write five hundred words on contribution of arithmetic into mathematics
Answers
Answer:
Mathematics is an important field of study. Mathematics is essential as it helps in developing lots of realistic skills, in fact study of mathematics itself include the concepts related to the routine lives of human. It not only develops mathematical skills and concepts, but it also helps in developing attitudes, interest, and appreciation and provides opportunities to develop one’s own thinking. So, mathematics is undoubtedly a discipline that is imperative to know and study. Figure 1 clearly specifies all the skills that are developed by mathematics. Mathematics starts from simple things and linear thinking that lead towards the more complex things and higher-order thinking skills. Mathematics has taken centuries to develop in its present form and that’s why it will be really fruitful to know about its development.
Mathematics has played a very significant role in the progress and expansion of Indian culture for centuries. Mathematical ideas that originated in the Indian subcontinent have had a thoughtful impact on the world. In ancient times, mathematics was primarily used in a supplementary or practical role. Thus mathematical methods were used to solve problems in architecture and construction (as in the public works of the Harappan civilization) in astronomy and astrology (as in the Jain mathematicians) and in the construction of Vedic altars (as in the case of the Shulba Sutras of Baudhayana and his successors). By the sixth or fifth century BC, mathematics was studied for its own sake, as well as for its relevance in other fields of knowledge. In fact, there was not a single period in Indian history when mathematics was not being developed and included in the lives of the people. The importance of mathematics in India can be seen by a well-known verse in Sanskrit of “VedangJyotish” (written 1000 BC) as:
This verse means that “As the crown on the head of a peacock and as the gem on the hood of a snake, so stands Mathematics crowned above all disciplines of knowledge.”
Indian were very well aware of this fact and it was the prime reason why they gave special and most needed importance to the development and progress of mathematics from the beginning. Indian mathematicians made immense contributions in developing arithmetic, algebra, geometry, infinite series expansions, and calculus. Indian contributions in the field of mathematics influenced the world mathematicians when the Indian works got translated.
Mathematics in ancient times (3000 to 600 BC)
Indus Valley Civilization is the earliest and the oldest confirmation of Indian mathematical understanding and its application. The metallic seals found in the excavations of Mohan-Jo-Daro and Harrapan indicate that the people of this civilization had the knowledge of numbers. It is also understandable from the pottery and other archaeological leftovers that they had the acquaintance of dimensions and geometry even in crude form. The Indus valley civilization existed around 3000 BC. Two of its most famous cities, Harappa and Mohenjo-Daro, present authentication that construction of buildings followed a standardized measurement which was decimal in nature.
The study of astronomy is even older than this, and there must have been some mathematical theories on which it was based. Even in later times, we notice that astronomy motivated significant mathematical development, especially in the field of trigonometry.
Vedic Mathematics is the most important era in the development of Indian mathematical ideas and a lot has been explored and written about it. In particular, the Shatapatha Brahmana, which is a part of the Shukla Yajur Veda, includes comprehensive descriptions of the geometric construction of altars for yajnas. In this period, the brick-making technology of the Indus Valley civilization extended to new uses. Shula Sutras are complementary to the Vedas. These texts are considered to date from 800 to 200 BC. Four in numbers, they are named after their authors: Baudhayana (600 BC), Manava (750 BC), Apastamba (600 BC), and Katyayana (200 BC). The sutras hold the famous theorem usually attributed to Pythagoras. The Shulba Sutras initiated the concept of irrational numbers, numbers that are not the ratio of two whole numbers.
Mathematical development of this period was associated with the solution of practical geometric problems, particularly the construction of religious altars. But, one can find a hint of the development of the series expansion which illustrates the development of an algebraic point of view. In later times, we locate a move towards algebra, with simplification of algebraic formulate and summation of series acting as catalysts for mathematical discovery.