A Study On Ancient Indian Arithmetic

The cultural origin of the world's four ancient civilizations is a topic which has always been being concerned in the history of science and technology.And Ancient Indian occupies an important position on the worldwide history of mathematics.At present,domestic mathematic historians have systematically studied the communication and dissemination of early Oriental mathematics,and the history of Ancient Indian has become an important part.However,there is still a lack of research on Ancient Indian arithmetic,and this thesis discusses this issue herein.The preliminary work of this thesis is to systematically sort out the development of Ancient Indian arithmetic,and believe that Ancient India has a profound foundation.So it focuses on the numeral theory,including the nomenclature and representation of Indian numerals in the period of characters to symbols,the origin and development of the Ancient Indian counting system,the establishment of the decimal notation,and the process of expanding the number system from only integers to containning fractions,irrational numbers and negative numbers.On this basis,it discusses eight algorithms of integers,fractions,negatives and zero,researches the theoretical algorithms such as square,cubic,square root and cube root,and analyzes the steps and the scope of practical algorithms like "the Rule of Three".In summary,it basically reviews the knowledge and development of Ancient Indian arithmetic.Through the research,it finds that the Ancient Indian arithmetic has the following three characteristics:Firstly,it has distinct sociality.So as social production and community service,Ancient Indian arithmetic was inseparable from astronomical research.Ancient Indian literary works were mostly written in the form of poetry.And there were a variety of rhetorical techniques were used in writing to made knowledge more acceptable to the public.Religious,theology and social customs impressed on arithmetic,too.Secondly,its algorithm is mechanically.It is represented by algebraic geometry primarily for some theories and methods of arithmetic were widely used in geometry.It also shows that the calculation methods were programmed,and each type of mathematical problem was abled to solve by programmable algorithmic steps.Thirdly,it is fragmented and limited.In Indian history,racial conflicts lasted continuously,the carriers for recording knowledge were difficult to preserve,and many religions were affecting the region for long.All the above led to the faulty logics and the imprecise academic research.Ancient India had rich cultural exchanges with other countries.The astronomy was influenced by Ancient Greece.And it has many similarities with China in terms of decimal notation,numerical theory,four arithmetic rules and ancient calculations,as it is likely to be influenced by Chinese arithmetic.Although the development was influenced by other civilizations,Ancient Indian arithmetic had its own characteristics and innovations.Some arithmetics were more mechanical and easier to operate.Ancient Indian numeral and decimal notation were introduced into the West by Arab countries,making great contributions to the progress of worldwide science and technology.Ancient Indian thriving arithmetic also has influence on the primary and higher mathematics education in modern India.