________________
94
etc. Fractional numbers also show the ratio of the divisor to the dividend e.g. 2/4 = 1/2; 20/4 5/1........ etc. They are, therefore, called rational numbers.
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Scientific Secrets of Jainism
Rational numbers are innumerable. Even between two consequent integers, there are innumerable rational numbers. Besides, there can be innumerable rational numbers even between two rational numbers. No two fractional or rational numbers can therefore be said to be quite adjacent. This class of rational numbers is, therefore, extremely dense. Since all integers are divisible by 1, they are also called rational numbers. Regarding fractional rational numbers,. it should, however, be noted that the divisor is not zero.
15
16
The idea of square-root emerges from the so called Pythagoras theorem. 'So called' because Indian mathematicians had detailed practical knowledge of this theorem centuries before the birth of Pythagoras." It is believed that among the forty-five Jain canonical scriptures Suryaprajñapti, Camdraprajñapti, Jambudvipaprajñapti etc. relating to mathematics, were orally communicated by Lord Mahavira during the period between 557 B.C. to 527 B.C. There square-root is named as Karaṇaprakriyā and it has been widely used. Moreover √10 was widely used as gross value of π pi. 17 A Jain Acārya named Acārya Virasēna used 355/113 instead of л рi. Śrinivāsa Rāmānujan, the modern mathematician found out this as late as in the nineteenth century.
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Jain Education International
If two sides of a right-angled triangle have the length of one unit of measurement, the length of its diagonal is √2. A number of attempts have been made to find the exact value of √2 but in vain. Similarly, the exact values of √√√√√6,√7 etc. can also not be found. Nor can these
3/2,3/3,42,43,
numbers be shown by the ratio of two natural numbers. These numbers are, therefore, called irrational numbers. Like the numbers shown above 19 etc. are also called irrational numbers. A number of attempts have been made to find out an estimated approximate value of these irrational numbers. These irrational numbers fall somewhere between two rational numbers. Only this can be determined." All these rational and irrational numbers are collectively commonly called Real numbers.
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