What is mathematics

What is mathematics

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  Mathematics in our dailylife Submitted by mayank saini, 10th A Roll no -14
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  REFRENCES
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  Indian mathematicians havemade a number of contributions to mathematics that have significantly influenced scientists and mathematicians in the modern era. These include place-value arithmetical notation, the ruler, the concept of zero, and most importantly, the Arabic-Hindu numerals predominantly used today.
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  ARYABHATTA
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  Aryabhata was bornin Taregna, which is a small town in Bihar, India, about 30 km from Patna (then known as Pataliputra), the capital city of Bihar State. Evidences justify his birth there. In Taregna Aryabhata set up an Astronomical Observatory in the Sun Temple 6th century. There is no evidence that he was born outside Patliputra and traveled to Magadha, the centre of instruction, culture and knowledge for his studies where he even set up a coaching institute. However, early Buddhist texts describe Ashmakas as being further south, in dakshinapath or the Deccan, while other texts describe the Ashmakas as having fought Alexander.
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  It is fairlycertain that, at some point, he went to Kusumapura for advanced studies and that he lived there for some time. A verse mentions that Aryabhatta was the head of an institution at Kusumapura, and, because the university of Nalanda was in Patliputra at the time and had an astronomical observatory, it is speculated that Aryabhata might have been the head of the Nalanda university as well. Aryabhata is also reputed to have set up an observatory at the Sun temple in Taregana, Bihar.
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  ARYABHATTA’S Contribution in math’s Place value system Trigonometry Algebra Approximation ofpie Numeration Indeterminate equation
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  The Aryabhatta numerationis a system of numerals based on Sanskrit phonemes. It was introduced in the early 6th century by Āryabhaṭa, in the first chapter titled Gītika Padam of his Aryabhatiya. It attributes a numerical value to each syllable of the form consonant vowel possible in Sanskrit phonology, from ka = 1 up to hau = 10
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  In Aryabhatiya Aryabhataprovided elegant results for the summation of series of squares and cubes: and
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  In Ganitapada 6,Aryabhata gives the area of a triangle as tribhujasya phalashariram samadalakoti bhujardhasamvargah that translates to: for a triangle, the result of a perpendicular with the half-side is the area. Aryabhata discussed the concept of sine in his work by the name of ardha-jya. Literally, it means "half-chord". For simplicity, people started calling it jya. When Arabic writers translated his works from Sanskrit into Arabic, they referred it as jiba
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  The place-value system,first seen in the 3rd century Bakhshali Manuscript, was clearly in place in his work. While he did not use a symbol for zero, the French mathematician Georges Ifrah explains that knowledge of zero was implicit in Aryabhata's place-value system as a place holder for the powers of ten with null coefficients However, Aryabhata did not use the Brahmi numerals. Continuing the Sanskrit tradition from Vedic times, he used letters of the alphabet to denote numbers, expressing quantities, such as the table of sine's in a mnemonic form.
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  Mentalmaths questions 1) Express1000 as a product of prime factor ? ➢ 23 x 53 = 1000. 2) Which prime numbers will be repeatedly multiplied in prime factorizatation of 3200 ? ➢ 2. 3) Find the digit at units place of 8n if n is a multiple of five ? ➢ 8. 4) What are the prime factors of denominators of fraction 7/80 ? ➢ 7/24 x 5
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  5) If HCFof two no is 68 & 85. what is the LCM of two numbers ? ➢ 340. 6) What is the HCF of 95 & 152 ? ➢ 14. 7) Find the no which when divided by 18 gives the quotient and reminder as 7 & 4? ➢ 130. 8) 176 when divided by a no gives the reminder 5 & quotient 9 ? What is the no? ➢ 19.
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  9)By which smallestirrational number±27 be multiplied so as to get a rational number ? ➢ should be multiply by ±3 to get a rational no. 10) What is the product of (±7 + ±5) and (±7-±5) ? ➢ 2.
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