PowerPoint Presentation: PAVAN KUMAR B Today’s Overview : Today’s Overview PowerPoint Presentation: What is Vedic Mathematics? Vedic mathematics is a system of mathematics consisting of a list of 16 basic sūtras . They were presented by a Hindu scholar and mathematician, Bharati Krishna Tirthaji Maharaja, during the early part of the 20th century. The calculation strategies provided by Vedic mathematics are said to be creative and useful, and can be applied in a number of ways to calculation methods in arithmetic and algebra, most notably within the education system. Some of its methods share similarities with the Trachtenberg system. PowerPoint Presentation: History ‘VEDA’ means ‘KNOWELDGE. Age of vedic texts :from 300bc Contains on medicine, metaphysics, grammar, astronomy etc. and ‘ ganitha shaatras ’ Bharati Krishna Tirthaji Maharaja. (1884-1960 ) Book by T irthaji moved to london . a list of 16 basic sūtras or word-formulae( Subsūtras or corollaries+14) Formulae completely related to human soul and mind. PowerPoint Presentation: The Vedic Mathematics Sutras. This list of sutras is taken from the book Vedic Mathematics, which includes a full list of the sixteen Sutras in Sanskrit. By one more than the one before. All from 9 and the last from 10. Vertically and Cross-wise Transpose and Apply If the Samuccaya is the Same it is Zero If One is in Ratio the Other is Zero By Addition and by Subtraction By the Completion or Non-Completion Differential Calculus By the Deficiency Specific and General The Remainders by the Last Digit The Ultimate and Twice the Penultimate By One Less than the One Before The Product of the Sum All the Multipliers PowerPoint Presentation: Main features Coherent Flexible Mental, improves memory Promotes creativity Appeals to everyone Increase mental agility Fast and efficient Easy and fun Special and general methods Applications: Applications In the UK, the method is used by teacher Satish Sharma with students in Slough, as well as by Kenneth Williams, teacher, author and spokesman for the Maharishi School in Skelmersdale , Lancashire, both of whom claim that the methods offer significant results for their pupils . Multiplier is an integral part of the processor. Vedic multiplier is based on the Vedic mathematics. Vedic multiplier's architecture is based on the Sutra called " Urdhva Tiryakbhyam ". Urdhva Tiryakbhyam (Vertically and Crosswise), deals with the multiplication of numbers Techniques used in the sutras’: Techniques used in the sutras’ By one more than the one before: By one more than the one before " Ekādhikena Pūrveṇa " is the Sanskrit a simple way of calculating values like 1/x9 (e.g.: 1/19, 1/29, etc.). Squaring numbers ending with 5. Procedure: 1/X9==1/19 1(RIGHTMOST DIGIT)/2(X+1) REMINDER.ANSWER%2(x+1) Repeat above till we get 4 digits 65 X 65 = 4225 ( 'multiply the previous digit 6 by one more than itself 7. Than write 25 ) All from 9 and the last from 10. : All from 9 and the last from 10. NIKHILAM NAVATAS’CHARAMAM DASATAH is the Sanskrit This formula can be very effectively applied in multiplication of numbers, which are nearer to bases like 10, 100, 1000 i.e., to the powers of 10 ( eg : 96 x 98 or 102 x 104) . 97 3 X 94 6 9 1 1 8 103 3 X 98 -2 1 0, 0 9 4 Vertically and cross wise: Vertically and cross wise URDHVA TIRYAGBHYAM is the Sanskrit This sutra is very handy in calculating squares of numbers near(lesser) to powers of 10 This sutra means whatever the extent of its deficiency, lessen it still further to that very exten t Step 1 : 5×2=10, write down 0 and carry 1 Step 2 : 7×2 + 5×3 = 14+15=29, add to it previous carry over value 1, so we have 30, now write down 0 and carry 3 Step 3 : 7×3=21, add previous carry over value of 3 to get 24, write it down. So we have 2400 as the answer. Vertically and cross wise: Vertically and cross wise 4 6 X 4 3 1 9 7 8 103 X 105 1 0, 8 1 5 Transpose and apply: Transpose and apply This formula complements "all from nine and the last from ten", which is useful in divisions by large numbers. This formula is useful in cases where the divisor consists of small digits. This formula can be used to derive the Horner's process of Synthetic Division. by addition and by subtraction: by addition and by subtraction SAŃKALANA – VYAVAKALANĀBHYAM It can be applied in solving a special type of simultaneous equations where the x - coefficients and the y - coefficients are found interchanged by alternate elimination and retention: by alternate elimination and retention LOPANA STHÂPANÂBHYÂM Consider the case of factorization of quadratic equation of type ax 2 + by 2 + cz 2 + dxy + eyz + fzx This is a homogeneous equation of second degree in three variables x, y, z. The sub-sutra removes the difficulty and makes the factorization simple For furthur more….. : For furthur more….. Agrawala , V. S. (1992). General editor's note. Vedic mathematics (pp. v-viii) Motilal Banarsidass Publishers Private Limited. Dutta , . (2002). Mathematics in Ancient India. Seattle, Wash.: Resonance Media. Gaskell, M. (2000). Try a sūtra . The Times Educational Supplement, M10. Glover, J. (2002, Vedic Mathematics Today (Only a Matter of 16 Sutras). Education Times. www. vedicmaths .org/ http://www.hinduism.co.za/vedic.htm http://www.vedicmathsindia.org/ http://e-gurukul.net/portal/ Working with Vedic math's: complexity Interest and love towards math's Working with Vedic math's simplicity THANKS GIVING, PARENTS, TEACHERS, KRISTU JAYANTI COLLEGE.: THANKS GIVING, PARENTS, TEACHERS, KRISTU JAYANTI COLLEGE. Questions?: Questions?