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square of the hypotenuse. The Pythagoreans belief that everything was made up of natural numbers and the ratio of these numbers was shaken by proof that there was no natural number, whose square was two. The proof proved their religious beliefs to be miserably wrong. Religion based on numbers is a veritable illusion. The fact that there exist other numbers in addition to the natural number unnerved them.
During sixth century B.C. Jain mathematicians flourished in India, when the ancient culture of China and Greek were also contributing to the development of mathematics. In the history of Indian mathematics, the popular names of mathematicians are Arya Bhatt (476A.D.), Bhram Gupta (628 A.D.), Shri Dhar, Shri patti (1038 A.D.) and others. Ganita Sar Sangrha is the first book of a Jain mathematician published in 1912, through its old manuscript. 'Mathematics of Dhavala' is another good book published later on.
Jain mathematics
Jain mathematics is a part of Indian mathematics. Its main features are as follows:
1. Pati-Ganita
Ancient mathematics had been popularly known as 'Pati-Ganita'. Various scholars have tried to find out the historical background of this peculiar word. According to them, this word is actually constituted of two words:
Pati-slate (board)
Ganita mathematics.
Hence it means that mathematics in which slate is needed to perform calculations. Due to want of paper up to the end of the nineteenth century, slate was in use. Even now its ample use is found in villages. Scholars regard that this word originated from a local dialect of northern India which was the offshoot of Sanskrit language. When the Sanskrit texts were translated into the Arabic, they called it 'Ilma-Hisaba-Al-takhta'. Takhta in Arabic language means a slate. They sometimes used another word - 'Hisaba-Alguvara', as the slate was often replaced by the sand-floors.
The original Sanskrit words used to describe a 'slate for writing' were - palaka and patta; not pati. The word pati finds mention in Sanskrit literature from circa 5th century. Therefore, the word pati-ganita should actually be referring to 'tabular' form of mathematics when the decimal counting began in the form of one, two, three, and four..... Some of the latter mathematicians have actually used the word "pati-ganita for mathematics of integers". This was meant to regard algebra as separate from the numerals.
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