learning of Rishi Veda Vyasa, that even his voluminous writings represent only the periphery of his knowledge. Virtually every Hindu sampradaya (order) traces their lineage to him, and wherever knowledge is propagated and respected is called a Vyaspeeth – Vyasa’s throne. Yet had Veda Vyasa, the compiler of the Vedas, lived in the later degenerate and perverted age of Hindu society, he may well have been considered an untouchable and not even allowed to touch the Vedas! His mother (Satyavati) used to sell fish to make a living, and in many parts of Hindu society in its later period of caste insanity this would have made him an untouchable. Yet Vyasa is considered by all Hindus to be the very epitome of wisdom! This is just one of many examples (another being Valmiki – author of the Ramayana) that shows that the terrible caste rigidity of Hindu society that we have seen at some points in our past, and which still persists today in some parts, was definitely not originally the state of things, and certainly does not represent the true spirit of Hinduism.

Shiva is demchog of Buddhism

In Theravada Buddhism, Vishnu = Upalvan
In Mahyana Buddhism, Shiva = Demchog(Chakrasamvara Tantra)

Upulvan is also known Guardian God of Buddhism or Protector of Buddhism.
Demchog is same as Shiva because According to Mahayana Buddhism, Mt.Kailash is residence of Demchog.

-Kunal Modi

In Theravada Buddhism, Vishnu = Upalvan In Mahyana Buddhism, Shiva = Demchog(Chakrasamvara Tantra) Upulvan is also known Guardian God of Buddhism or Protector of Buddhism. Demchog is same as Shiva because According to Mahayana Buddhism, Mt.Kailash is residence of Demchog. -Kunal Modi

33 crore gods , deva- explanation

Hindus have 33 crore gods -explanation
**************************************************33 divinities are mentioned in the Yajur-veda, Atharva-veda, occurs in the Parsi scriptures of Avesta as well.The expression trayastrimsa deva is found in the list of classes of gods in Sanskrit Buddhist texts like the Divyavadana and Suvarnaprabhasa-sutra.The word koti in ‘trayastrimsati koti’ does not mean the number '33 crore’ or '330 million’. Here koti means 'supreme’, pre-eminent, excellent, that is, the 33 'supreme’ divinities. It has been documented in Brihadaranyaka Upanishad Śākalya : “How many gods are there?” Yājñavalkya : “Three hundred and three.” Then he says, “Three thousand and three.” Śākalya : “Is this the answer that you give me to my question, how many gods are there? Three thousand and three; three hundred and three! Have you no other answer to this question?” Yājñavalkya : There are thirty-three gods. Śākalya : “All right!” (not satisfied with answer) …Tell me again properly; how many gods are there?“ Yājñavalkya : "Six are there.” Śākalya : “How many gods are there. Tell me again. Think properly.” Yājñavalkya : “Only three gods are there.” Śākalya : “How many gods are there? Tell again. Yājñavalkya : "Two gods are there.” Śākalya : “Tell again; how many gods are there?” Yājñavalkya : “One and a half gods” (Then he was very much upset) Śākalya : “What is this you say, one and a half gods. Tell again properly; how many gods are there?” Yājñavalkya : “One god is there,” Śākalya : “All these numbers that you have mentioned – three thousand and three, three hundred and three – what are these gods? Give the names of these gods, the deities.” Yājñavalkya : “All these three thousand and all that I mentioned – they are not really gods. They are only manifestations of the thirty-three. The thirty-three are the principal manifestations, and others are only their glories, radiances, manifestations, magnificences or forces, energies, powers.” Śākalya : “But what are these thirty-three?” Yājñavalkya : “The thirty-three gods are eight Vasus, eleven Rudras, twelve Ādityas, then Indra and Prajāpati – these make thirty-three gods.” Śākalya : “What are these Vasus which are eight in number?” Yājñavalkya : “Fire is one deity; earth is one deity; air is another; the atmosphere is one deity; the sun is one deity; the heaven is one deity; moon is one deity; the stars are one deity. These constitute eight groups” Śākalya : “Why do you call them Vasus?” Yājñavalkya : “Everything is deposited as it were in these constituent principles. Therefore, they are called Vasus.” Śākalya : “Who are the Rudras?” Yājñavalkya : “The ten senses and the mind make eleven. These are the Rudras.” Śākalya : “What are the twelve Ādityas, the suns?” Yājñavalkya : “They are twelve forces of the sun, takes away the vitality of people.” Śākalya : “Who is Indra? Who is Prajāpati?” Yājñavalkya : “The rain cloud can be called Indra. Sacrifice can be called Prajāpati.” Śākalya : “What do you mean by rain cloud?” Yājñavalkya : “By rain cloud I do not actually mean the cloud, but the lightning which is the embodiment of energy.”

Durba or darbha grass

Darbha (Desmotachya bipinnata) is a tropical grass considered a sacred material in Vedic scriptures and is said to purify the offerings during such rituals.

Traditional tropical grass, Darbha, has been identified as an eco-friendly food preservative.

This finding was evolved in a research study undertaken jointly by the Centre for Nanotechnology and Advanced Biomaterials (CeNTAB) and the Centre for Advanced Research in Indian System of Medicine (CARISM) of the SASTRA University, Thanjavur, under the supervision of Dr. P. Meera and Dr. P. Brindha respectively.

At the time of eclipse, people place that grass in food items that could ferment and once the eclipse ends the grass is removed.

A systematic research was conducted by the SASTRA University researchers, in which cow’s curd was chosen as a food item that could ferment easily.

Five other tropical grass species, including lemon grass, Bermuda grass, and bamboo were chosen for comparison based on different levels of antibiotic properties and hydro phobicity.

Electron microscopy of different grasses revealed stunning nano-patterns and hierarchical nano or micro structures in darbha grass while they were absent in other grasses.

On studying the effect of various grasses on the microbial community of the curd, darbha grass alone was found to attract enormous number of bacteria into the hierarchical surface features.

These are the bacteria responsible for fermentation of cow’s curd.

During eclipse, the wavelength and intensity of light radiations available on the earth’s surface is altered. Especially, the blue and ultraviolet radiations, which are known for their natural disinfecting property, are not available in sufficient quantities during eclipse.

This leads to uncontrolled growth of micro-organisms in food products during eclipse and the food products are not suitable for consumption. Darbha was thus used as a natural disinfectant on specific occasions, say researchers at SASTRA University.

Further, the scientists say that darbha could be used as a natural food preservative in place of harmful chemical preservatives and the artificial surfaces mimicking the hierarchical nano patterns on the surface of darbha grass could find applications in health care where sterile conditions were required.

This entire research was funded by the SASTRA University’s Research Fund.

http://m.thehindu.com/news/cities/Tiruchirapalli/darbha-grass-a-natural-preservative/article7000098.ece/

Darbha (Desmotachya bipinnata) is a tropical grass considered a sacred material in Vedic scriptures and is said to purify the offerings during such rituals. Traditional tropical grass, Darbha, has been identified as an eco-friendly food preservative. This finding was evolved in a research study undertaken jointly by the Centre for Nanotechnology and Advanced Biomaterials (CeNTAB) and the Centre for Advanced Research in Indian System of Medicine (CARISM) of the SASTRA University, Thanjavur, under the supervision of Dr. P. Meera and Dr. P. Brindha respectively. At the time of eclipse, people place that grass in food items that could ferment and once the eclipse ends the grass is removed. A systematic research was conducted by the SASTRA University researchers, in which cow’s curd was chosen as a food item that could ferment easily. Five other tropical grass species, including lemon grass, Bermuda grass, and bamboo were chosen for comparison based on different levels of antibiotic properties and hydro phobicity. Electron microscopy of different grasses revealed stunning nano-patterns and hierarchical nano or micro structures in darbha grass while they were absent in other grasses. On studying the effect of various grasses on the microbial community of the curd, darbha grass alone was found to attract enormous number of bacteria into the hierarchical surface features. These are the bacteria responsible for fermentation of cow’s curd. During eclipse, the wavelength and intensity of light radiations available on the earth’s surface is altered. Especially, the blue and ultraviolet radiations, which are known for their natural disinfecting property, are not available in sufficient quantities during eclipse. This leads to uncontrolled growth of micro-organisms in food products during eclipse and the food products are not suitable for consumption. Darbha was thus used as a natural disinfectant on specific occasions, say researchers at SASTRA University. Further, the scientists say that darbha could be used as a natural food preservative in place of harmful chemical preservatives and the artificial surfaces mimicking the hierarchical nano patterns on the surface of darbha grass could find applications in health care where sterile conditions were required. This entire research was funded by the SASTRA University’s Research Fund.http://m.thehindu.com/news/cities/Tiruchirapalli/darbha-grass-a-natural-preservative/article7000098.ece/

Ancient Indian mathematics

ANCIENT INDIAN MATHEMATICS ********************************************* Despite developing quite independently of Chinese (and probably also of Babylonian mathematics), some very advanced mathematical discoveries were made at a very early time in India. Mantras from the early Vedic period invoke powers of ten from a hundred all the way up to a trillion, and provide evidence of the use of arithmetic operations such as addition, subtraction, multiplication, fractions, squares, cubes and roots. A 4th Century AD Sanskrit text reports Buddha enumerating numbers up to 1053, as well as describing six more numbering systems over and above these, leading to a number equivalent to 10421. Given that there are an estimated 1080 atoms in the whole universe, this is as close to infinity as any in the ancient world came. It also describes a series of iterations in decreasing size, in order to demonstrate the size of an atom, which comes remarkably close to the actual size of a carbon atom (about 70 trillionths of a meter). As early as the 8th Century BC, long before Pythagoras, a text known as the “Sulba Sutras” (or “Sulva Sutras”) listed several simple Pythagorean triples, as well as a statement of the simplified Pythagorean theorem for the sides of a square and for a rectangle (indeed, it seems quite likely that Pythagoras learned his basic geometry from the “Sulba Sutras”). The Sutras also contain geometric solutions of linear and quadratic equations in a single unknown, and give a remarkably accurate figure for the square root of 2, obtained by adding 1 + 1⁄3 + 1⁄(3 x 4) + 1⁄(3 x 4 x 34), which yields a value of 1.4142156, correct to 5 decimal places. As early as the 3rd or 2nd Century BC, Jain mathematicians recognized five different types of infinities: infinite in one direction, in two directions, in area, infinite everywhere and perpetually infinite. Ancient Buddhist literature also demonstrates a prescient awareness of indeterminate and infinite numbers, with numbers deemed to be of three types: countable, uncountable and infinite. Like the Chinese, the Indians early discovered the benefits of a decimal place value number system, and were certainly using it before about the 3rd Century AD. They refined and perfected the system, particularly the written representation of the numerals, creating the ancestors of the nine numerals that (thanks to its dissemination by medieval Arabic mathematicans) we use across the world today, sometimes considered one of the greatest intellectual innovations of all time. The Indians were also responsible for another hugely important development in mathematics. The earliest recorded usage of a circle character for the number zero is usually attributed to a 9th Century engraving in a temple in Gwalior in central India. But the brilliant conceptual leap to include zero as a number in its own right (rather than merely as a placeholder, a blank or empty space within a number, as it had been treated until that time) is usually credited to the 7th Century Indian mathematicians Brahmagupta - or possibly another Indian, Bhaskara I - even though it may well have been in practical use for centuries before that. The use of zero as a number which could be used in calculations and mathematical investigations, would revolutionize mathematics. Brahmagupta established the basic mathematical rules for dealing with zero: 1 + 0 = 1; 1 - 0 = 1; and 1 x 0 = 0 (the breakthrough which would make sense of the apparently non-sensical operation 1 ÷ 0 would also fall to an Indian, the 12th Century mathematician Bhaskara II). Brahmagupta also established rules for dealing with negative numbers, and pointed out that quadratic equations could in theory have two possible solutions, one of which could be negative. He even attempted to write down these rather abstract concepts, using the initials of the names of colours to represent unknowns in his equations, one of the earliest intimations of what we now know as algebra. The so-called Golden Age of Indian mathematics can be said to extend from the 5th to 12th Centuries, and many of its mathematical discoveries predated similar discoveries in the West by several centuries, which has led to some claims of plagiarism by later European mathematicians, at least some of whom were probably aware of the earlier Indian work. Certainly, it seems that Indian contributions to mathematics have not been given due acknowledgement until very recently in modern history. Golden Age Indian mathematicians made fundamental advances in the theory of trigonometry, a method of linking geometry and numbers first developed by the Greeks. They used ideas like the sine, cosine and tangent functions (which relate the angles of a triangle to the relative lengths of its sides) to survey the land around them, navigate the seas and even chart the heavens. For instance, Indian astronomers used trigonometry to calculated the relative distances between the Earth and the Moon and the Earth and the Sun. They realized that, when the Moon is half full and directly opposite the Sun, then the Sun, Moon and Earth form a right angled triangle, and were able to accurately measure the angle as 1⁄7°. Their sine tables gave a ratio for the sides of such a triangle as 400:1, indicating that the Sun is 400 times further away from the Earth than the Moon. Although the Greeks had been able to calculate the sine function of some angles, the Indian astronomers wanted to be able to calculate the sine function of any given angle. A text called the “Surya Siddhanta”, by unknown authors and dating from around 400 AD, contains the roots of modern trigonometry, including the first real use of sines, cosines, inverse sines, tangents and secants. As early as the 6th Century AD, the great Indian mathematician and astronomer Aryabhata produced categorical definitions of sine, cosine, versine and inverse sine, and specified complete sine and versine tables, in 3.75° intervals from 0° to 90°, to an accuracy of 4 decimal places. Aryabhata also demonstrated solutions to simultaneous quadratic equations, and produced an approximation for the value of π equivalent to 3.1416, correct to four decimal places. He used this to estimate the circumference of the Earth, arriving at a figure of 24,835 miles, only 70 miles off its true value. But, perhaps even more astonishing, he seems to have been aware that π is an irrational number, and that any calculation can only ever be an approximation, something not proved in Europe until 1761. Bhaskara II, who lived in the 12th Century, was one of the most accomplished of all India’s great mathematicians. He is credited with explaining the previously misunderstood operation of division by zero. He noticed that dividing one into two pieces yields a half, so 1 ÷ 1⁄2 = 2. Similarly, 1 ÷ 1⁄3 = 3. So, dividing 1 by smaller and smaller factions yields a larger and larger number of pieces. Ultimately, therefore, dividing one into pieces of zero size would yield infinitely many pieces, indicating that 1 ÷ 0 = ∞ (the symbol for infinity). However, Bhaskara II also made important contributions to many different areas of mathematics from solutions of quadratic, cubic and quartic equations (including negative and irrational solutions) to solutions of Diophantine equations of the second order to preliminary concepts of infinitesimal calculus and mathematical analysis to spherical trigonometry and other aspects of trigonometry. Some of his findings predate similar discoveries in Europe by several centuries, and he made important contributions in terms of the systemization of (then) current knowledge and improved methods for known solutions. The Kerala School of Astronomy and Mathematics was founded in the late 14th Century by Madhava of Sangamagrama, sometimes called the greatest mathematician-astronomer of medieval India. He developed infinite series approximations for a range of trigonometric functions, including π, sine, etc. Some of his contributions to geometry and algebra and his early forms of differentiation and integration for simple functions may have been transmitted to Europe via Jesuit missionaries, and it is possible that the later European development of calculus was influenced by his work to some extent.