Indian Mathematics (300 BCE-1200 AD) PDF

INDIAN MATHEMATICS (300 BCE- 1200 AD)  Time Frame of Indian Mathematics The first use of mathematics in the Indian subcontinent was in the Indus valley and dates as far back as 3000 BC [Wheeler]. The mathematics used by the early Harappan civilization had mostly practical intent and was...

INDIAN MATHEMATICS (300 BCE- 1200 AD)  Time Frame of Indian Mathematics The first use of mathematics in the Indian subcontinent was in the Indus valley and dates as far back as 3000 BC [Wheeler]. The mathematics used by the early Harappan civilization had mostly practical intent and was concerned with weights and measuring scales. Excavations present knowledge of basic geometry. This culture also produced artistic designs. On carvings there is evidence that these people could draw concentric and intersecting circles and triangles.  Nature of Indian Mathematics > Developed Hindu-Arabic numerals and the concept of zero as a number > Created the decimal system-counting system based on unitof ten > Use circle as a concept of zero.  Material Used Sulba Sutras (800-200 BC) > Sulba-sutras represent the 'traditional' material along with further related elaboration of Vedic mathematics. > These include first 'use' of irrational numbers, quadratic equations of the form ax² = c and ax² + bx = c, unarguable evidence of the use of Pythagoras theorem and Pythagorean triples, predating Pythagoras (c 572 - 497 BC), and evidence of a number of geometrical proofs.  Symbol Used Evolution of Hindu-Arabic Numerals Brahmi Numerals  The Origin of Zero When stone is removed from the sand, a small round hole was left in its place representing the movement of something to nothing. The ancient Hindu symbol of a circle with a dot in the middle, known as bindu or bindhu, symbolizing the void and the negation of the self, was probably instrumental in the use of a circle as a representation of the concept of zero A portion of a dedication in a rock-cut Vishnu Temple in Gwalior Built in 876 AD. The number 270 seen in the inscription features the oldest extant zero in India. Decimal number system, also called Hindu-Arabic, or Arabic, number system It ispositional numeral system employing 10 as the base and requiring 10 different numerals, the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. It also requires a dot (decimal point) to represent decimal fractions. PROMINENT PEOPLE  ARYABHATA ( 476-550 AD) > Aryabhatiya and Aryasiddhanta > Invented the decimal system and used zero as a placeholder. > He names the first 10 decimal places and gives algorithms for obtaining square and cubic roots using decimal. > He solved the value of pi and yielded the approximate value. He treats geometric measurements employing 62, 832/20,000 (3.1416) for π. > He also considered that the value of pi is irrational > correctly calculated the areas of a triangle and of a circle. Ganitapada " for a triangle the result of a perpendicular with the half -side is the area" BRAHMAGUPTA ( 589 A.D.) > Important contribution to mathematics was introducing the concept of zero and computing methods. > He use the initials of the names of colors to represent unknowns in his equations > He pointed out that quadratic equations could in theory have two possible solutions, one of which could be negative BHÀSKARA II ( Bhaskaracharya) > A proof of the Pythagorean theorem by calculating the same area in two different ways and then cancelling out terms to get a²+b²=c². > He made a significant discovery of differential calculus principles and their application to astronomical problems. > His important pieces of work was the Siddhanta Siromani consisting four part: LILAVATI, arithmetic and geometry BIJAGANITA, treatise on algebra GOLADHAYAYA, astronomy GRAHAGANITA , planetary positions and eclipses BAUDHAYANA > He discovered Pythagoras theorem > He wrote one of the oldest book on advanced Mathematics which is Baudhāyana Sulbasûtra. MADHAVA OF SANGAMAGRAMA > credited with discovering infinite series expansions for trigonometric functions such as sine, cosine and arctangent Madhava series or Kerala series > also made contributions to astronomy, including the computation of planetary positions. CONTRIBUTIONS TO THE LIFE OF PEOPLE The people of the Indus Valley civilization manufactured bricks whose dimensions were in the proportion 4:2:1 considered favourable for the stability of a brick structure. They designed a ruler - the Mohenjo-daro ruler whose unit of length ( approximately 1.33 inches or 3.4 centimeters) was divided into ten equal parts.  Early geometry of the Sulbasûtras was based on religious needs with regards to the construction of altars such as agnitis, vedis, mandapas, etc. that are required for sacrificial ritual. Ideas like the sine, cosine, and tangent functions (which relate the angles of a triangle to the relative lengths of its sides) to survey the land around them, navigate the season and even chart the heavens. Indian Astronomers used trigonometry and calculated the relative distances between the Earth and the Moon and the Sun.  CONTRIBUTIONS TO MATH DEVELOPMENT The decimal number system in use today was first recorded in Indian Mathematics. Made early contributions to the study of the concept of zero as a number, negative numbers, arithmetic and algebra. Trigonometry was further advanced in Indi, and in particular, the modern definitions of sine, and cosine were developed there. Value of pi Introduced the Brhami Numerals which was the origin of Hindu-Arabic Numerals  REFERENCES https://byjus.com/free-ias-prep/indian- amazon.co.uk mathematicians-and-contributions/ https://www.storyofmathematics.com/indian.html) https://www.linkedin.com/pulse/mathematical- geocachingtoolbox.com genius-bhaskaracharya-ganesh-swaminathan https://www.thehindu.com/sci- https://vajiramandravi.com/quest-upsc-notes/aryabhatta/ tech/science/understanding-ancient-indian- mathematics/article2747006.ece https://www.mathsisfun.com/binary-decimal-hexadecimal.html https://upload.wikimedia.org/wikipedia/commons/thumb/8/8c https://www.booksfact.com/images/science/anc ient_science/Madhava_of_Sangamagrama.jpg https://images.squarespace-cdn.com/content/ https://d138zd1ktt9iqe.cloudfront.net/media/seo_landing_files/imag