16 Sutras Of Vedic Maths Pdf
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The sutras of Vedic Mathematics in Geometry Inasmuch as the sutras express thought processes and mathematical principles, many of them are applicable to geometrical problems. Of course, a sutra such as “All form nine and the last from 10” seems only to apply to number but others, such as Particular and General, have a closer relationship. Presents a list of 16 enigmatic sutras, and illustrates how these are to be used in various mathematical operations. 5 A sutra in the vedic and post-vedic literature is a short, enigmatic statement, that required considerable commentary to elucidate. This book presents a set of sixteen sutras, claiming these as Vedic.
- Vedic mathematics is an ancient system of mathematics which performs unique technique of calculations based on 16 sutras. The performance of high speed multiplier is designed based on Urdhva Tiryabhyam, Nikhilam Navatashcaramam Dashatah, and Anurupye algorithms.
- Vedic Mathematics is an ancient technique consisting of sixteen sutras and sixteen sub-sutras. These sutras are not only important in dealing with simple arithmetic and algebraic concepts but are equally good in solving complex problems of higher algebra, trigonometry, calculus and co-ordinate geometry.
- Field of Vedic Mathematics is supposedly based on 16 one-to- three-word sutras (aphorisms) in Sanskrit, which they claim can solve all modern mathematical problems.
- Vedic Mathematics is a collection of Techniques/Sutras/Formulas to solve mathematical arithmetics problems in easy and very faster way. It consists of 16 Sutras (Formulae) and 13 sub-sutras (Sub Formulae) which can be used for problems involved in arithmetic, algebra, geometry, calculus, conics.
16 Sutras Of Vedic Maths Pdf Worksheets
16 SUTRAS OF VEDIC MATHEMATICS The sixteen sutras of VEDIC MATHEMATICS. Sutras 1 Ekadhikina Purvena COROLLARY: Anurupyena Meaning: By one more than the previous one 2 Nikhilam Navatashcaramam Dashatah.
Jump to navigationJump to search| Country | India |
|---|---|
| Language | English |
| Subject | Mental calculation |
| Publisher | Motilal Banarsidass |
| 1965 | |
| ISBN | 978-8120801646 |
| OCLC | 217058562 |
Vedic Mathematics is a book written by the Indian monkSwami Bharati Krishna Tirtha and first published in 1965. It contains a list of mental calculation techniques claimed to be based on the Vedas. The mental calculation system mentioned in the book is also known by the same name or as 'Vedic Maths'. Its characterization as 'Vedic' mathematics has been criticized by academics, who have also opposed its inclusion in the Indian school curriculum.
History[edit]
Although the book was first published in 1965, Tirthaji had been propagating the techniques since much earlier, through lectures and classes.[1] He wrote the book in 1957.[2]:10 It was published in 1965, five years after his death as 367 pages in forty chapters. Reprints were made in 1975 and 1978 with fewer typographical errors.[3] Several reprints have been made since the 1990s.[2]:6
Contents[edit]
The book contains sixteen sutras and fifteen sub-sutras, each of which lists a mental calculation technique. The sixteen sutras are as follows:[2]:11[4]
| # | Name | Upa Sutra | Meaning | Corollory |
|---|---|---|---|---|
| 1 | Ekadhikena Purvena | Anurupyena | By one more than the previous one | Proportionately |
| 2 | Nikhilam Navatashcaramam Dashatah | Sisyate Sesasamjnah | All from 9 and the last from 10 | The Remainder Remains Constant |
| 3 | Urdhva-Tiryagbyham | Adyamadyenantyamantyena | Vertically and crosswise | The First by the First and the Last by the Last |
| 4 | Paraavartya Yojayet | Kevalaih Saptakam Gunyat | Transpose and adjust | For 7 the Multiplicand is 143 |
| 5 | Shunyam Saamyasamuccaye | Vestanam | When the sum is the same that sum is zero | By Osculation |
| 6 | Anurupye Shunyamanyat | Yavadunam Tavadunam | If one is in ratio, the other is zero | Lessen by the Deficiency |
| 7 | Sankalana-vyavakalanabhyam | Yavadunam Tavadunikritya Varga Yojayet | By addition and by subtraction | Whatever the Deficiency lessen by that amount and set up the Square of the Deficiency |
| 8 | Puranapuranabyham | Antyayordashake'pi | By the completion or non-completion | Last Totalling 10 |
| 9 | Chalana-Kalanabyham | Antyayoreva | Differences and Similarities | Only the Last Terms |
| 10 | Yaavadunam | Samuccayagunitah | Whatever the extent of its deficiency | The Sum of the Products |
| 11 | Vyashtisamanstih | Lopanasthapanabhyam | Part and Whole | By Alternate Elimination and Retention |
| 12 | Shesanyankena Charamena | Vilokanam | The remainders by the last digit | By Mere Observation |
| 13 | Sopaantyadvayamantyam | Gunitasamuccayah Samuccayagunitah | The ultimate and twice the penultimate | The Product of the Sum is the Sum of the Products |
| 14 | Ekanyunena Purvena | Dhvajanka | By one less than the previous one. | On the Flag |
| 15 | Gunitasamuchyah | Dwandwa Yogiji | The product of the sum is equal to the sum of the product. | |
| 16 | Gunakasamuchyah | Adyam Antyam Madhyam | The factors of the sum is equal to the sum of the factors |
Criticism[edit]
Tirthaji claimed that he found the sutras after years of studying the Vedas, a set of sacred ancient Hindu scriptures. However, the Vedas do not contain any of the 'Vedic mathematics' sutras.[1][5] First, Tirthaji’s description of the mathematics as Vedic is most commonly criticised on the basis that, thus far, none of the sūtras can be found in any extant Vedic literature (Williams, 2000). When challenged by Professor K.S. Shukla to point out the sutras in question in the Parishishta of the Atharvaveda, Shukla reported that the Tirthaji said the sixteen sutras were not included in standard editions of the Parishishta and that they occurred in his own Parishishta and not any other.[6][7]
Professor Vasudeva Saran Agrawala, the editor of the first edition of Tirthaji's book, notes that there is no evidence that the sutras are 'Vedic', as such, in their origin.[2]:6 Similarly, S. G. Dani of IIT Bombay points out that the contents of the book have 'practically nothing in common' with the mathematics of the Vedic period or even with subsequent developments in Indian mathematics. For example, multiple techniques in the book involve the use of decimal fractions, which were not known during the Vedic times: even the works of later mathematicians such as Aryabhata, Brahmagupta and Bhaskara do not contain any decimal fractions. He contends that Tirthaji liberally interpreted three-word Sanskrit phrases to associate them with arithmetic.[1]
Tirthaji's claim that the sutras are relevant to advanced mathematical techniques such as successive differentiation or analytical conics have also been dismissed by Dani. He terms 'ludicrous' Tirthaji's claim that 'there is no part of mathematics, pure or applied, which is beyond their jurisdiction'. He also points out that while Tirthaji's methods were not unique, they may have been invented by him independently, as Tirthaji held an MA in mathematics. Similar systems include the Trachtenberg system or the techniques mentioned in Lester Meyers's 1947 book High-speed Mathematics.[1]Alex Bellos points out that several of the calculation tricks can also be found in certain European treatises on calculation from the early Modern period.[8]
16 Sutras Of Vedic Maths With Examples
Use in schools[edit]
The book was previously included in the school syllabus of Madhya Pradesh and Uttar Pradesh.[2]:6 Some schools and organizations run by Hindu nationalist groups, including those outside India, have also included Tirthaji's techniques in their curriculum. The Hindu nationalists have also made several attempts to have Tirthaji's 'Vedic mathematics' system included in the Indian school curriculum via the NCERT books.
A number of academics and mathematicians have opposed these attempts on the basis that the techniques mentioned in the book are simply arithmetic tricks, and not mathematics. They also pointed out that the term 'Vedic' mathematics is incorrect, and there are other texts that can be used to teach a correct account of the Indian mathematics during the Vedic period. They also criticized the move as a saffronization attempt to promote religious majoritarianism.[9][10]
Dani points out that while Tirthaji's system could be used as a teaching aid, there was a need to prevent the use of 'public money and energy on its propagation, beyond the limited extent'. He pointed out that the authentic Vedic studies had been neglected in India even as Tirthaji's system received support from several Government and private agencies.[1]
Proponents of Vedic Mathematics however argue that the methods are not merely mathematical tricks and that there is an underlying psychology because the aphorisms describe personal approaches to problem-solving. As pedagogic tools, the methods are useful because they invite students to deal with strategies.[11]
References[edit]
- ^ abcdeS. G. Dani (December 2006). 'Myths and reality : On ‘Vedic mathematics’'. Originally published as a 2-part article in Frontline, 22 October and 5 November 1993. The updated version appears in Kandasamy and Smarandache (2006).
- ^ abcdeW.B. Vasantha Kandasamy; Florentin Smarandache (December 2006). Vedic Mathematics: Vedic Or Mathematics: A Fuzzy and Neutrosophic Analysis(PDF). American Research Press. ISBN978-1-59973-004-2. Retrieved 23 May 2013.
- ^Biographical sketch by Manjula Trivedi, 1965 in book Vedic Mathematics, pages x, xi.
- ^R. K. Thakur (1 November 2009). Vedic Mathematics. Unicorn and Dragon Books. ISBN978-81-7806-177-1. Retrieved 23 May 2013.
- ^The Fraud of Vedic Maths. Hartosh Singh Bal. Open Magazine. 14 August 2010.
- ^K.S. Shukla, Vedic mathematics — the illusive title of Swamiji’s book, Mathematical Education, Vol 5: No. 3, January–March 1989
- ^K.S. Shukla, Mathematics — The Deceptive Title of Swamiji’s Book, in Issues in Vedic Mathematics, (ed: H.C.Khare), Rashtriya Veda Vidya Prakashan and Motilal Banarasidass Publ., 1991.
- ^Alex Bellos (2010). '3'. Alex's Adventures in Numberland. Bloomsbury.
- ^Neither Vedic nor Mathematics
- ^Legitimisation of Vedic mathematics, astrology opposed. The Hindu, 14 August 2001.
- ^Glover, James (17 October 2014). 'Everything Vedic in 'Vedic Maths''. The Hindu. Retrieved 4 January 2016.
16 Sutras Of Vedic Mathematics
16 SUTRAS OF VEDIC MATHS PDF
16 SUTRAS OF VEDIC MATHEMATICS. The sixteen sutras of VEDIC MATHEMATICS. Adobe acrobat 9 pro portable download. Sutras 1 Ekadhikina Purvena COROLLARY. Vedic Mathematics provides principles of high speed multiplication. discussed 16 Vedic Mathematics Sutra which can be used to increase. Sutras 1 Ekadhikina Purvena COROLLARY: Anurupyena Meaning: By one more than the previous one 2 Nikhilam Navatashcaramam.
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Easy Vedic Maths ™: Sixteen ( 16 ) Sutras of Vedic Mathematics
Therefore 2 is the multiplier for the conversion. We use this sutra in following two cases:. Hence in our case, the base has 2 zeros and hence sqaure of 3 is 09 and not just 9.
Find the square of We can use it in following three cases:. We use it to find the value of variable from the equations which have one solution. Sixteen mahts Sutras of Vedic Mathematics.
When both the numbers are higher than the base. Note that in each case the sum of the last digit of first number to the last digit of second number is The procedure of multiplication using the Nikhilam involves minimum number of steps, space, time saving and only mental calculation.
Sixteen Sutras of Vedic Mathematics
Decrease the given number further by an amount equal to the deficiency. For the number 25, the last digit is 5 and the ‘previous’ digit is 2. Since is 9 more than basewe call 9 as the surplus.
The Sutra ‘ Adyamadyena-Antyamantyena’ means ‘the first by the first and the last by the last’. Learn Vedic Maths sutras, Solve difficult calculations mentally and instantaneously.
Therefore, let us take as our base. The product of the sum. By one more than the one before. S portion is same i. Hence the answer is The only contribution we seek from our readers is to Bookmark our site to make people aware of this blog.
16 Sutras Of Vedic Maths Pdf Grade 8
This is a homogeneous equation of second degree in three variables x, y, z. Know more About Vedic Mathematics.
Sixteen Sutras of Vedic Mathematics
It becomes the L. Generally we continue the problem like this. Download virtual dj 7. 4. exe. Here ‘one’ and ‘zero’ are in normal form. Increase the given number further by an amount equal to the surplus.
16 Sutras Of Vedic Maths With Examples Pdf
16 Sutras Of Vedic Maths In Hindi Pdf
The remainders by the last digit. Leave a Reply Cancel reply Your email address will not be published.
Further the portion of digits or numbers left wards to the last digits remain the same. Let us work another problem by placing the carried over digits under the first row and proceed.
General rule for a 3 digit by 3 digit multiplication: With this methods and tricks, You can solve difficult maths calculations, mentally and instantantly figure out the right answer to the matths, which you were used to calculate with paper or a calculator. Ekadhikena to the remaining digits means, increment the remaining digits by 1 and multiply it sutdas the same.
The ‘1’ in becomes ‘carry’ to The Sutra, in this context, gives the procedure ‘to multiply the previous digit 2 by one more than itself, that is, by 3. Try out calculating squares of 96, Now try to find the square of Shesanyankena Charamena The remainders by the last digit By one less than the one before.