Ganita Kaumudi

Ganita Kaumudi is an article on mathematics written by Indian mathematician Narayana Pandit in 1356. This is an arithmetic thesis and it is in line with another algebra paper "Bijganita Vatamsa" by Narayana Pandit. It was written as a comment by Bhāskara II in Līlāvatī.

Ganita Kaumudi contains many combinatorial score and continuous score results. In the text, Narayana Pandit uses knowledge of a simple iterative continuous fraction in solving the type of uncertain equation. Narayana Pandit noticed that it expresses the equality of the number of figures and the expression of the number of combinations of so many different things at the same time. [1]

This book contains a rule for determining the number of n object placements and a classic algorithm for finding the next permutation in lexicographic order, but the calculation method far exceeds the old algorithm It is. Donald Knuth explained numerous algorithms devoted to efficiently organizing generations and explained his history in his book The Art of Computer Programming. [2]

Unit scores are known in Indian mathematics in the Vedic era: [3] ŚulbaSūtras gives an approximation of the equivalent of √ 2. The system rule for expressing the score as the sum of the unit scores was previously given in Mahāvīra's Gaṇita-sāra-saṅgraha (c.850). [3] Gaṇita-kaumudi of Nārāyaṇa gives some rules: The part of bhāgajāti in the chapter entitled a ṃ śvatāra-vyavahāra contains eight rules. [3] The first few are as follows. [3]

Manipulate the new score and find the continuous denominator in the same way. If I was always chosen as such a minimum integer, this is equivalent to the greedy algorithm of Egyptian scores, but Gaṇita-Kaumudī's rule does not give a unique procedure, but rather evamiṣṭavaśādbahudhā "(" So much There is a way, my choice. ") [3]

S L Singh, director of science at Haridwar 's Gurukul Kangri Vishwavidyalaya, says: "Translation of the foundation of Ganita Kaumudi in modern mathematics and history notes"

Ganita Kaumudi, Volume 1 - Volume 2, Nārāyana Pandita (Salsvati Bhavana Granthamala, No. 57: Abhinavanibandhamālā Padmakara Dwivedi Jyautishacharya 1936)

Kusuba, Takanori (2004), Academic Split and Separation Rules, Charles Burnett, Jan P. Hogendijk, Kim Plofker, et al., Accurate History of Scientific History by David Perry, Brill, ISBN 9004132023, ISSN 0169 - 8729

Bhāskara II (1114 - c. 1185) was a major mathematician in the 12th century. In algebra, he gives a general solution to the Pell equation. He is the author of Lilavati and Vija-Ganita and deals with the problem of determining deterministic and uncertain linear equations and quadratic equations, as well as Pythagoras triads that can not distinguish between exact sentences and approximate sentences . Since many problems with Lilavati and Vija-Ganita come from other Hindu resources, Bhaskara is best in dealing with uncertainty analysis.

Ganita Kaumudi contains many combinatorial score and continuous score results. In the text, Narayana Pandit uses knowledge of a simple iterative continuous fraction in solving the type of uncertain equation. Narayana Pandit noticed that it expresses the equality of the number of figures and the expression of the number of combinations of so many different things at the same time. This book contains a rule for determining the number of n object placements and a classic algorithm for finding the next permutation in lexicographic order, but the calculation method far exceeds the old algorithm It is. Donald Knuth explained numerous algorithms devoted to efficient permutation generation and explained his history in his book The Art of Computer Programming.

Aryabhatiya deals with mathematics and astronomy. This includes an astronomical table and an introduction to Aryabhata phonemic symbols. This work consists of three parts: Ganita (meaning mathematics), Kala-kriya (meaning time calculation), and Gola (meaning sphere). Ganita covers solutions to decimal, squared and cube root algorithms, geometric measurements, Pi algorithm, sign tables, quadratic equations, proportional and linear equations using the Pythagorean theorem. This explains the approach to solve the mathematical problem of Aryabhata, Kuttaka (which means shredder) is also known as the Aryabhata algorithm. This algorithm proposes to solve the problem with a small score. Karasuriya talks about astronomy. It deals with the movement of the planet and is about the definition of various units including time, eccentricity, planetary motion pattern of the planet, longitude and latitude.