Vedic mathematics details


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Vedic mathematics details

  2. 2. “a gift given to this world by the ancientsages of India. A system which is far more simple and enjoyable than modern mathematics.” “Research shows that the application ofVedic mathematics makes use of both parts of the brain.”
  3. 3. Vedic Maths, a Forgotten Science….. It is being taught in some of the most prestigiousinstitutions in England and Europe. NASA scientists applied its principles in the area of artificial intelligence. And yet, in the country of its birth it languishes as a forgotten science.
  4. 4. What is Vedic Mathematics…???“It is an ancient technique, which simplifiesmultiplication, divisibility, complexnumbers, squaring, cubing, square and cube roots.”“Even recurring decimals and auxiliary fractions canbe handled by Vedic mathematics.”“In the Vedic system difficult problems or hugesums can often be solved immediately by the Vedicmethod.”
  5. 5. Brought Vedic Maths to limelight…???“Vedic Mathematics was revived largely due to theefforts of Jagadguru Swami BharathikrishnaTirthaji of Govardhan Peeth, Puri Jaganath(1884-1960), which he claimed that it based on alost appendix of Atharvaveda, an ancient text ofthe Indian teachings called Veda.”Having researched the subject for years, even hisefforts would have gone in vain but for theenterprise of some disciples who took down notesduring his last days.
  6. 6. What is the basis of Vedic Mathematics…???The basis of Vedic mathematics, are the 16 sutras, whichattribute a set of qualities to a number or a group ofnumbers.The ancient Hindu scientists (Rishis) of Bharat in 16 Sutras(Phrases) and 120 words laid down simple steps for solving allmathematical problems in easy to follow 2 or 3 steps.Vedic System can be used effectively for solvingdivisions, reciprocals, factorisation, HCF, squares and squareroots, cubes and cube roots, algebraic equations, multiplesimultaneous equations, quadratic equations, cubicequations, bi-quadratic equations, higher degreeequations, differential calculus, Partialfractions, Integrations, Pythagoras theorem, ApolloniusTheorem, Analytical Conics and so on.
  7. 7. Is it useful today…???Given the initial training in modern maths in todaysschools, students will be able to comprehend the logic ofVedic mathematics after they have reached the 8thstandard.It will be of interest to every one but more so toyounger students keen to make their mark incompetitive entrance exams.Indias past could well help them make it in todaysworld.It is amazing how with the help of 16 Sutras and 16 sub-sutras, the Vedic seers were able to mentally calculatecomplex mathematical problems.
  8. 8. Why did the Vedic Seers need Vedic Mathematics…???The Vedic Seers were highly ritualistic in practice. All the four Vedasnamely Rig Veda, Yajur Veda, Sama Veda and AtharvaVeda, consist of Samhitas, Brahmanas, Aranyakas and Upanishads.Of these four, the first three namely Samhitas, Brahmanas andAranyakas contain several thousand Mantras or Hymns, Ritualpractices and their interpretations.The Vedic Seers were very particular about the time of doing therituals. Hence they needed a very scientific and accurate calendar andtime measurements. Hence we have the adage IST which once meantIndian Standard Time. But in recent times due to our laziness andcarelessness, it has come to mean Indian Stretchable Time.The Vedic culture was that of Yajna and the Vedic Purohits or priestswere also very particular about the shape and size of the Yajna Kund.For this they needed a very highly developed Geometry andTrigonometry.
  9. 9. Sutras (Phrases) used in Vedic Mathematics…1.Ekadhikena Purvena (One More than the Previous) It is useful in solving Special Multiplications like 25×25, 95×95, 105×105 etc Special Divisions like 1 divided by 19, 29, 39, …. 199 etc.Sub sutras:Anurupyena or Sunyamanyat (Proportionately)2.Ekanyunena Purvena (One less than the Previous) It is useful in solving Special Multiplications like 777×999, 123456789×9999999993.Urdhva-Tiryaghyam (Vertically and Cross-wise) It is useful in General Multiplication of any number by any number.Sub sutras:Adhyam-Adhyena, Antyam-Antyena (first by the first and the last by the last) It is useful in solving Quadratics.
  10. 10. 4. Paravartya Yojayet (Transpose and Apply) It is useful in solving Algebraic factors and divisions of some numbers etc.5.Sunyam Samya samuccaye (when Samuccaya is the same, that Samuccaya is zero) Samuccaya is a technical term which has several meanings. This is useful in solving many complex factors and equations.Sub sutras:Veshtanam6.Sankalana-vyavakalanaSub sutras:Yavadunam Tavadunikrtya Vargamca Yojayet7.Purna PurnabhyamSub sutras:Antyayor Dasakepi It is used for two numbers whose last digits together total 10
  11. 11. 8.Calana-KalanabhyamSub sutra:Antyayoreva9.YavadunamSub sutra:Samuccayagunitah10.Vyashti samashtiSub sutra:Lopana-stapana-bhyam (by Elimination and Retention) It is useful in factorizing long and harder quadratics. very useful in HCF, Solid Geometry, Coordinate Geometry11.Seshanyankena caramenaSub sutra:Vikolanam
  12. 12. 12.Sopantya dvayamantyamSub sutra:Gunita-Samuchhayah Samuchhaya-gunitah It means "The product of the sum of the coefficients in the factors is equal to the sum of the coefficients in the product" It immense utility for the purpose of verifying the correctness of our answers in multiplications, divisions and factorizations.13.Nikhilam Navatascaram Dashtah14.Gunaka Samuccayah15.Gunita Samuccayah16.Anurupye or Sunyamanyat