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The Celts believed in three worlds, they were obsessed with the number three, which is very different than four.
Length of time studying is more a matter of life expectancy and age of maturity, hardly a solid link.
The Celtics believed that sex gave spiritual power, which is completely the opposite of Vedic beliefs.
Memorization when writing was not readily available, paper, pen and all that, is a custom in all cultures, or in other words a cultural universal.
The Celts believed that we rotated through the three worlds, which is different than the reincarnation beliefs of the Vedics.
Religious practices with fire is another cultural universal.
There is no reason to believe that poetry was not a cross culture exchange, where everybody contributed.
This whole Vedic culture is older and better, and the Vedics taught Europeans everything, our culture is better than yours argument that you continue to make is pathetic.
There was no Europe before the Vedic Aryans. Europe was mostly uninhabitable and the few habitation it had was primitive stone age people.
Your Baudhayana rules are a long ways away from A^2=B^2 + C^2, which allows one to calculate any side of a triangle if one knows the other two sides. What you quote does not even speak of is the far more important development.
1.9. The diagonal of a square produces double the area [of the square].
1.12. The areas [of the squares] produced separately by the lengths of the breadth of a rectangle together equal the area [of the square] produced by the diagonal.
1.13. This is observed in rectangles having sides 3 and 4, 12 and 5, 15 and 8, 7 and 24, 12 and 35, 15 and 36.
First you said Vedics believe in four worlds, now you say three, glad to see you are getting an education here.
Triloka: Hindu - Hinduism Dictionary on Triloka
By Himalayan Academy
triloka: (Sanskrit) "Three worlds." The physical, astral and causal planes (Bhuloka, Antarloka and Sivaloka).
See: world, loka.
For more articles related to Triloka , see: Hinduism, Hinduism Dictionary, Triloka , Body Mind and Soul.
The cities of the Indus Valley Civilization were well-organised
Pot sherd from Harappa and solidly built out of brick and stone. Their drainage systems, wells and water storage systems were the most sophisticated in the ancient world. They also developed systems of weights and trade. They made jewellery and game pieces and toys for their children. From looking at the structures and objects which survive we are able to learn about the people who lived and worked in these cities so long ago.
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 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. 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 it's properties and applications to geography, planetary mean motion, 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 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 till 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.
Originally posted by poet1b
It doesn't matter how you label the variables, as long as you know that the square of the hypotenuse is equal to the sum o fthe square of the other two sides. This equation allows you to calculate the length of the hypotenuse, or any of the three sides, as long as you have the length of the other two, which is the huge advantage of having this equation, and what makes it so valuable.
Originally posted by poet1b
If you know the two adjacent sides to a triangle, then you can calculate the area of the triangle using the Vedic rules provided, but you can't determine the length of the other leg, unless you use standard triangle sizes, like 3,4, and 5. This was known for thousands of years before Pythagorean's. Pythagorean's solved a big problem in geometry which had existed for millenniums.
Who Were the Aryans?
The Aryans were semi-nomadic Nordic Whites, perhaps located originally on the steppes of southern Russia and Central Asia, who spoke the parent language of the various Indo-European languages.
Traditionally Greek, Latin and Sanskrit were considered the closest languages to PIE, and much of the reconstructed Aryan proto-language is based on them. Modern Lithuanian, however, is the most archaic living language, closer to the original Aryan speech than any other. There is even an IE language, Tocharian, attested in Chinese Turkestan, which indicates that Aryans must have made an appearance in the Far East, a long-standing piece of linguistic evidence which has been recently confirmed by the discovery of the physical remains of a blond-haired people in China.
The birth of a European culture, however, predates the arrival of the Indo-Europeans: The cave art of Lascaux, which some have identified as the first flowering of Western man's creative genius, was the work of Old Europeans, as were Stonehenge in the North and the Minoan Palace culture of Crete in the South. A pan-European religious symbolism had already evolved, much of which was later incorporated into IE mythologies, including various regional adaptations of the ubiquitous Old European reverence for the Mother Goddess. Many of the principal figures in Greek mythology predate the arrival of Aryans, and during the course of ancient history Old European religious beliefs and practices continually reasserted themselves. [Image: Minoan snake goddess, from the Palace of Minos, circa 1600 BC]
Actually, while the introduction of the theorem into western thought may have been through Pythagoras, this doesn't mean that Pythagoras was the first to find it out (and I'm not just talking about the well known Pythagorean triples).
This is observed in rectangles having sides 3 and 4, 12 and 5, 15 and 8, 7 and 24, 12 and 35, 15 and 36.