Vedic Mathematics (book)
Under Vedic mathematics is understood calculation rules, which were of Bharati Krishna Tirthaji (1884-1960) reportedly worked out 1911-1918 from the Veda. They were published posthumously in 1965 and will be based on a lost appendix of Atharvaveda. Traceability to the Veda was, however, disputed from the beginning and Tirthaji could never cite evidence for his assertion. This type of calculation is based on 16 rules. It has similarities to the Trachtenberg quick calculation method as it accelerates some arithmetic calculations.
Critics doubt not only the term " Vedic " to, but also feel these rules did not deserve the name " mathematics ". They point out that there is no Sutras of the Vedic period, consistent with these rules.
Proponents emphasize the speed, can be carried out with the bills. They could be used much more efficiently than the calculation rules that are generally taught in elementary school. One advantage is, for example, that one must master the basics only to 5 to multiply all numbers can.
Tirthaji was from 1925 until his death, the abbot ( Sankaracharya ) of the monastery Govardhana matha at Puri.
There are also genuine, traditional from the Vedic literature, mathematics, see Sulbasutras.
- 3.3.1 Case 1: Both figures are just under a power of ten
- 3.3.2 Case 2: Both of these numbers are just above a power of ten
- 3.3.3 Case 3: A number above and one number under a power of ten
The Sutras
The sub - sutras
Application
Subtraction
The second sutra " all from nine and the last from 10" helps to subtract any number from a natural power of ten. To do this is for each digit the difference to 9 and for the last digit of the difference to 10
Example:
Multiplying two-digit numbers
Special case: first digits equal last digits added result 10
With the Vedic rule " One more than the one before " can easily multiply two -digit numbers where the first digits are the same and the last digits added equal 10. The first digit of the numbers, multiplied with its successor, the front digits of the result. The second digit of the two numbers multiplied together give the posterior digits of the result.
Example:
Front digits:
Posterior digits:
Squaring numbers with last digit 5
The squaring of numbers ending in 5 is a special case of the previous rule, since this in the case also with three-digit numbers (and more) is applicable.
Example:
Multiplication of any two-digit numbers
Any two -digit numbers can be " vertically and crosswise " multiplied by the Vedic rule. To this end, the numbers are written below each other and then multiplies the digits vertically and crosswise multiplied and added. It transfers can arise when intermediate results (which represent only one digit ) values greater than 9 accept.
Example:
Explanation: The result consists of three parts: . These three numbers are next to each other. Then, the dissolution of the carries from right to left follows. 18 has to carry one which is added to 27. The resulting 28 then has the transfer 2 (the decimal point ), which is added to the opposite 10. This produces the result 1288th
Other examples are:
→ See also: Vedic multiplication
Also according to the Vedic rule " vertically and crosswise " you can multiply numbers, which are just above or under a power of ten.
Case 1: Both figures are just under a power of ten
First, you write the two numbers next to each other and the difference to the next order of magnitude ( power of ten minus number). The differences are then crosswise subtracted from the numbers. Subsequently, the differences are multiplied together. The result is composed of these two partial results, with a carry has to be formed from the first result in more than three places.
Example:
Case 2: Both of these numbers are just above a power of ten
Similarly as in the first case, the numbers are written below each other and next to it the difference from the nearest power of ten, but again with a positive sign (ie number minus power of ten ). The differences are now crosswise added to the numbers and multiplies the differences with each other. The result sits back together from the two partial results.
Example:
Alternatively, you can also just as in the first case to proceed, but be warned as negative differences.
Case 3: A number above and one number under a power of ten
In this case, must be reckoned with negative balance carry. Otherwise, one procedure is analogous to the first case.
Example:
Explanation: In order to make the -24 to a positive number, added to 100 (-24 100 = 76). It follows a carryover from -1 to 90 ( 90-1 = 89 ).
Multiplication by 11
For the simple multiplication of a number with 11 to write the number twice under each other, they are offset by one digit. Then, digit by digit added. It transfers can arise when intermediate results (which represent only one digit ) values greater than 9 accept.
Example:
Example, with carry:
Division by 9 with remainder
The result of division by 9 with remainder obtained quickly with the following procedure: The first digit of the result is the first digit of the number that is shared. The second digit of the result is the sum of the first and second digit of the number. This one continues up to the penultimate digit of the number. It transfers can arise when intermediate results, which represent only a number, assume values greater than 9. The sum of the number is the rest This can be greater than 9, so you then have to make another division or must reduce the residual by transmitting.
Simple example:
Example:
Example, with carry:
Fractions
" Vertically and crosswise " can be with the Sutra add fractions and subtract. In this case, the denominator of the result is the product of the denominator. The numerator of the result obtained from the counter of the first break times the denominator of the second fracture plus ( or minus) the numerator of the second break times denominator of the first fraction. Or in short: counter 1 times denominator 2 plus ( or minus) counter 2 times denominator 1
Example for addition:
Example for subtraction: