Pub Date : 1900-01-01DOI: 10.58517/itmsc.2022.15103
Prajakti Gokhale
The ancient mathematics of India is an amalgamation of poetry, literature, art, architecture and also scientific thought. Looking at Sanskrit literature, the literature developed for expressing mathematical thoughts and ideas have their special place in linguistic evolution. We can observe that the technical Sanskrit language evolved through the centuries as rich mathematical ideas developed. For the expression of these ideas, the strong technical vocabulary ofthe language was needed. This language approach was very different, it can be compared to today’s technical vocabulary we have developed for modern computer which was alien even 30 years ago. The ancient technical vocabulary was difficult for contemporary scholars to understand and hence mathematical ideas remain hidden in it for a longer time. The new approach of mathematics invented and developed by Bharti Krishna Tirtha, which did not show such language barriers. It was written in the form of one-line simple Sanskrit words called ‘sutra’. The deep meaning of sutra, its connection and its interpretation to different branches of mathematics and also the deep spiritual thought behind the sutra, is worth studying and researching. In my research paper, I will be presenting the technicalities of ancient mathematical language and exploring the method of Pythagorean triples through the Vedic mathematics ‘sutras’ formulated by Bharati Krishna Tirtha. I will also be highlighting the applications of triples in current mathematical scenario, to connect the different fields of mathematics, implication of which is making mathematics easy, conceptually clear and alsoperceived with a new dimension of thought.
{"title":"PYTHAGOREAN TRIPLES: THE CONNECTION BETWEEN NUMBER THEORY, GEOMETRY AND ALGEBRA THROUGH THE VEDIC MATHEMATICS PERSPECTIVE","authors":"Prajakti Gokhale","doi":"10.58517/itmsc.2022.15103","DOIUrl":"https://doi.org/10.58517/itmsc.2022.15103","url":null,"abstract":"The ancient mathematics of India is an amalgamation of poetry, literature, art, architecture and also scientific thought. Looking at Sanskrit literature, the literature developed for expressing mathematical thoughts and ideas have their special place in linguistic evolution. We can observe that the technical Sanskrit language evolved through the centuries as rich mathematical ideas developed. For the expression of these ideas, the strong technical vocabulary ofthe language was needed. This language approach was very different, it can be compared to today’s technical vocabulary we have developed for modern computer which was alien even 30 years ago. The ancient technical vocabulary was difficult for contemporary scholars to understand and hence mathematical ideas remain hidden in it for a longer time. The new approach of mathematics invented and developed by Bharti Krishna Tirtha, which did not show such language barriers. It was written in the form of one-line simple Sanskrit words called ‘sutra’. The deep meaning of sutra, its connection and its interpretation to different branches of mathematics and also the deep spiritual thought behind the sutra, is worth studying and researching. In my research paper, I will be presenting the technicalities of ancient mathematical language and exploring the method of Pythagorean triples through the Vedic mathematics ‘sutras’ formulated by Bharati Krishna Tirtha. I will also be highlighting the applications of triples in current mathematical scenario, to connect the different fields of mathematics, implication of which is making mathematics easy, conceptually clear and alsoperceived with a new dimension of thought.","PeriodicalId":305885,"journal":{"name":"International Transactions in Mathematical Sciences and Computer","volume":"80 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133607702","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.58517/itmsc.2022.15107
Sunil Manohar Patankar
Veda is a most ancient treatise having spiritual knowledge and the scientific one for all the subjects. By studying the verse 24,the eighteenth chapter of Yajurveda,Shri S. V. Aagashe(आआआआआ)elaborated on some arithmetical operations in his book titled "Rudra Trikona (आआआआआ आआआआआआआ).Square, square root and cube of the natural numbers can be calculated simply using this triangle. Here, these methods are explained stepwise with amendments in each case.
{"title":"Applications of Rudra Trikona","authors":"Sunil Manohar Patankar","doi":"10.58517/itmsc.2022.15107","DOIUrl":"https://doi.org/10.58517/itmsc.2022.15107","url":null,"abstract":"Veda is a most ancient treatise having spiritual knowledge and the scientific one for all the subjects. By studying the verse 24,the eighteenth chapter of Yajurveda,Shri S. V. Aagashe(आआआआआ)elaborated on some arithmetical operations in his book titled \"Rudra Trikona (आआआआआ आआआआआआआ).Square, square root and cube of the natural numbers can be calculated simply using this triangle. Here, these methods are explained stepwise with amendments in each case.","PeriodicalId":305885,"journal":{"name":"International Transactions in Mathematical Sciences and Computer","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114738706","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.58517/itmsc.2022.15104
R. Thakur
Hinduism is undoubtedly the oldest religion of the world and though there are disagreement over the period amongst some historian but it was during 1900 to 1500 BC when Hindu religion came into existence. The foremost religious text of Hindu is Vedas and the origin of the Vedas can be traced back as far as 1500 BCE, when a large group of Aryans crossed the Hindu Kush Mountains and came to Indian subcontinent. The Vedas are full of knowledge.The Vedas have guided the Indian civilization for thousands of years and the Four Vedas are the pillar of Hinduism. The very word Veda has a derivational meaning – the fountainhead and illimitable storehouse of all knowledge. This article will only focus on the mathematical content available in Vedas, Puranas, Ramayana and Mahabharata. In Rig Veda and Atharva Veda, there are several instance where numbers in the power of tens, even numbers, odd numbers, multiples of four, value of pi, mathematical operation such as addition, subtraction, multiplication and division have been discussed not in the way we use in our courses but the presence of larger number even up to 1060 is evident. The speed of light, about seven colourful rays of sunlight all these are enough to make a belief that Vedas have put a strong foundation of number system and decimal system. Not even that, even geometrical knowledge found in Sulbha sutra as par excellence and many of them have origin prior to Greek mathematician to whom we owe everything.
{"title":"Large Number System from Vedas and Vedic Literature","authors":"R. Thakur","doi":"10.58517/itmsc.2022.15104","DOIUrl":"https://doi.org/10.58517/itmsc.2022.15104","url":null,"abstract":"Hinduism is undoubtedly the oldest religion of the world and though there are disagreement over the period amongst some historian but it was during 1900 to 1500 BC when Hindu religion came into existence. The foremost religious text of Hindu is Vedas and the origin of the Vedas can be traced back as far as 1500 BCE, when a large group of Aryans crossed the Hindu Kush Mountains and came to Indian subcontinent. The Vedas are full of knowledge.The Vedas have guided the Indian civilization for thousands of years and the Four Vedas are the pillar of Hinduism. The very word Veda has a derivational meaning – the fountainhead and illimitable storehouse of all knowledge. This article will only focus on the mathematical content available in Vedas, Puranas, Ramayana and Mahabharata. In Rig Veda and Atharva Veda, there are several instance where numbers in the power of tens, even numbers, odd numbers, multiples of four, value of pi, mathematical operation such as addition, subtraction, multiplication and division have been discussed not in the way we use in our courses but the presence of larger number even up to 1060 is evident. The speed of light, about seven colourful rays of sunlight all these are enough to make a belief that Vedas have put a strong foundation of number system and decimal system. Not even that, even geometrical knowledge found in Sulbha sutra as par excellence and many of them have origin prior to Greek mathematician to whom we owe everything.","PeriodicalId":305885,"journal":{"name":"International Transactions in Mathematical Sciences and Computer","volume":"88 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134336959","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.58517/itmsc.2022.15105
Ravi Asrani
The Vedic Mathematics system provides us with a large number of options at each stage of working. Depending upon the pattern of the problem, one of these options is going to give the result with very little effort and in minimum time. Therefore the very first step is to look for the pattern of the problem which essentially involves systematic use of the right half of the brain. Then the logical computations are done by the left half. Even while computing, due to various options available, the mind is always kept alert to pick up the path of least effort. Thus while practicing the Vedic Maths, Human brain gets the systematic training of integrated functioning of the two halves of the brain. Due to multidimensional thinking, overall development of human brain takes place through Vedic Mathematics. Study was conducted on two samples of 25 students each. They are 6th to 10th grade students. The sample for the study was selected on the basis of the random sampling technique. I have performed experiments on them. The results of statistical t test of significance of difference in means indicate that Vedic Mathematics can help any person achieve greater skill, comprehension and efficiency in mathematics. These methods can improve logical thinking, computational speed, creativity and positive Mathematics attitude
{"title":"Entire development of the human brain through Vedic Mathematics","authors":"Ravi Asrani","doi":"10.58517/itmsc.2022.15105","DOIUrl":"https://doi.org/10.58517/itmsc.2022.15105","url":null,"abstract":"The Vedic Mathematics system provides us with a large number of options at each stage of working. Depending upon the pattern of the problem, one of these options is going to give the result with very little effort and in minimum time. Therefore the very first step is to look for the pattern of the problem which essentially involves systematic use of the right half of the brain. Then the logical computations are done by the left half. Even while computing, due to various options available, the mind is always kept alert to pick up the path of least effort. Thus while practicing the Vedic Maths, Human brain gets the systematic training of integrated functioning of the two halves of the brain. Due to multidimensional thinking, overall development of human brain takes place through Vedic Mathematics. Study was conducted on two samples of 25 students each. They are 6th to 10th grade students. The sample for the study was selected on the basis of the random sampling technique. I have performed experiments on them. The results of statistical t test of significance of difference in means indicate that Vedic Mathematics can help any person achieve greater skill, comprehension and efficiency in mathematics. These methods can improve logical thinking, computational speed, creativity and positive Mathematics attitude","PeriodicalId":305885,"journal":{"name":"International Transactions in Mathematical Sciences and Computer","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132333894","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.58517/itmsc.2022.15108
Salil Sharma, Vaidehi Pandit
Physical and chemical parameters are monitored and used for assessment of water quality for three seasons namely rainy, winter, and summer of a medium-sized river “Chhoiya” in Bijnor District of Uttar Pradesh(India) so that it can be ascertained that the quality of water is fit for public consumption, recreation, irrigation and other purposes. The parameters are pH, electrical conductivity, total dissolved solids, total alkalinity, total hardness, total suspended solids, Nitrate, Sulphate, Dissolved oxygen, BOD, COD, and turbidity. There is a relationship between these parameters that shows that one parameter actually causes change in another parameter. We have used the statistical regression analysis method of three observation stations in all three seasons. A systematic correlation and regression study shows the significant linear relationship among different pairs of water quality parameters. The purpose of the present study is to establish a regression equation between two parameters, which can be used to predict the value of one parameter if the value of the other is known. This helps to find a tool that can be used to assess the value of physicochemical parameters and the extent of pollution theoretically, which is time-saving and cost- effective. This study was done from July 2017 to June 2018 on river Chhoiya to assess the quality of water and its suitability for various purposes.
{"title":"Correlation Study and Regression Analysis of Water Quality of Chhoiya River (a tributary of river Ganga) in Bijnor District (UP, India)","authors":"Salil Sharma, Vaidehi Pandit","doi":"10.58517/itmsc.2022.15108","DOIUrl":"https://doi.org/10.58517/itmsc.2022.15108","url":null,"abstract":"Physical and chemical parameters are monitored and used for assessment of water quality for three seasons namely rainy, winter, and summer of a medium-sized river “Chhoiya” in Bijnor District of Uttar Pradesh(India) so that it can be ascertained that the quality of water is fit for public consumption, recreation, irrigation and other purposes. The parameters are pH, electrical conductivity, total dissolved solids, total alkalinity, total hardness, total suspended solids, Nitrate, Sulphate, Dissolved oxygen, BOD, COD, and turbidity. There is a relationship between these parameters that shows that one parameter actually causes change in another parameter. We have used the statistical regression analysis method of three observation stations in all three seasons. A systematic correlation and regression study shows the significant linear relationship among different pairs of water quality parameters. The purpose of the present study is to establish a regression equation between two parameters, which can be used to predict the value of one parameter if the value of the other is known. This helps to find a tool that can be used to assess the value of physicochemical parameters and the extent of pollution theoretically, which is time-saving and cost- effective. This study was done from July 2017 to June 2018 on river Chhoiya to assess the quality of water and its suitability for various purposes.","PeriodicalId":305885,"journal":{"name":"International Transactions in Mathematical Sciences and Computer","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130667123","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.58517/itmsc.2022.15101
Nidhi Handa, P. Taneja
In applied mathematics Binomial Expansion and Multinomial expansion are of great importance. In around 300 BCE Indian mathematician Pingala had derived the method of obtainng a triangular arrangement known as “Meru-Prastar” for attainment of coefficients of binomial expansion. In sixteenth century, CE it was rediscovered by French mathematician Blasé Pascal (1588-1688CE) and termed as Pascal’s triangle. This paper discusses the development of binomial expansion, multinomial expansion with its applications. The paper also emphasizes the fact that the historical roots of binomial expansion are embedded in Pingalacharya’s Meru-Prastar.
{"title":"History of Binomial and Multinomial Expansions","authors":"Nidhi Handa, P. Taneja","doi":"10.58517/itmsc.2022.15101","DOIUrl":"https://doi.org/10.58517/itmsc.2022.15101","url":null,"abstract":"In applied mathematics Binomial Expansion and Multinomial expansion are of great importance. In around 300 BCE Indian mathematician Pingala had derived the method of obtainng a triangular arrangement known as “Meru-Prastar” for attainment of coefficients of binomial expansion. In sixteenth century, CE it was rediscovered by French mathematician Blasé Pascal (1588-1688CE) and termed as Pascal’s triangle. This paper discusses the development of binomial expansion, multinomial expansion with its applications. The paper also emphasizes the fact that the historical roots of binomial expansion are embedded in Pingalacharya’s Meru-Prastar.","PeriodicalId":305885,"journal":{"name":"International Transactions in Mathematical Sciences and Computer","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134403661","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.58517/itmsc.2022.15102
Naveen Kumar, Rashmi Yadav, S. Gupta
Mathematical science has a lots of importance in our life, this encourages logical reasoning, critical thinking, creative thinking, abstract or spatial thinking, problem solving ability etc. Everyone requires mathematics in their daily lives. Analytical and reasoning skills are important because they help us solve problems and look for solutions.If we solve any problem based on division by using Vedic Mathematics formula such as flag method, then our time is saved as well as our logical and mental development also increases. This paper includes action research on the group of 20 students who are selected from the 50 students. This study is based on the uses of the Flag Method and Urdhava-Triyagbhyam Method to solve division problems involving tables near 60, 100. Division operations are used in many problems such as square roots, cube roots, etc. Vedic Method based on Urdhava-Triyagbhyam sutra is used by these for enhancing the mental exercise and reduced the time duration during the session.
{"title":"Implementation of Vedic Sutras to Resolve Division","authors":"Naveen Kumar, Rashmi Yadav, S. Gupta","doi":"10.58517/itmsc.2022.15102","DOIUrl":"https://doi.org/10.58517/itmsc.2022.15102","url":null,"abstract":"Mathematical science has a lots of importance in our life, this encourages logical reasoning, critical thinking, creative thinking, abstract or spatial thinking, problem solving ability etc. Everyone requires mathematics in their daily lives. Analytical and reasoning skills are important because they help us solve problems and look for solutions.If we solve any problem based on division by using Vedic Mathematics formula such as flag method, then our time is saved as well as our logical and mental development also increases. This paper includes action research on the group of 20 students who are selected from the 50 students. This study is based on the uses of the Flag Method and Urdhava-Triyagbhyam Method to solve division problems involving tables near 60, 100. Division operations are used in many problems such as square roots, cube roots, etc. Vedic Method based on Urdhava-Triyagbhyam sutra is used by these for enhancing the mental exercise and reduced the time duration during the session.","PeriodicalId":305885,"journal":{"name":"International Transactions in Mathematical Sciences and Computer","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126826132","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.58517/itmsc.2022.15106
S. K. Kapoor, Ved Ratan
Vedic Scriptural text are of Panchvretiya....
吠陀经典文本是Panchvretiya....
{"title":"VEDIC GANIT SUTRAS TEXT Dwetiyavriti/Second (Inner)fold","authors":"S. K. Kapoor, Ved Ratan","doi":"10.58517/itmsc.2022.15106","DOIUrl":"https://doi.org/10.58517/itmsc.2022.15106","url":null,"abstract":"Vedic Scriptural text are of Panchvretiya....","PeriodicalId":305885,"journal":{"name":"International Transactions in Mathematical Sciences and Computer","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114320176","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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