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Vedic short

  1. 1. Introduction Multiplication Vedic Mathematics Division Square Roots . . . Teaching an Old Dog New Tricks Contact Information Uwe Wystup mathfinance.com Title Page uwe.wystup@mathfinance.com March 2010 Page 1 of 23 Go Back Full Screen Close Quit
  2. 2. Introduction Multiplication Division 1. Introduction Square Roots . . . Contact Information veda (Sanskrit) means: knowledge mathfinance.com Veda Upaveda Title Page Rigveda Ayurveda Samaveda Gandharvaveda Yajurveda Dhanurveda Page 2 of 23 Go Back Atharvaveda Sthapatyaveda Full Screen Close Table 1: Vedas and Upavedas (supplementary vedas) Quit
  3. 3. 1.1. The 16 Sutras are part of a Parisista (Appendix) of the Atharvaveda 1. By one more than the one before 2. All from 9 and the last from 10 Introduction Multiplication 3. Vertically and crosswise Division Square Roots . . . 4. Transpose and apply Contact Information 5. If the Samuccaya is the same it is zero 6. If one is in ratio the other is zero mathfinance.com 7. By addition and by subtraction Title Page 8. By the completion or non-completion 9. Differential calculus 10. By the deficiency Page 3 of 23 11. Specific and general Go Back 12. The remainders by the last digit Full Screen 13. The ultimate and twice the penultimate Close 14. By one less than the one before Quit 15. The product of the sum 16. All the multipliers
  4. 4. 1.2. Jagadguru Swami Sri Bharati Krsna Tirthaji Maharaja Introduction Explained the sutras in his books (e.g. [2]). Multiplication Division Jagadguru Swami Sri Bharati Square Roots . . . Krsna Tirthaji Maharaja Contact Information (March, 1884 - February 2, 1960) was the Jagadguru mathfinance.com (literally, teacher of the Title Page world; assigned to heads of Hindu mathas) of the Govardhana matha of Puri during 1925-1960. He was Page 4 of 23 one of the most significant Go Back spiritual figures in Hinduism Full Screen during the 20th century. He is particularly known for his Close work on Vedic mathematics. Quit
  5. 5. 2. Multiplication Introduction Multiplication Division Square Roots . . . Contact Information mathfinance.com Title Page Page 5 of 23 Go Back Full Screen Close Quit Figure 1: Vertically and Crosswise
  6. 6. Introduction 2.1. Example with working base 10 Multiplication Division Square Roots . . . 9 - 1 7 - 3 13 + 3 12 + 2 Contact Information × × × × mathfinance.com 7 - 3 6 - 4 12 + 2 8 - 2 Title Page 6 / 3 3 /1 2 15 / 6 10 / ¯ 4 = 63 = 42 = 156 = 96 Page 6 of 23 Reason: (x + a)(x + b) = x(x + a + b) + ab Go Back Full Screen Origin of the ×-sign comes from this method Close Quit
  7. 7. Introduction Multiplication Division 2.2. Example with working base 100 Square Roots . . . Contact Information 91 - 9 111 + 11 108 + 8 mathfinance.com × × × Title Page 96 - 4 109 + 9 97 - 3 87 / 36 120 / 99 105 / ¯ 24 Page 7 of 23 = 8736 = 12099 = 10476 Go Back Full Screen Close Quit
  8. 8. Introduction Multiplication 2.3. Other working bases (division case) Division Square Roots . . . Contact Information 100/2=50 100/2=50 49 - 1 54 + 4 mathfinance.com × × Title Page 49 - 1 46 - 4 2)48 / 01 2)50 / ¯¯ 16 Page 8 of 23 24 / 01 25 / ¯¯ 16 Go Back = 2401 = 2484 Full Screen Close Quit
  9. 9. Introduction Multiplication 2.4. Other working bases (multiplication case) Division Square Roots . . . Contact Information 10× 2=20 10× 6=60 19 - 1 62 + 2 mathfinance.com × × Title Page 19 - 1 48 - 12 × 2)18 / 1 × 6)50 /¯ 2 ¯ 4 Page 9 of 23 36 / 1 300 /¯ 2 ¯ 4 Go Back = 361 = 2976 Full Screen Close Quit
  10. 10. Introduction Multiplication Division Square Roots . . . Contact Information 2.5. Exercise: Multiply the following mentally mathfinance.com a 667 × 998 Title Page b 78989 × 99997 c 1222 × 1003 Page 10 of 23 Go Back Full Screen Close Quit
  11. 11. Introduction Multiplication Division 3. Division Square Roots . . . 1 Contact Information • Find the exact decimal representation of 19 . • Using the “Ekadhika Purva” Sutra it is easy: mathfinance.com Title Page . 0 5 2 6 3 1 5 7 8 1 1 1 1 1 1 / 9 4 7 3 6 8 4 2 1 Page 11 of 23 Go Back 1 1 1 Full Screen Close Quit
  12. 12. Introduction Multiplication Division • Start with 1 and then work from right to left multi- Square Roots . . . plying by 2. Contact Information . 0 5 2 6 3 1 5 7 8 mathfinance.com 1 1 1 1 1 1 Title Page / 9 4 7 3 6 8 4 2 1 1 1 1 Page 12 of 23 Go Back Full Screen Close Quit
  13. 13. • A further shortcut is the insight that Introduction Multiplication Division . 0 5 2 6 3 1 5 7 8 Square Roots . . . + 9 4 7 3 6 8 4 2 1 Contact Information = 9 9 9 9 9 9 9 9 9 mathfinance.com Title Page 1 • The same works for all periodic decimals, e.g. 7 . 1 4 2 Page 13 of 23 + 8 5 7 Go Back Full Screen = 9 9 9 Close Quit
  14. 14. Introduction Multiplication Division Square Roots . . . Contact Information 4. Square Roots (Vargamula) mathfinance.com • Square numbers only have digit sums 1, 4, 7, 9 Title Page • and they only end in 1, 4, 5, 6, 9, 0. • If the given number has n digits, then the square root will contain n or n+1 digits. 2 2 Page 14 of 23 Go Back • Systematic computation of an exact square root re- quires the Dvandvayoga (Duplex) process. Full Screen Close Quit
  15. 15. Introduction Multiplication Division Square Roots . . . 4.1. Duplex Process (Dvandvayoga) Contact Information D(4) = 16 (1) mathfinance.com D(43) = 24 (2) Title Page D(137) = 23 (3) D(1034) = 8 (4) D(10345) = 19 (5) Page 15 of 23 Got it? Go Back Full Screen Close Quit
  16. 16. 4.2. Square Root of a Perfect Square √ Introduction Find 1849. Multiplication Division Group in pairs, taking a single extra digit on the left as Square Roots . . . Contact Information extra digit. mathfinance.com 1 8 — 4 9 Title Page 8) 2 4 Page 16 of 23 Go Back Full Screen 4 is the largest integer whose square does not exceed 18. Close 18/4 is 4 with remainder 2. The divisor 8 is two times 4. Quit
  17. 17. Introduction Multiplication Next we divide 24 by the divisor 8. This gives 3 remainder Division 0, placed as Square Roots . . . Contact Information 1 8 — 4 9 8) 2 0 mathfinance.com Title Page 4 3 Page 17 of 23 Now we see 09 and we deduct from this the duplex of Go Back the last answer figure 3, i.e. 09 − D(3) = 09 − 32 = 09 − 9 = 0. This means that the answer is exactly 43. Full Screen Close Quit
  18. 18. 1 3 — 6 9 6) 4 Introduction 3 Multiplication Division Square Roots . . . Contact Information 3 is the largest integer whose square does not exceed 13. 13/3 is 3 with remainder 4. mathfinance.com The divisor 6 is two times 3. Title Page Next we divide 46 by the divisor 6. This gives 7 remainder 4, placed as 1 3 — 6 9 Page 18 of 23 Go Back 6) 4 4 Full Screen 3 7 Close Quit 49 − D(7) = 0, so 37 is the exact square root of 1369.
  19. 19. 4.3. Larger Numbers Introduction 2 9 3 7 6 4 Multiplication Division 10) 4 Square Roots . . . Contact Information 5 . mathfinance.com Title Page 2 9 3 7 6 4 10) 4 3 Page 19 of 23 5 4 . Go Back Full Screen Close Quit 37 − D(4) = 37 − 16 = 21 = 2 × 10 + 1.
  20. 20. 2 9 3 7 6 4 Introduction Multiplication 10) 4 3 1 Division Square Roots . . . 5 4 2. Contact Information mathfinance.com 16 − D(42) = 16 − 16 = 0 = 0 × 10 + 0. Title Page 2 9 3 7 6 4 10) 4 3 1 0 Page 20 of 23 5 4 2. 0 Go Back Full Screen Close Quit 4 − D(420) = 4 − 4 = 0. Complete.
  21. 21. Introduction Multiplication Division Square Roots . . . 4.4. General Square Roots Contact Information Find the first 5 figures of the square root of 38: mathfinance.com 3 8 . 0 0 0 0 0 Title Page 12) 2 8 7 10 8 6 . 1 6 4 4 Page 21 of 23 Go Back Full Screen Close Quit
  22. 22. 5. Contact Information Introduction Multiplication Division Square Roots . . . Contact Information Uwe Wystup MathFinance AG mathfinance.com Mainluststraße 4 Title Page 60329 Frankfurt am Main Germany +49-700-MATHFINANCE Page 22 of 23 Go Back Full Screen Close Quit http://www.mathfinance.com/wystup/papers.php http://www.mathfinance.com/seminars/vedic.php
  23. 23. References [1] Datta, B. and Singh, A.N. (1962). History of Hindu Mathematics. Asia Introduction Publishing House, Calcutta. Multiplication [2] Maharaja, Bharati Krsna Tirthaji (1992). Vedic Mathematics, Motilal Division Banarsidass Publishers Private Ltd, Delhi. Square Roots . . . Contact Information [3] Schonard, A. and Kokot, C. (2006). Der Mathekn¨ller. http://www. u matheknueller.de. mathfinance.com [4] Williams, K.R. (2002). Vedic Mathematics - Teacher’s Manual. Ad- vanced Level. Motilal Banarsidass Publishers Private Limited, Delhi. Title Page http://www.mlbd.com Page 23 of 23 Go Back Full Screen Close Quit
  24. 24. Index Introduction Multiplication division, 11 Division duplex, 15 dvandvayoga, 15 Square Roots . . . Contact Information multiplication, 5 square root, 14 mathfinance.com sutras, 3 Title Page vedas, 2 Page 24 of 23 Go Back Full Screen Close Quit

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