
:''Note: Vedic mathematics is not to be confused with Vedic physics or any other vedic science, which is a kind of Hindu philosophy, and is unrelated to the practice of actual science, (that is, to mathematics or the application of the scientific method.)'' Vedic mathematics is a system of mental calculation developed by Shri Bharati Krishna Tirthaji which he claimed he had based on a lost appendix of Atharvaveda, an ancient text of the Indian teachings called Veda. It has some similarities to the Trachtenberg system in that it speeds up some arithmetic calculations. It claims to have applications to more advanced mathematics, such as calculus and linear algebra. The system was first published in the book ''Vedic Mathematics(book)'' ISBN 8120801644 in 1965. The system has since been developed further and there have been several other books released. Critics have questioned whether this subject deserves the name ''Vedic'' or indeed ''mathematics''. They point to the lack of evidence of any sutras from the Vedic period consistent with the system, the inconsistency between the topics addressed by the system (such as decimal fractions) and the known mathematics of early India, the substantial extrapolations from a few words of a sutra to complex arithmetic, and the restriction of applications to convenient cases. They have also been worried that it deflects attention from genuine achievements of ancient and modern Indian mathematics and mathematicians, and that its promotion by Hindutva may damage mathematics education in India. The system is based upon sixteen formulas and their corollaries, some of which are described below. ==All from nine and the last from ten== Corollary 1: Whatever the extent of its deficiency, lessen it still further to that very extent; and also set up the square of that deficiency. For instance, in computing the square of 9 we go through the following steps: #The nearest power of 10 to 9 is 10. Therefore, let us take 10 as our base. #Since 9 is 1 less than 10, decrease it still further to 8. This is the left side of our answer. #On the right hand side put the square of the deficiency, that is 12. Hence the answer is 81. #Similarly, 82 = 64, 72 = 49. #For numbers above 10, instead of looking at the deficit we look at the surplus. For example: : : : :and so on. This is based on the identities and . ==By one more than the one before== The proposition "by" means the operations this formula concerns are either multiplication or division. [ In case of addition/subtraction proposition "to" or "from" is used.] Thus this formula is used for either multiplication or division. It turns out that it is applicable in both operations. An interesting application of this formula is in computing squares of numbers ending in five. Consider: : 35 × 35 = (3 × (3 + 1)),25 = 12,25 The latter portion is multiplied by itself (5 by 5) and the previous portion is multiplied by one more than itself (3 by 4) resulting in the answer 1225. This is a simple application of when and , i.e. :. It can also be applied in multiplications when the last digit is not 5 but the sum of the last digits is the base (10) and the previous parts are the same. Consider: : 37 × 33 = (3 × 4),7 × 3 = 12,21 : 29 × 21 = (2 × 3),9 × 1 = 6,09 This uses twice combined with the previous result to produce: :. We illustrate this formula by its application to conversion of fractions into their equivalent decimal form. Consider fraction 1/19. Using this formula, this can be converted into a decimal form in a single step. This can be done by applying the formula for either a multiplication or division operation, thus yielding two methods. ====Method 1: using multiplications==== 1/19, since 19 is not divisible by 2 or 5, the fractional result is a purely circulating decimal. (If the denominator contains only factors 2 and 5 is a purely non-circulating decimal, else it is a mixture of the two.) So we start with the last digit : 1 Multiply this by "one more", that is, 2 (this is the "key" digit from Ekadhikena) : 21 Multiplying 2 by 2, followed by multiplying 4 by 2 : 421 → 8421 Now, multiplying 8 by 2, sixteen : 68421 : 1 ← carry multiplying 6 by 2 is 12 plus 1 carry gives 13 : 368421 : 1 ← carry Continuing : 7368421 → 47368421 → 947368421 : 1 Now we have 9 digits of the answer. There are a total of 18 digits (= denominator − numerator) in the answer computed by complementing the lower half: : 052631578 : 947368421 Thus the result is .052631578,947368421 ====Method 2: using divisions==== The earlier process can also be done using division instead of multiplication. We divide 1 by 2, answer is 0 with remainder 1 : .0 Next 10 divided by 2 is five : .05 Next 5 divided by 2 is 2 with remainder 1 : .052 next 12 (remainder,2) divided by 2 is 6 : .0526 and so on. As another example, consider 1/7, this same as 7/49 which as last digit of the denominator as 9. The previous digit is 4, by one more is 5. So we multiply (or divide) by 5, that is, ...7 => 57 => 857 => 2857 => 42857 => 142857 => .142,857 (stop after 7 − 1 digits) 3 2 4 1 2 ==Vertically and crosswise== This formula applies to all cases of multiplication and is very useful in division of one large number by another large number. ==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. ==When the samuccaya is the same, that samuccaya is zero== This formula is useful in solution of several special types of equations that can be solved visually. The word samuccaya has various meanings in different applications. For instance, it may mean a term which occurs as a common factor in all the terms concerned. A simple example is equation "12''x'' + 3''x'' = 4''x'' + 5''x''". Since "''x''" occurs as a common factor in all the terms, therefore, ''x'' = 0 is a solution. Another meaning may be that samuccaya is a product of independent terms. For instance, in (''x'' + 7)(''x'' + 9) = (''x'' + 3)(''x'' + 21), the samuccaya is ''7'' × 9 = 3 × 21, therefore, ''x'' = 0 is a solution. Another meaning is the sum of the denominators of two fractions having the same numerical numerator, for example: 1/(2''x'' − 1) + 1/(3''x'' − 1) = 0 means 5''x'' - 2 = 0. Yet another meaning is "combination" or total. This is commonly used. For instance, if the sum of the numerators and the sum of denominators are the same then that sum is zero. Therefore, : Therefore, 4''x'' + 16 = 0 or ''x'' = −4. This meaning ("total") can also be applied in solving quadratic equations. The total meaning can not only imply sum but also subtraction. For instance when given ''N''1''D''1 = ''N''2/''D''2, if ''N''1 + ''N''2 = ''D''1 + ''D''2 (as shown earlier) then this sum is zero. Mental cross multiplication reveals that the resulting equation is quadratic (the coefficients of ''x''2 are different on the two sides). So, if ''N''1 − ''D''1 = ''N''2 − ''D''2 then that samuccaya is also zero. This yield the other root of a quadratic equation. Yet interpretation of "total" is applied in multi-term RHS and LHS. For instance, consider : Here ''D''1 + ''D''2 = ''D''3 + ''D''4 = 2''x'' − 16. Thus ''x'' = 8. There are several other cases where samuccaya can be applied with great versatility. For instance "apparently cubic" or "biquadratic" equations can be easily solved as shown below: : Note that ''x'' − 3 + ''x'' − 9 = 2(''x'' − 6). Therefore (''x'' − 6) = 0 or ''x'' = 6. (remark by different author: Note also that:, whereas Thus: x=6 is NOT a solution!) (Another note. This example does work if one considers all exponants to be cubic, in which case will give .) Consider : Observe: ''N''1 + ''D''1 = ''N''2 + ''D''2 = 2''x'' + 8. Therefore, ''x'' = −4. This formula has been extended further. ==If one is in ratio, the other one is zero== This formula is often used to solve simultaneous simple equations which may involve big numbers. But these equations in special cases can be visually solved because of a certain ratio between the coefficients. Consider the following example: :6''x'' + 7''y'' = 8 :19''x'' + 14''y'' = 16 Here the ratio of coefficients of ''y'' is same as that of the constant terms. Therefore, the "other" is zero, i.e., ''x'' = 0. Hence the solution of the equations is ''x'' = 0 and ''y'' = 8/7. (alternatively: :19''x'' + 14''y'' = 16 is equivalent to: :(19/2)''x'' +7''y'' = 8. Thus it is obvious that x has to be zero, no ratio needed, just div by2!) This formula is easily applicable to more general cases with any number of variables. For instance :''ax'' + ''by'' + ''cz'' = ''a'' :''bx'' + ''cy'' + ''az'' = ''b'' :''cx'' + ''ay'' + ''bz'' = ''c'' which yields ''x'' = 1, ''y'' = 0, ''z'' = 0. A corollary says By addition and by subtraction. It is applicable in case of simultaneous linear equations where the ''x''- and ''y''-coefficients are interchanged. For instance: :45''x'' − 23''y'' = 113 :23''x'' − 45''y'' = 91 By addition: 68''x'' − 68 ''y'' = 204 => 68(''x'' − ''y'') = 204 => ''x'' − ''y'' = 3. By subtraction: 22''x'' + 22''y'' = 22 => 22(''x'' + ''y'') = 22 => ''x'' + ''y'' = 1. ==External links== * [http://www.amazon.com/exec/obidos/tg/detail/-/0313232008/104-7253290-5011962?v=glance Trachtenberg Speed System of Basic Mathematics at Amazon.com] * [http://mathforum.org/dr.math/faq/faq.trachten.html The Math Forum @ Drexel] * [http://vedicmaths.org/ VedicMaths.Org] * [http://www.vedicmaths.com/ Vedic Mathematics Books] * [http://www.bespokewear.com/vm/ The Vedic Mathematics Society] * [http://mathforum.org/epigone/math-history-list/zhimpjufrer Indian mathematics by Richard Askey] * [http://www.sacw.net/DC/CommunalismCollection/ArticlesArchive/NoVedic.html ''Neither Vedic Nor Mathematics''] * [http://www.tifr.res.in/~vahia/dani-vmsm.pdf Myths and reality: on "Vedic Mathematics" by Prof. S. G. Dani] Computation
Some equations on this page are incorrect. ---- I removed some commentary that had been interspersed with the article text. You can read it here: [http://en.wikipedia.org/w/wiki.phtml?title=Vedic_mathematics&diff=6938195&oldid=6938100] Such commentary is perfectly okay, if it contributes toward the improvement of the article, but it should be placed here on the talk page. User:Aranel_(\"User:Aranel/Sarah\")">User:Aranel|User:Aranel (\"User:Aranel/Sarah\") 19:57, 28 Oct 2004 (UTC)
----
It is strange that there is so much more doubt thrown on the progresses of the Ancient Indian Civilization then towards any other on the planet. We do not doubt that the Egyptions actually built the pyramids nor do we doubt that the Greeks came up with equations to measure the angles of a triangle.
This is so much so that there is even a Conspiracy Theory that Indians are trying to take credit for their own mathematics system. I find it shocking that a lot of the Lokayatran Science [meaning layman, non-spiritual, material] of the Vedic period is being misrepresented here on wikipedia as a Hindu Fundamentalist doctrine when these have nothing to do with either religion or politics.
We don't see every bit of Arabian culture on Wikipedia being identified with terrorism do we? We don't see every bit of English culture on Wikipedia being identified with imperialism do we? Why is this so with Indian culture?
Especially since it is a culture whose foundations have always been non-violence and tolerance. There is a lot of misrepresentation being done outside the Hindu community defining the community for them. We have seen this in Wendy Donigers books on Hindu mythology where she gives Freudian analysis to a culture that comes from an entirely different perspective to suspicians given to any Indian who writes about anything good in their own culture.
Don't fear dear math student, no one is trying to convert you into a religion. Like Judaism, there is no conversion here. A little mathematics isn't going to make you turn into an Indian, feel safe.
== Origins of Vedic Science ==
What many have failed to notice is that mathematics played a large part in the ancient Indian culture. Panini's Sanskrit grammar texts are based on the principles of algebra and what we would today call semiotics. Aryabatta and Charvaka were examples of two ancient philosophers who emphasised that this material world is the only world and that we should only believe that which we can observe and analyze. A term given to this thought is called Lokayatra or "layman" school which is entirely materialistic.
Mathematical formulas are in the Vedas for the building of architecture and the designing of Yantras which are very complex. The verses are also mathematical based so they can be memorized. A logic system called Nyaya - literaly "not this" - encourages doubt and skeptism. It is an analyitic system based on logic, proof and observation in much the same way as the scientific method is in the west.
Vedic mathematics is quite well known many south Indians of the previous generation as they had a much more complete text of the Arthaveda in Tamil. Written Tamil carved into wood slabs is much older than written Sanskrit texts though the later is usually credited as the source. This is where much of what is called Vedic mathematics originated from.
It has been questioned if the Arthaveda - along with maybe 11 other lesser known Vedas - are actually part of the original Vedas. This is mostly due to the translations into local dialects being the only known or existing source, yet this does not question the age in which these works were made nor that they were indegous to India as they all were.
== Decimal Fractions ==
The western method of deviding a circle is in degrees where 360 measures the full continuum. This was derived from the ancient Greeks. India had an independent method of measuring a circle which was to have the full continuum measure 1. This meant that the angles would be broken into decimal fractions as apposed to degrees. It was introduced into modern mathematics in the west as radions and is not widely used. The division of circles and angles was very important in the designing of yantras and the building of architecture for the ancient Hindus. So to say that the decimal system did not exist in Indian mathematics already discredits your article by showing that a thorough and rigorous attitude has not been done even in your elementary research that would give you the authority to write on this topic.
:Repeated from my talk page where you made a similar comment. You seem to be saying that ancient Indian mathematicians measured angles as a fraction of a circle. That implies neither radians nor decimal fractions. If you look at the article on Decimal#Decimal_writers, you will see that it says
:*"''c. 598–670 Brahmagupta – decimal integers, negative integers, and zero''"
:*"''c. 920–980 Abu'l Hasan Ahmad ibn Ibrahim Al-Uqlidisi – first direct treatment of decimal fractions''"
:So to be clear, this is not an attempt to put European mathematics first. Are you saying that this is wrong and that the Vedas, more than a thousand years before the latter of these dates, used decimal fractions directly? That would be news indeed and well worth clarifying. "Vedic mathematics" does deal with decimal fractions directly: see Vedic_mathematics#Method_1:_using_multiplications for an example. --User:Henrygb 23:37, 31 Oct 2004 (UTC)
== Verbose ==
I find the reluctance of some members of the community to accept that Vedic mathematics is a system of useful shortcuts in mental arithmetic to be quite shocking.
Personally I do find the politics quite irrelevant - for whatever reason, these shortcuts in this form are labelled 'Vedic' whether or not there is historic justification for that. Just like Pythagoras' Theorem is named after Pythagoras.
On that point, Vedic mathematics IS a system of useful shortcuts, but at the moment it is laid out in a completely unwieldy and useless fashion -- it was originally cobbled together from some rather verbose sources and hasn't ever been rewritten in a sensible manner.
I would be interested to see more of a summary version of this article. Any objections to a rewrite? --User:Mysteronald 23:55, 22 Dec 2004 (UTC)
:If you're interested in doing a rewrite, go for it — I'd like to see the information in here presented in a more approachable way. Of course, the political aspects, including the name issue, are still relevant to the article, even though they're less interesting than the mathematics of it. User:Factitious 06:14, Dec 23, 2004 (UTC)
:I don't mind listing the shortcuts and describing why they work. The neatest one I have seen is how to square a multiple of 5 by multiplying the higher digit by the next number and following the result by 25. For example
::752=5625 since 7×8=56
:or more verbosely
::(''x''×10+5)2=''x''×(''x''+1)×100+25 because (''a''+''b'')2=''a''2+2''ab''+''b''2.
:But I do mind if we remove the suggestion that critics think the shortcuts were a 20th century compilation and that the shortcuts are not a substitute for conventional mathematics teaching. --User:Henrygb 23:57, 27 Feb 2005 (UTC)
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Vedic mathematics
:''Note: Vedic mathematics is not to be confused with Vedic physics or any other vedic science, which is a kind of Hindu philosophy, and is unrelated to the practice of actual science, (that is, to mathematics or the application of the scientific method.)'' Vedic mathematics is a system of mental calculation developed by Shri Bharati Krishna Tirthaji which he claimed he had based on a lost appendix of Atharvaveda, an ancient text of the Indian teachings called Veda. It has some similarities to the Trachtenberg system in that it speeds up some arithmetic calculations. It claims to have applications to more advanced mathematics, such as calculus and linear algebra. The system was first published in the book ''Vedic Mathematics(book)'' ISBN 8120801644 in 1965. The system has since been developed further and there have been several other books released. Critics have questioned whether this subject deserves the name ''Vedic'' or indeed ''mathematics''. They point to the lack of evidence of any sutras from the Vedic period consistent with the system, the inconsistency between the topics addressed by the system (such as decimal fractions) and the known mathematics of early India, the substantial extrapolations from a few words of a sutra to complex arithmetic, and the restriction of applications to convenient cases. They have also been worried that it deflects attention from genuine achievements of ancient and modern Indian mathematics and mathematicians, and that its promotion by Hindutva may damage mathematics education in India. The system is based upon sixteen formulas and their corollaries, some of which are described below. ==All from nine and the last from ten== Corollary 1: Whatever the extent of its deficiency, lessen it still further to that very extent; and also set up the square of that deficiency. For instance, in computing the square of 9 we go through the following steps: #The nearest power of 10 to 9 is 10. Therefore, let us take 10 as our base. #Since 9 is 1 less than 10, decrease it still further to 8. This is the left side of our answer. #On the right hand side put the square of the deficiency, that is 12. Hence the answer is 81. #Similarly, 82 = 64, 72 = 49. #For numbers above 10, instead of looking at the deficit we look at the surplus. For example: : : : :and so on. This is based on the identities and . ==By one more than the one before== The proposition "by" means the operations this formula concerns are either multiplication or division. [ In case of addition/subtraction proposition "to" or "from" is used.] Thus this formula is used for either multiplication or division. It turns out that it is applicable in both operations. An interesting application of this formula is in computing squares of numbers ending in five. Consider: : 35 × 35 = (3 × (3 + 1)),25 = 12,25 The latter portion is multiplied by itself (5 by 5) and the previous portion is multiplied by one more than itself (3 by 4) resulting in the answer 1225. This is a simple application of when and , i.e. :. It can also be applied in multiplications when the last digit is not 5 but the sum of the last digits is the base (10) and the previous parts are the same. Consider: : 37 × 33 = (3 × 4),7 × 3 = 12,21 : 29 × 21 = (2 × 3),9 × 1 = 6,09 This uses twice combined with the previous result to produce: :. We illustrate this formula by its application to conversion of fractions into their equivalent decimal form. Consider fraction 1/19. Using this formula, this can be converted into a decimal form in a single step. This can be done by applying the formula for either a multiplication or division operation, thus yielding two methods. ====Method 1: using multiplications==== 1/19, since 19 is not divisible by 2 or 5, the fractional result is a purely circulating decimal. (If the denominator contains only factors 2 and 5 is a purely non-circulating decimal, else it is a mixture of the two.) So we start with the last digit : 1 Multiply this by "one more", that is, 2 (this is the "key" digit from Ekadhikena) : 21 Multiplying 2 by 2, followed by multiplying 4 by 2 : 421 → 8421 Now, multiplying 8 by 2, sixteen : 68421 : 1 ← carry multiplying 6 by 2 is 12 plus 1 carry gives 13 : 368421 : 1 ← carry Continuing : 7368421 → 47368421 → 947368421 : 1 Now we have 9 digits of the answer. There are a total of 18 digits (= denominator − numerator) in the answer computed by complementing the lower half: : 052631578 : 947368421 Thus the result is .052631578,947368421 ====Method 2: using divisions==== The earlier process can also be done using division instead of multiplication. We divide 1 by 2, answer is 0 with remainder 1 : .0 Next 10 divided by 2 is five : .05 Next 5 divided by 2 is 2 with remainder 1 : .052 next 12 (remainder,2) divided by 2 is 6 : .0526 and so on. As another example, consider 1/7, this same as 7/49 which as last digit of the denominator as 9. The previous digit is 4, by one more is 5. So we multiply (or divide) by 5, that is, ...7 => 57 => 857 => 2857 => 42857 => 142857 => .142,857 (stop after 7 − 1 digits) 3 2 4 1 2 ==Vertically and crosswise== This formula applies to all cases of multiplication and is very useful in division of one large number by another large number. ==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. ==When the samuccaya is the same, that samuccaya is zero== This formula is useful in solution of several special types of equations that can be solved visually. The word samuccaya has various meanings in different applications. For instance, it may mean a term which occurs as a common factor in all the terms concerned. A simple example is equation "12''x'' + 3''x'' = 4''x'' + 5''x''". Since "''x''" occurs as a common factor in all the terms, therefore, ''x'' = 0 is a solution. Another meaning may be that samuccaya is a product of independent terms. For instance, in (''x'' + 7)(''x'' + 9) = (''x'' + 3)(''x'' + 21), the samuccaya is ''7'' × 9 = 3 × 21, therefore, ''x'' = 0 is a solution. Another meaning is the sum of the denominators of two fractions having the same numerical numerator, for example: 1/(2''x'' − 1) + 1/(3''x'' − 1) = 0 means 5''x'' - 2 = 0. Yet another meaning is "combination" or total. This is commonly used. For instance, if the sum of the numerators and the sum of denominators are the same then that sum is zero. Therefore, : Therefore, 4''x'' + 16 = 0 or ''x'' = −4. This meaning ("total") can also be applied in solving quadratic equations. The total meaning can not only imply sum but also subtraction. For instance when given ''N''1''D''1 = ''N''2/''D''2, if ''N''1 + ''N''2 = ''D''1 + ''D''2 (as shown earlier) then this sum is zero. Mental cross multiplication reveals that the resulting equation is quadratic (the coefficients of ''x''2 are different on the two sides). So, if ''N''1 − ''D''1 = ''N''2 − ''D''2 then that samuccaya is also zero. This yield the other root of a quadratic equation. Yet interpretation of "total" is applied in multi-term RHS and LHS. For instance, consider : Here ''D''1 + ''D''2 = ''D''3 + ''D''4 = 2''x'' − 16. Thus ''x'' = 8. There are several other cases where samuccaya can be applied with great versatility. For instance "apparently cubic" or "biquadratic" equations can be easily solved as shown below: : Note that ''x'' − 3 + ''x'' − 9 = 2(''x'' − 6). Therefore (''x'' − 6) = 0 or ''x'' = 6. (remark by different author: Note also that:, whereas Thus: x=6 is NOT a solution!) (Another note. This example does work if one considers all exponants to be cubic, in which case will give .) Consider : Observe: ''N''1 + ''D''1 = ''N''2 + ''D''2 = 2''x'' + 8. Therefore, ''x'' = −4. This formula has been extended further. ==If one is in ratio, the other one is zero== This formula is often used to solve simultaneous simple equations which may involve big numbers. But these equations in special cases can be visually solved because of a certain ratio between the coefficients. Consider the following example: :6''x'' + 7''y'' = 8 :19''x'' + 14''y'' = 16 Here the ratio of coefficients of ''y'' is same as that of the constant terms. Therefore, the "other" is zero, i.e., ''x'' = 0. Hence the solution of the equations is ''x'' = 0 and ''y'' = 8/7. (alternatively: :19''x'' + 14''y'' = 16 is equivalent to: :(19/2)''x'' +7''y'' = 8. Thus it is obvious that x has to be zero, no ratio needed, just div by2!) This formula is easily applicable to more general cases with any number of variables. For instance :''ax'' + ''by'' + ''cz'' = ''a'' :''bx'' + ''cy'' + ''az'' = ''b'' :''cx'' + ''ay'' + ''bz'' = ''c'' which yields ''x'' = 1, ''y'' = 0, ''z'' = 0. A corollary says By addition and by subtraction. It is applicable in case of simultaneous linear equations where the ''x''- and ''y''-coefficients are interchanged. For instance: :45''x'' − 23''y'' = 113 :23''x'' − 45''y'' = 91 By addition: 68''x'' − 68 ''y'' = 204 => 68(''x'' − ''y'') = 204 => ''x'' − ''y'' = 3. By subtraction: 22''x'' + 22''y'' = 22 => 22(''x'' + ''y'') = 22 => ''x'' + ''y'' = 1. ==External links== * [http://www.amazon.com/exec/obidos/tg/detail/-/0313232008/104-7253290-5011962?v=glance Trachtenberg Speed System of Basic Mathematics at Amazon.com] * [http://mathforum.org/dr.math/faq/faq.trachten.html The Math Forum @ Drexel] * [http://vedicmaths.org/ VedicMaths.Org] * [http://www.vedicmaths.com/ Vedic Mathematics Books] * [http://www.bespokewear.com/vm/ The Vedic Mathematics Society] * [http://mathforum.org/epigone/math-history-list/zhimpjufrer Indian mathematics by Richard Askey] * [http://www.sacw.net/DC/CommunalismCollection/ArticlesArchive/NoVedic.html ''Neither Vedic Nor Mathematics''] * [http://www.tifr.res.in/~vahia/dani-vmsm.pdf Myths and reality: on "Vedic Mathematics" by Prof. S. G. Dani] Computation
Vedic mathematics
Some equations on this page are incorrect. ---- I removed some commentary that had been interspersed with the article text. You can read it here: [http://en.wikipedia.org/w/wiki.phtml?title=Vedic_mathematics&diff=6938195&oldid=6938100] Such commentary is perfectly okay, if it contributes toward the improvement of the article, but it should be placed here on the talk page. User:Aranel_(\"
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Words begining with Vedic_mathematics:
Vedic_mathematics
Vedic_mathematics
Vedic_Mathematics(book)
Vedic_Mathematics_(book)
Vedic_Mathematics_(book)
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