Indian numerals

Mantras from the early Vedic period before BCE 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 CE Sanskrit text reports Buddha enumerating numbers up to , as well as describing six more numbering systems over and above these, leading to a number equivalent to Given that there are an estimated 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 metre. As early as the 3rd or 2nd Century BCE, Jain mathematicians recognized five different types of infinities: Ancient Buddhist literature also demonstrates a prescient awareness of indeterminate and infinite numbers, with numbers deemed to be of three types: 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 CE. 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 earliest use of a circle character for the number zero was in India The Indians were also responsible for another hugely important development in mathematics.

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Pingala (Devanagari: पिङ्गल piṅgala) (c. 3rd/2nd century BCE) was an ancient Indian mathematician who authored the Chandaḥśāstra (also called Pingala-sutras), the earliest known treatise on Sanskrit prosody.. The Chandaḥśāstra is a work of eight chapters in the late Sūtra style, not fully comprehensible without a commentary. It has been dated to the last few centuries BCE.

History of the Hindu—Arabic numeral system A decimal place system has been traced back to c. Before that epoch, the Brahmi numeral system was in use; that system did not encompass the concept of the place-value of numbers. Instead, Brahmi numerals included additional symbols for the tens, as well as separate symbols for hundred and thousand.

The Indian place-system numerals spread to neighboring Persia , where they were picked up by the conquering Arabs. In , Severus Sebokht – a Nestorian bishop living in Syria wrote: I will omit all discussion of the science of the Indians I wish only to say that this computation is done by means of nine signs. If those who believe that because they speak Greek they have arrived at the limits of science would read the Indian texts they would be convinced even if a little late in the day that there are others who know something of value.

But it is in Khmer numerals of modern Cambodia where the first extant material evidence of zero as a numerical figure , dating its use back to the seventh century, is found. In academic circles they[ which? The significance of the development of the positional number system is probably best described by the French mathematician Pierre Simon Laplace — who wrote: Tobias Dantzig [7] had this to say in Number:

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Indian mathematics

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Golden Age Indian mathematicians made fundamental advances in the theory of trigonometry, a method of linking geometry and numbers first developed by the 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.

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Indian Mathematics

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