Thursday, November 24, 2011

Huge Calculations are Easy now...!!

Hey friends!, as i was doing calculations mainly some huge multiplications, divisions and squares, i found that they are consuming longer time than the whole problem has to be solved. So i tried to browse for the better shortcuts of doing them. After sparing some time in practicing those methods i gradually reduced the time of doing those calculations. So here in this post i will write the methods of using them.



  • NOTE:

Before entering into the explanation, i want the reader of this article has to remember one key point before starting implementing. That is, almost all methods uses the technique of excess carried over. As one single place will have only one digit, if the method gives the result in 2 digits for one place then the excess will be forwarded to the next place. Ex: If units place has 12 as a result, then 2 will be places in units place and 1 will be forwarded to the next cell i.e., tens place.


Firstly, we will deal with MULTIPLICATION:

To multiply two numbers (of two or more digits), split each number into two parts. If the first number is a1 + b1 and the second number is a2 + b2, then the product of the two numbers is:



(a1 x a2) + (a1 x b2 + b1 x a2) + (b1 x b2)
The solution comprises three parts (as shown by the boxes and arrows above): the head, the middle, and the tail.
  1. The digits on the right are multiplied vertically to get the tail part: b1 x b2 (excess carried over)
  2. All digits are multipled crosswise and added together to get the middle part: a1 x b2 + b1 x a2 (excess carried over)
  3. The digits on the left are multiplied vertically to get the head part: a1 x a2
Here is a simple example to illustrate this technique.


23 x 41 = 943
The steps are:
  1. 3 x 1 = 3
  2. 2 x 1 + 3 x 4 = 14, put down 4 and carry over 1
  3. 2 x 4 = 8, plus the 1 carried over, is 9
The speed gain using this technique (over the conventional method of multi-line long multiplication) becomes more apparent when handling larger numbers. Here is another example involving excess carryover at each stage.


108 x 64 = 6912
The steps are:
  1. 8 x 4 = 32, put down 2 and carry over 3
  2. 10 x 4 + 8 x 6 = 88, plus the 3 carried over, is 91; put down 1 and carry over 9
  3. 10 x 6 = 60, plus the 9 carried over, is 69
Maybe this method looks some what crazy and funny but it really works on every calculation.









Now we will deal with DIVISIONS:

It is very easy to understand with an example rather than understanding with the theoretical method.

Take for example, 716769 ÷ 54. Yes, you too CAN work it out manually -- and in one line -- without having to reach for the calculator! "on top of the flag". The trick is to reduce the divisor to a mentally manageable value by putting its other digits "on top of the flag". In this example, the divisor will be reduced to 5 (instead of 54) by pushing the 4 up the flagpost, as shown below. Corresponding to the number of digits flagged on top (in this case, one), the rightmost part of the number to be divided is split to mark the placeholder of the decimal point or the remainder portion.

Now observe carefully as we walk through the steps of this example:


716769 ÷ 54 = 13273.5
  1. 7 ÷ 5 = 1 remainder 2. Put the quotient 1, the first digit of the solution, in the first box of the bottom row and carry over the remainder 2
  2. The product of the flagged number (4) and the previous quotient (1) must be subtracted from the next number (21) before the division can proceed. 21 - 4 x 1 = 17

    17 ÷ 5 = 3 remainder 2. Put down the 3 and carry over the 2
  3. Again subtract the product of the flagged number (4) and the previous quotient (3), 26 - 4 x 3 = 14

    14 ÷ 5 = 2 remainder 4. Put down the 2 and carry over the 4
  4. 47 - 4 x 2 = 39

    39 ÷ 5 = 7 remainder 4. Put down the 7 and carry over the 4
  5. 46 - 4 x 7 = 18

    18 ÷ 5 = 3 remainder 3. Put down the 3 and carry over the 3
  6. 39 - 4 x 3 = 27. Since the decimal point is reached here, 27 is the raw remainder. If decimal places are required, the division can proceed as before, filling the original number with zeros after the decimal point

    27 ÷ 5 = 5 remainder 2. Put down the 5 (after the decimal point) and carry over the 2
  7. 20 - 4 x 5 = 0. There is nothing left to divide, so this cleanly completes the division.

This takes a little bit time to understand. But its easy to solve rather than BALDING your head :P










As we are clear about the Multiplications and Divisions, without any waste of time we will deal with

SQUARES:

The HUGE knowledge needed to solve the following method is  (a + b)2 = a2 + 2ab + b2
Yeah you heard right....... above formula is enough to solve the following method. Te method is as follows.

First, a nifty shortcut! The square of a number ending in 5 is almost a no-brainer.
If n is the number formed by the preceding digit/s (before the 5), get the product of n and n+1.
Then just append 25 (i.e. 5 x 5) to this product.
For example, 752:


7 x 8 = 56; therefore solution is 5625.
Another example, 1152:


11 x 12 = 132; therefore solution is 13225
For other cases of squaring, the same shortcut techniques used in multiplication may be utilised.
Especially the general-purpose Urdhva Tiryagbhyam (Vertically and Crosswise) formula.
To get the square of a number (of two or more digits), simplify by splitting it into at least two parts, a and b.
Thus (a + b)2 = a2 + 2ab + b2
Squaring shortcut technique
The solution comprises three parts, neatly fitting the three boxes shown above. Just adjust for excess carry over.
  1. the head: a2
  2. the middle: crosswise multiplication and doubling a x b x 2
  3. the tail: b2
Here is a simple example to illustrate this technique.


232 = 529
The steps are:
  1. tail: 32 = 9, put it down in the rightmost box
  2. middle: 2 x 3 x 2 = 12, put down the 2 in the middle box and carry over the 1
  3. head: 22 = 4, plus the 1 carried over, is 5 in the left box
Another example.


1082 = 11664
The steps are:
  1. tail: 82 = 64, put down the 4 and carry over the 6
  2. middle: 10 x 8 x 2 = 160, plus the 6 carried over, is 166; put down the 6 and carry over the 16
  3. head: 10 x 10 = 100, plus the 16 carried over, is 116.

So i hope that  the reader has understood these crazy methods and makes his MATH simple and avoid ambiguity and avoid wastage of time.


Thanks for reading my post..... :) :)










                                                                               --- PaVaN KoUndiNyA                                                         


Sunday, November 20, 2011

Julian Assange Arrest. Bad time for wikileaks?

Hey everybody as i posted about Julian Assange and his dare work on the wikileaks, here i post some information about the latest arrest of Julian Assange....

Swedish Judicial Authority v Julian Assange is the set of legal proceedings relating to claims that Julian Assange committed sexual offences in Sweden.
When an arrest warrant was issued in November 2010, Assange had been living in England for 1-2 months. An extradition hearing took place in an English court in February 2011 to consider an application by Swedish authorities for the extradition of Assange to Sweden. The outcome of the hearing was announced on 24 February 2011, when the extradition warrant was upheld. Assange appealed to the High court and on 2 November 2011 the court upheld the extradition decision and rejected all four grounds for the appeal as presented by Assange's legal representatives. £19,000 costs was also awarded against Assange. A decision will be taken before the end of November as to whether Assange will be granted permission by the High Court to appeal to the Supreme Court. If permission is refused, by both of the High Court and the Supreme Court, Assange will be extradited to Sweden within 10 days of the final decision. Assange continues to deny the allegations, and remains on bail in the United Kingdom.

On 20 August 2010, two women came to Swedish police inquiring whether it was possible to require that Julian Assange be submitted to an HIV-test. Within the filed report, the police officers found signs of sexual misconduct. In response, the police opened an investigation.The women involved were a 26-year-old in Enköping and a 31-year-old in Stockholm.



In answer to questions surrounding the incidents, the following day, Chief Prosecutor Eva Finné declared, "I don't think there is reason to suspect that he has committed rape." However, Karin Rosander, from the Swedish Prosecution Authority, said Assange remained suspected of molestation. Police gave no further comment at that time, but continued to investigate.

After learning of the investigation, Assange said, "The charges are without basis and their issue at this moment is deeply disturbing."

On 18 August 2010, Assange applied for a work and residence permit in Sweden. He left Sweden on 27 September 2010. On 18 October 2010, his request was denied.

On 18 November 2010, prosecutor Marianne Ny asked the local district court for a warrant for the arrest of Assange in order for him to be interviewed by the prosecutor. As he was now living in England, the court ordered him detained in absentia.

The Supreme Court of Sweden decided not to consider a further appeal as no principle was at stake.On 6 December 2010, Scotland Yard notified Assange that a valid European arrest warrant had been received.

Assange presented himself to the Metropolitan Police the next morning and was remanded to London's Wandsworth Prison. On 16 December, he was granted bail with bail conditions of residence at Ellingham Hall, Norfolk and wearing of an electronic tag. Bail was set at £240,000 surety with a deposit of £200,000 ($312,700).

On release on bail, Assange said "I hope to continue my work and continue to protest my innocence in this matter,"and told the BBC, "This has been a very successful smear campaign and a very wrong one."He claimed that the extradition proceedings to Sweden were "actually an attempt to get me into a jurisdiction which will then make it easier to extradite me to the US." Swedish prosecutors have denied the case has anything to do with WikiLeaks.

On 2 March 2011, Assange's lawyers lodged papers at the High Court in London, to challenge the decision to extradite him to Sweden. Assange remains on conditional bail. 

The founder of WikiLeaks, Julian Assange, is to apply for a supreme court hearing to appeal against extradition to Sweden to face sex crime allegations.

His solicitor, Gareth Peirce, confirmed he will ask senior judges in London on 5 December to certify that his case should be considered by the highest court in the land. He must establish that his case raises "a question of law of general public importance".

Assange, 40, lost a high court battle against removal on 2 November but has announced he wants to fight on against a European arrest warrant that has been outstanding since last December.
A supreme court hearing would be the third stage of the 40-year old Australian's appeal against extradition to face allegations of rape, sexual molestation and unlawful coercion by two women he met on a visit to Stockholm in August 2010.

Assange's decision means a verdict on whether he should be extradited could be delayed until as late as next summer, legal observers said.
 If he can persuade the high court that there is a question of law at stake, he must then seek leave to appeal, probably directly from the supreme court. That could take at least three months.

Only then, if he is successful, could a date be set for a supreme court hearing, possibly around early summer. If Assange fails to persuade the high court judges there is a question of law at stake on 5 December, then he could be removed in the following days, under the terms of the warrant.

The warrant was "proportionate", they said, dismissing Assange's argument that it was not issued by a valid authority. The court also rejected Assange's assertion that the descriptions of the offences were unfair and inaccurate.

After the hearing Assange said: "I have not been charged with any crime in any country. The European arrest warrant (EAW) is so restrictive that it prevents UK courts from considering the facts of a case, as judges have made clear here today.

"No doubt there will be many attempts made to try to spin these proceedings as they occurred today but they were merely technical."

Assange remains on bail, living at Ellingham Hall in Norfolk, the home of Vaughan Smith, founder of the Frontline Club for journalists. The decision to appeal again means it looks likely Assange will be spending a second consecutive Christmas with his host.