2. Vedic Mathematics Vishnu S. Pendyala

3. Copyright(c) Vishnu S. Pendyala The Roots of Vedic Math Sri Bharati Krsna Tirthaji (1884-1960)  All of mathematics is based on sixteen Sutras  St James' School, Queensgate, London began to teach vedic mathematics in early 1980s.  The Vedic Mathematics Research Group publishes books and does research.  A school in Skelmersdale, Lancashire has a full course for 11 to 14 year old pupils, called The Cosmic Computer.  According to Maharishi Mahesh Yogi, the cosmic computer runs the entire universe.  Vedic Math is the software for the cosmic computer

4. Copyright(c) Vishnu S. Pendyala Insights Vedas contain densely packed, cryptic, systematic, knowledge in form of sanskrit slokas. The knowledge is complete in itself: everything that is needed by the mankind is in there. In process of knowing the absolute truth, all intermediary truths also become known. All branches of Math: Arithmetic to Astronomy can be explained using 16 basic sutras. These sutras are the shortest and surest ways to a galaxy of largely unexplored knowledge.

5. Copyright(c) Vishnu S. Pendyala Mathematical mantras Formulae and laws are in form of mantras. For e.g., consider the numbering scheme: ka, ta, pa, ya = 1gna, na, ma, scha = 5 kha, tha, pha, ra = 2cha, ta, sha = 6 ga, da, ba, la = 3chha, tha, sa = 7 gha, dha, bha, va = 4ja, da, ha =8 This sloka on God Krishna gives the value of pi: gopi bhaagya madhu vraata - shrngisho dadhisandhiaga khalajivita khaataava galahaataarasandhara 31415926535897932384626433832792 (32 dec places)

6. 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 The sixteen Sutras

7. Copyright(c) Vishnu S. Pendyala 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

8. Copyright(c) Vishnu S. Pendyala Why Vedic Math? Fun: A different way to think and get surprised. Easy: No need of laborious methods. Simple: Simple to understand and practice. Spiritual: Formulae can be remembered in form of slokas in praise of God. Powerful: Use in complicated calculations Potential: Vedas are still vastly unexplored; new studies could lead to newer knowledge.

9. Copyright(c) Vishnu S. Pendyala Key Elements Think different: Dare to be unconventional when you see a need. Vilokanam: Observation for patterns; look for solution in the problem itself. Analysis: Break the problem into manageable, known sub-problems. Special cases first: These are simpler, so start with them first and then generalize.

10. A. By Multiplication B. By Division 1/19 =.0 5 2 6 3 1 5 7 8 | 9 4 7 3 6 8 4 2 1 1 1 1 1 1 1 1 1 1 1/49 =.0 2 0 4 0 8 1 6 3 2 6 5 3 0 6 1 2 2 4 4 8 1 2 4 3 1 1 3 2 1 3 1 1 2 2 4 4 9 7 9 5 9 1 8 3 6 7 3 4 6 9 3 8 7 7 5 5 1 3 4 2 4 4 1 3 3 1 2 3 4 1 4 3 3 2 2. 0 5 2 6 3 1 5 7 8 Try more: 9 4 7 3 6 8 4 2 11/29, 1/39, 1/59 9 9 9 9 9 9 9 9 9

11. Gives a method to multiply numbers, where the first digits are same and the last digits add up to 10: 56 x 54 = (5 x (5+1)) | (6x4) = 30|24 68 x 62 = (6 x (6+1)) | (2 x 8) = 42|16 95 2 = (9 x (9+1)) | (5 2 ) = 90|25 Algebraic justification: (10x + 10 -y)(10x + y) = 100x(x+1) + y(10-y) Try more: 24 x 2631 x 3992 x 9873 x 77

12. Corollary: yaavadoonam thaavadoonikrutya varga ca yojayeth (whatever the extent of its deficiency, lessen it still further to that very extent; and also square the deficiency) 8 2 =(8-2) | 2 2 = 64 11 2 =(11+1)|1 2 = 121 999996 2 =(999996-4)|4 2 =999992|000016 Give algebraic justification and try more: 100000004 2 99999999997 2 Used in subtractions from powers of 10

13. A. 9 x 8 B. 5 x 7C. 13 x 12 9 - 1 5 - 5 13 + 3 8 - 2 7 - 3 12 + 2 7 | 2 2 | 1 5 = 35 15 | 6 D. 10006 x 9999 E. 46 x 44 F. 87965 x 99998 10006 + 6 46 - 4 87964 - 12036 9999 - 1 44 - 6 99998 - 2 10005|-0006 2)40|24 87962 | 24072 =10004|9994 = 20|24

14. Copyright(c) Vishnu S. Pendyala 10x-9=4x+3 Transpose: 10x-4x=3+9 and adjust: x = (3+9)/(10-4) = 12/6 = 2 Similarly, if (x+a)(x+b) = (x+c)(x+d), cd-ab => x = --------- a+b-c-d

15. Copyright(c) Vishnu S. Pendyala When the samuccaya is the same, that samuccaya =0 2x + 9 2x + 7 -------- = -------- What is the samuccaya here? 2x + 7 2x + 9 How about: (x-3) 3 + (x-9) 3 = 2(x-6) 3 ? And: 1 1 1 1 ------ + ------ = --------- + -------- x-7 x-9 x-5 x-11 ((2x + 9) + (2x + 7)) = 0 (x-3)+(x-9)=2(x-6)=0 (x-7)+(x-9) = (x-5)+(x-11)= (2x-16)=0

16. ax+by+cz=a bx+cy+az=bx=1, y=0, z=0 cx+ay+bz=c 2 3 4 1 ------- + ------- = --------- + --------- x+2 x+3 x+4 x+1 2/1 + 3/1 = 4/1 +1/1 and 2/2 + 3/3 = 4/4 + 1/1 so, one root is 0. For the other root, use samuccaye sutra, because (x+2) + (x+3) = (x+4) + (x+1) = 2x+5 =0

17. Copyright(c) Vishnu S. Pendyala 12x-10y = 24Add: 22x-22y=44 =>x-y=2 10x-12y = 20Sub: 2x+2y =4 =>x+y=2 Try More: 23x-5y = 135x+25y=85 10x+11y=94 45x-6y = 3325x+5y=65 11x+10y=95

18. Copyright(c) Vishnu S. Pendyala Conclusion Think different! Observe - Vilokanam! Analyze - See milk from water! Revere - God shows the way! Probe - Search for the invisible!

19. Copyright(c) Vishnu S. Pendyala References Jagadguru Swami Sri Bharati Krsna Tirthaji Maharaja, “Vedic Mathematics”, Motilal Banarasidass Publishers, New Delhi, 1965. Http://www.vedicmathematics.org http://www.pendyala.org http://www.ics.uci.edu/~rgupta/vedic.html http://www.gosai.com/chaitanya/saranagati/html/math/math_7.html http://www.geocities.com/CapeCanaveral/7348/math.html http://www.magicalmethods.com/ http://members.aol.com/vedicmaths/vm.htm