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Geometry in Ancient and Medieval India

Unlike Aryabhata, Brahmagupta believed that the Earth was stationary, but he, too, calculated the length of the year with remarkable precision. The numeration system developed in India facilitated further advances in mathematics. Earlier ways of writing numbers, such as Roman numerals, used symbols to represent individual quantities, and these were added to determine the value.

More to the point, there is no convenient way to do computations with them. People who used Roman numerals and other similar systems did their calculations with counting aids such as the abacus. In contrast, Hindu arithmetic used number symbols that went only from 1 to 9, and instead of using more symbols for higher numbers, they introduced a place-value system for multipliers of Each place had an individual name: dasan meant the tens place, sata meant the hundreds place, and so on.

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To express the number , the Hindus would write "2 sata, 3 dasan, 5". Seven hundred and eight would be "7 sata, 8". Toward the end of the Gupta period, Indian mathematicians found a way to eliminate the place names while keeping the advantages of the place-value system. They used a symbol called sunya, or "empty" to designate a place with no value in it. This is equivalent to the symbol we call zero.

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With this they could write for "7 sata, 8," and easily distinguish it from "7 dasan, 8," or The physical alignment of tens, hundreds, etc. About , the Hindu mathematician Mahavira demonstrated that zero was not simply a placeholder, but had an actual numerical value. His tenth-century successor Sridhara further recognized that the zero was as meaningful a number as any of the others.

Without the zero, modern mathematics, and therefore most of modern science, would have been impossible. The twelfth century mathematician Bhaskara often called Bhaskara the Learned was, like many of his predecessors such as Brahmagupta , head of the Ujjain observatory and a gifted astronomer. His two mathematical works, Lilivati The graceful and Bijaganita Seed counting from the series Siddhantasiromani , were the first to expound systematically the use of the decimal system , based on powers of He compiled many problems with which earlier mathematicians had struggled, and presented solutions.

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He was, however, unable to generalize this to any number divided by zero. He enumerated the convention of signs in multiplication and division: two positives or two negatives divided or multiplied yields a positive result, and a positive and a negative divided or multiplied gives a negative result. In algebra, Bhaskara built on the work of Aryabhata and Brahmagupta. He used letters to represent unknowns, as we do in algebra today.

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Bhaskara developed new methods for solving quadratic equations, that is, equations containing at least one variable raised to the second power x 2. One of the first Muslim mathematicians to write about Indian techniques was Muhammad ibn Musa al-Khwarizmi, a teacher in the mathematical school at Baghdad. The Latinization of his name from "al-Khwarizmi" to "Algoritmi" eventually became our word for a mathematical procedure, algorithm.

When his book on elementary mathematics Kitab al-jabr wa al-muqabalah The book of integration and equation was translated into Latin in the twelfth century, the term al-jabr became algebra.

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Indian mathematical techniques were disseminated in the West through texts such as these. They were first brought to Moorish Spain, where they then spread to the rest of Europe. However, they did not come into common use there until the digit symbols were standardized after the invention of the movable-type printing press in the mids. During the thousand years that followed the Gupta dynasty , successive waves of invaders poured through India.

First came the Huns, who descended from central Asia beginning around , finally conquering the Gupta empire 50 years later. Muslims arrived from Arabia in the s, and from Afghanistan and Persia at the turn of the millennium. Muslim sultans ruled from Delhi between and , helping to disseminate Indian mathematical advances throughout the Islamic world. Because Indian symbols were introduced to the West by Muslim mathematicians, they came to be known as "Arabic" numerals.

Today scholars generally refer to our way of expressing numbers as the Hindu-Arabic numeration system. Bose, D. Sen, and B. Subbarayappa eds. A Concise History of Science in India. The comma-shaped curls on the back, tail and crest indicate a southern origin. Similar peacocks prance upon the step-risers of the fantastic Throne of Prosperity represented in the Nujum al Ulum , an astrological manuscript dated which, according to a note written with the text, is known to have been in the royal library at Bijapur.

Since this particular shape was obviously well defined by this date, and its vigorous design shows little of the naturalism associated with Mughal taste which began to affect Deccani art in the late sixteenth century, we can confidently assign it an earlier date, in the late fifteenth or early sixteenth century. Victoria and Albert Museum, Published: Festival of India in the United States Foreword by Pupul Jayakar. New York: Harry N. Abrams, Inc. Publishers, , pp.

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In the ancient cultures of Asia, ornament, patterns, symbols, flowers, geometric forms found on everyday objects, textiles and architecture stem from meanings in religion and literature, and have layered references. Trade and travel allows for floral and geometric motifs to proliferate through a territory that is vast, spanning from Spain to China.

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  • Indian artists, artisans and patrons with keen sensibilities adapt and evolve ancient motifs of Primitive, Buddhist and Hindu origin with Islamic, Chinese and European styles to create marvellous and luxurious hybrids. An aesthetic and design evolution is manifest in the arts of the region from the past two millennia and more. Geometry, theoretical and practical sciences and mathematics were widely understood and applied in ancient and medieval India, the Architectural wonders stand as testimony.

    Geometric design is the basis of Ornament and floral design, however with the advent of Islam it takes on a new, central role and flourishes.