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Origin of Vedic Mathematics

admin — Thu, 27 Oct 2011 13:49:35 +0000

Origin of Vedic Maths or Vedic Ganit

At the beginning of the twentieth century, when there was a great interest in the Sanskrit texts in Europe, Bharati Krsna Swamiji tells us some scholars ridiculed certain texts which were headed 'Ganita Sutras'- which means mathematics. They could find no mathematics in the translation and dismissed the texts as rubbish. Bharati Krsna Swamiji, who was himself a scholar of Sanskrit, Mathematics, History and Philosophy, studied these texts and after lengthy and careful investigation was able to reconstruct the mathematics of the Vedas. According to his research all of mathematics is based on sixteen Sutras, or word-formulae.

Bharati Krsna wrote sixteen volumes expounding the Vedic system, which you can find in the book named Vedic Mathematics by Bharati Krsna Tirthaji. These sutras were unaccountably lost and when the loss was confirmed in his final years he wrote a single book: Vedic Mathematics, currently available. It was published in 1965, five years after his death. The term Vedic Mathematics now refers to a set of sixteen mathematical formulae or sutras and their corollaries derived from the Vedas.

You can find more details about Origin of Vedic Maths here at wikipedia - http://en.wikipedia.org/wiki/Bharati_Krishna_Tirtha's_Vedic_mathematics

Why is 1 not a Prime Number?

admin — Thu, 14 Jan 2010 13:59:51 +0000

Is 1 a Prime Number?

Friends, in one of the post where I have described ‘Prime’ and ‘Composite’ Numbers, one of the curious visitor have asked me a very logical question. I will quote that question for your reference –
Text from Previous post-

“Prime and Composite : Any integer which is divisible by 1 and itself only is called a prime number.
unquote

quote
N.B.: 1 is not a prime number.”

Question

Could you explaine what is the creteria thar excludes 1 from the list of prime numbers?
a) 1 is integer
b) 1 is divisible by 1 and itself (1)
Since anybody in the past has declared that 1 is not prime number, why we should follow this without thinking and contravene the general rule for prime numbers?
Is 1 as a figure is something which has come from the thin air. It is and always will be an integer. The criteria for 2 are the same – divisible by 1 and itself. And for all prime numbers.
Most probably the 1 is “guilty” because with 1 starts the series on numbers (natural, odd or prime). Suppose 2 was the beginning of the series. Should we ignore 2, because series starts with 2?

My Explanation-

1 can be rejected being a prime number because of the given reasons-

The "real" definition of a prime number is "a natural number that has exactly two distinct natural number divisors." This definition can be considered little confusing for general masses. This in essence means " Any integer which is divisible by 1 and itself only is called a prime number.", which is easier to digest. The only problem is that if one uses that phrasing, the number 1 is a little grey zone case. "Well, it is divisible by 1, and it is divisible by itself," you could think. "Isn't it also a prime number then?"

No, not by the official definition, because it only has a single natural number divisor: 1. This is why the "exception" had to be made, that 1 is not a prime number.

In short: the definition as we know it is a simplification that doesn't work completely - except if we specify that 1 is not included.

Is it really important whether 1 is or not a prime number?

It is indeed very crucial to make the distinction. If we consider 1 not to be a prime number, then any composite number (such as 20) can be written as a product of primes in only one way (here, 2*2*5), not counting different orders. However, if 1 were a prime number, there would be infinitely many ways! We could write 20 for example, as 2*2*5, or 1*2*2*5, or 1*1*1*1*1*2*2*5. Having only one way to write a number as a product of primes is very useful when doing math.

Friends if you have similar questions or doubts hunting you, please feel free to write us@ info@fireup.co.in or leave a comment on any post. "We will be Happy to Help You"

Comparison of Fractions

admin — Mon, 04 Jan 2010 11:03:43 +0000

Comparison of fractions: Suppose, some fractions are to be arranged in ascending or descending order of magnitude.

Fractions can be compared in many ways. Find below 4 different ways of doing it. If denominators are same, like 56/98 and 57/98, then just compare the numerators,

So the rule is:

a b

--- > ---, if a > b

n n

Since 56 < 57,

56/98 < 57/98.

They are in the same order as their numerators.

Second, suppose the numerators are the same, as in your problem, 5/9

and 5/6. Then it works the opposite way: The bigger the denominator, the smaller the fraction. So the rule

is:

n n

--- > --- if a < b

a b

Since 9 > 6, 5/9 < 5/6. They are in the reverse order of their

denominators.

Thirdly, in general cases, you simply convert the fractions to the first case, by giving them a common denominator.

You do not really have to worry about finding the least common denominator, though sometimes that will save a lot of work. Let us compare 5/9 and 4/7. Since we do not see any common factors immediately (and in fact there are not any), we can just multiply the denominators to get a common denominator, 63. To convert 5/9 to 63rds, we multiply

by 7; to convert 4/7 to 63rds, we multiply by 9:

5 4

--- ? ---

9 7

5*7 4*9

--- ? ---

9*7 7*9

35 < 36,

5 4

--- < ---

9 7

You may not calculate the value of denominator because it will be same in both cases.

5*7=35 4*9=36; since this is bigger, 4/7 is bigger

\ /

5 4

--- ? ---

9 7

If there is a common multiple in denominators, for instance, which is bigger, 5/9 or 44/81? I see that

81 is a multiple of 9, so I do not have to go to the trouble of

multiplying 5 by 81 and 44 by 9; I just multiply 5 by 9 and compare to

44:

5 44

--- ? --

9 81

5*9 44

--- ? --

9*9 81

45 > 44 so

5 44

--- > --

9 81

Fractions can be compared in many ways. Find below 3 differnet ways of doing it.
If denominators are same, like 56/98 and 57/98, then just compare the numerators,
So the rule is:
a b --- > --- if a > b n n
Since 56 < 57, 56/98 < 57/98. They are in the same order as their numerators.
Second, suppose the numerators are the same, as in your problem, 5/9 and 5/6. Then it works the opposite way: The bigger the denominator, the smaller the fraction. So the rule is: n n --- > --- if a < b a b
Since 9 > 6, 5/9 < 5/6. They are in the reverse order of their denominators.

Thirdly, in general cases, you simply convert the fractions to the first case, by giving them a common denominator. You do not really have to worry about finding the least common denominator, though sometimes that will save a lot of work. Let us compare 5/9 and 4/7. Since we do not see any common factors immediately (and in fact there are not any), we can just multiply the denominators to get a common denominator, 63. To convert 5/9 to 63rds, we multiply by 7; to convert 4/7 to 63rds, we multiply by 9:
5 4   --- ? ---   9 7
5*7 4*9   --- ? ---   9*7 7*9
35 < 36, so
5 4   --- < ---   9 7
You may not calculate the value of denominator because it will be same in both cases.

5*7=35 4*9=36; since this is bigger, 4/7 is bigger   \ /   5 4   --- ? ---   9 7
If there is a common multiple in denominators, for instance, which is bigger, 5/9 or 44/81? I see that 81 is a multiple of 9, so I do not have to go to the trouble of multiplying 5 by 81 and 44 by 9; I just multiply 5 by 9 and compare to 44:   5 44   --- ? --   9 81
5*9 44   --- ? --   9*9 81
45 > 44 so
5 44   --- > --   9 81
Finally, convert each one of the given fractions in the decimal form. Now, arrange them in ascending order

as per requirements.

Recurring Decimal: - If, in a decimal fraction, a figure or a set of figures is repeated continuously, then such a number is called a recurring decimal. In a recurring decimal, if a single figure is repeated, then it is expressed by putting a dot on it. If a set of figures is repeated, it is expressed by putting a bar on the set.

Pure Recurring Decimal: A decimal fraction, in which all the figures after the decimal point are repeated, is called a pure recurring decimal e.g. 2/3 = 0.666…=0.6.

Converting a Pure Recurring Decimal into Vulgar Fraction:-Rule: - Write the repeated figures only once in the numerator and take as many nines in the denominator as is the number of repeating figures.

Decimal: - a decimal fraction in which some figures do not repeat and some of them are repeated is called a mixed recurring decimal, e.g. 0.173333…= 0.173.

Decimal Fraction Rules

admin — Mon, 04 Jan 2010 05:45:23 +0000

Multiplication of a decimal Fraction by a Power of 10: Rule: Shift the decimal point to the right by as many places of decimal as is the power of 10.

Multiplication of Decimal fractions:- Rule :- Multiply the given numbers considering them without the decimal point. Now, in the product, the decimal point is marked off to obtain as many places of decimal as is the sum of the number of decimal in the given numbers.

Dividing a Decimal fraction By a Counting Number

Rule: - Divide the given number without considering the decimal point by the given counting number. Now, in the quotient, put the decimal point to give as many places of decimal as are there in the dividend.

Dividing a Decimal fraction By a Decimal Fraction

Rule: - Multiply both the dividend and the divisor by a suitable power of 10 to make divisor a whole number. Now, proceed as above.

H. C. F. & L. C. M. of Decimal fractions:- Rule :- In given numbers, make the same number of decimal places by annexing zeros in some numbers, if necessary. Considering these numbers as without decimal point, find H. C. F. or, L.C.M., as the case may be. Now, in the result, make off as many decimal places as are there in each of the given numbers.