Friday 9 February 2018

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Vedic Maths Tricks for students

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What is Vedic Maths?
Vedic Mathematics is a super fast way of calculation whereby you can do supposedly complex calculations like 998 x 997 in less than five seconds flat. It is highly beneficial for school and college students and students who are appearing for their entrance examinations.

Vedic Mathematics is far more systematic, simplified and unified than the conventional system. It is a mental tool for calculation that encourages the development and use of intuition and innovation, while giving the student a lot of flexibility, fun and satisfaction. For your child, it means giving them a competitive edge, a way to optimize their performance and gives them an edge in mathematics and logic that will help them to shine in the classroom and beyond.

Therefore it’s direct and easy to implement in schools – a reason behind its enormous popularity among academicians and students
It complements the Mathematics curriculum conventionally taught in schools by acting as a powerful checking tool and goes to save precious time in examinations.The methods & techniques are based on the pioneering work of late Swami Shri Bharati Krishna Tirthaji, Sankracharya of Puri, who established the system from the study of ancient Vedic texts coupled with a profound insight into the natural process of mathematical reasoning.
There are just 16 Sutras or Formulae which solve all known mathematical problems in the branches of Arithmetic, Algebra, Geometry and Calculus. They are easy to understand, easy to apply and easy to remember.
vedic
Benefits of Vedic Maths?
  • Eliminates math-phobia.
  • Increases speed and accuracy.
  • More systematic, simplified, unified & faster than the conventional system.
  • Gives the student flexibility, fun and
    immense satisfaction
  • powerful checking tool.
  • Saves precious time in examinations.
  • Gives the student a competitive edge.
  • Develops Left & Right Sides of the brains
    by increasing visualization and
    concentration
     abilities.
Some Vedic Maths Tricks 
Trick 1 : Multiply any two numbers from 11 to 20 in your head.
Take 15 × 13 for example… Place the larger no. first in your mind and then do something like this Take the larger no on the top and the second digit of the smaller no. in the bottom.
15
3
The rest is quite simple. Add 15+3 = 18 . Then multiply 18 × 10 = 180 …
Now multiply the second digit of both the no.s (ie; 5 × 3 = 15) Now add 180 + 15Here is the answer 180 + 15 = 195 . Think over it. This is a simple trick. It will help you a lot.
Trick 2 : Multiply any two digit number with 11.
This trick is much simpler than the previous one and it is more useful too. Let the number be 27 . Therefore 27 × 11
Divide the number as 2 _ 7
Add 2+ 7 = 9
Thus the answer is 2 9 7
Wasn’t this one simple. But there is one complication. If you take a number like 57 Thus 5_7 x 11
Divide the number as 5 _ 7
Add 5 + 7 = 12
Now add 1 to 5 and place 2 in the middle so the answer is 5+1_2 _7 = _627
Thus the answer is 627.
Trick 3: Square a two digit number ending in five. This one is as easy as the previous ones but you have to pay a little more attention to this one . Read carefully :Let the number be 35
35 × 35
Multiply the last digits of both the numbers ; thus ___ 5 × 5 = 25
now add 1 to 3 thus 3 + 1 = 4
multiply 4 × 3 = 12
thus answer 1225

You will have to think over this one carefully.As 5 has to come in the end so the last two digits o the answer will be 25 . Add 1 to the first digit and multiply it by the original first digit . Now this answer forms the digits before the 25. Thus we get an answer.
Trick 4 : Square any two digit number.

Suppose the number is 47 . Look for the nearest multiple of 10 . ie; in this case 50. We will reach 50 if we add 3 to 47. So multiply (47+3) x (47-3) = 50 × 44 = 2200 This is the 1st interim answer.


We had added 3 to reach the nearest multiple of 10 that is 50 thus 3x 3 = 9 This is the second interim answer.
The final answer is 2200 + 9 = 2209 … Practice This one on paper first.

Trick 5
 : Multiply any number by 11 .

Trick number 2 tells you how to multiply a two digit number by 11 but what if you have a number like 12345678. Well that is very easy if you our trick as given below. Read it carefully.


Let the number be 12345678 __ thus 12345678 × 11


Write down the number as 012345678 ( Add a 0 in the beginning)

Now starting from the units digit write down the numbers after adding the number to the right, so the answer will be 135802458

This one is simple if you think over it properly all you got to do is to add the number on the right . If you are getting a carry over then add that
to the number on the left. So I will tell you how I got the answer . Read carefully. The number was 12345678 ___ I put a 0 before the number ____ so the new number 012345678 Now I wrote ___ 012345678


Then for the answer
8 + 0 = 8
7 + 8 = 15 (1 gets carry carried over)
6+1+7 = 14 ( 1 gets carried over)
5 + 1 + 6 = 12 ( 1 gets carried over)
4 + 1 + 5 = 10 ( 1 gets carried over)
3 + 1 + 4 = 8
2 + 3 = 5
1 + 2 = 3
0 + 1 = 1
Thus the answer = 135802458
Trick 6 : Square a 2 Digit Number, for this example 37:
Look for the nearest 10 boundary
In this case up 3 from 37 to 40.
Since you went UP 3 to 40 go DOWN 3 from 37 to 34.
Now mentally multiply 34×40
The way I do it is 34×10=340;
Double it mentally to 680
Double it again mentally to 1360
This 1360 is the FIRST interim answer.
37 is “3” away from the 10 boundary 40.
Square this “3” distance from 10 boundary.
3×3=9 which is the SECOND interim answer.
Add the two interim answers to get the final answer.
Answer: 1360 + 9 = 1369
With practice this can easily be done in your head.

Shortcut Tricks to Solve Square Roots and Cube Roots in less time.
These simple methods on how to find the cube root of a number and square root of a number make easy and simple to implement. In almost we get the questions on numerical ability and also there will be a time constraint. So we have speed up our ability in doing calculations faster. Though speed improves by practicing more problems we have to use some shortcut tricks too. Here, to perform these calculations simple. The job seekers have to remember “Cubes” and “Squares” of only these first 10 natural numbers.
Squares of 1 to 10 Numbers:
1= 1, 22 = 4, 32 = 9, 4= 16, 5=25.
62 = 36, 72 = 49, 82 Cubes of 1 to 10 Numbers:
13 = 1, 2= 8, 33 = 27, 43 = 48, 53 = 125.
63 = 216, 73 = 343, 83 = 512, 93 = 729, 103 = 1000.

How to find Square Root of a Number?

Example 1: Suppose we need to calculate the square root of number 529.
Follow the Step by Step process below.
  1. Check the unit’s place digit. Here it is 9.
  2. From 1 to 10 squares of numbers we need to check the square of which numbers unit digit is 9.
  3. For the number 32 = 9 and 72 =49.
  4. Here we have to decide the square root of 529 has 3 or 7 in its units place.
  5. Check the first digit is 5 from 529. We have to check approx. the square root of 5 i.e. 2. So 2 is the first digit of our answer and have to decide 3 or 7 as 2nd .
  6. Between 23 and 27 there is 25 check the square of 25 i.e. 625.
529 < 625. So we have to select small number as our answer from 23 and 25.
The answer is 23.
Note: Once you understand the logic behind this you can able to solve in seconds of time.

Example 2: How to find the square root of a number  6084.

Here also follow the same process as above clearly explained in the below image.
Examples to practice: (Solve yourself using above procedure).
  1. 8649 = 93.
  2. 7559 = 87.
  3. 12544 = 112.

How to Find Cube Root:

To find the cube root of a number is the little bit different from the process of finding the square root. Follow the process as shown in the below image. If you unable to understand please comment I will make it clear.

Example 1: How to find the Cube root of a number 103823.

Examples to practice: (Solve yourself using above procedure)
  1. 531441 = 81.
  2. 35937 = 33.
  3. 175616 = 56.
= 64, 92 =81, 102 = 100
Tirthaji Maharaj has mentioned tricks to Square Numbers in Vedic mathsmaticds in Specific and General Methods. Specific Multiplication Methods can be applied when numbers satisfy certain conditions like number ending with 5 or number closer to power of 10, etc. While General Multiplication Methods can be applied to any type of number.
Depending on Specific and General Techniques, Squares in Vedic Mathematics are classified in the form of Sutras as below. Lets see the  Vedic Mathematics Squares shortcut techniques.
Calculating Vedic Math Square Tricks can be classified in following types:
  1. Yavadunam (Specific Method)
  2. Ekadhikena Purvena (Specific Method)
  3. DvandaYoga (General Method)

Yavadunam:

It is a specific and shorcut to square numbers using Vedic Mathematics whenever number is closer to power of 10. (10, 100, 1000, ….)
Lets see examples for  vedic maths square method of Yavadunam:
Square of 14:
142 = (14+4)/42 = 18/16  = 196
Here 14 is 4 more than 10(Base 10), So Excess = 4
Increase it still further to that extent, So (14+4) = 18
Square its excessive, So 42= 16
Final Answer:� 196
Square of 97:
972 = (97-3)/32 = 94/09  = 9409
Here 97 is 3 less than 100(Base 100), So deficiency =3
Reduce it still further to that extent, So (97-3) = 94.
Square its deficiency, So 32 = 09. (As base is 100, we need exactly 2 digits. Hence 09).
Final Answer:� 9

Ekadhikena Purvena:

This is another specific� vedic maths tricks for square of a number ending with 5.
Lets see examples for vedic squares tricks using Ekadhikena Purvena.
  1. Check if last digit is 5, if yes – square of 5 is 25
  2. Apply Ekadhikena Purvena for rest of the number i.e. Add 1 to the previous number and multiply each other. Example in case of square of 85, Add 1 to 8 to get 9 and multiply this with 8.
  3. Steps 1 and 2 together gives final an

DvandaYoga (Duplex Method):

Dvanda Yoga is general method to square any number in vedic maths. Dvanda Yoga or Duplex Method is shortcut method for squares of large numbers.
How to calculate Dvanda
Concept:
D(3) = 32 = 9
D(43) = 2x4x3 = 24
D(567) = 2x5x7 + 62 = 70 + 36 = 106
D(3456) = 2x3x6 + 2x4x5 = 36 + 40 = 76
D(34567) = 2x3x7 + 2x4x6 + 52 = 42 + 48 + 25 = 115
Example:
Trick to square a number in Vedic Mathematics

Saturday 25 November 2017

Anyone can learn math whether they're in higher math at school or just looking to brush up on the basics. After discussing ways to be a good math student, this article will teach you the basic progression of math courses and will give you the basic elements that you'll need to learn in each course. Then, the article will go through the basics of learning arithmetic, which will help both kids in elementary school and anyone else who needs to brush up on the fundamentals.

art1
Keys to Being a Good Math Student

  1. 1
    Show up for class. When you miss class, you have to learn the concepts either from a classmate or from your textbook. You'll never get as good of an overview from your friends or from the text as you will from your teacher.
    • Come to class on time. In fact, come a little early and open your notebook to the right place, open your textbook and take out your calculator so that you're ready to start when your teacher is ready to start.
    • Only skip class if you are sick. When you do miss class, talk to a classmate to find out what the teacher talked about and what homework was assigned.
  2. 2
    Work along with your teacher. If your teacher works problems at the front of your class, then work along with the teacher in your notebook.
    • Make sure that your notes are clear and easy to read. Don't just write down the problems. Also write down anything that the teacher says that increases your understanding of the concepts.
    • Work any sample problems that your teacher posts for you to do. When the teacher walks around the classroom as you work, answer questions.
    • Participate while the teacher is working a problem. Don't wait for your teacher to call on you. Volunteer to answer when you know the answer, and raise your hand to ask questions when you're unsure of what's being taught.
  3. 3
    Do your homework the same day as it's assigned. When you do the homework the same day, the concepts are fresh on your mind. Sometimes, finishing your homework the same day isn't possible. Just make sure that your homework is complete before you go to class.
  4. 4
    Make an effort outside of class if you need help. Go to your teacher during his or her free period or during office hours.
    • If you have a Math Center at your school, then find out the hours that it's open and go get some help.
    • Join a study group. Good study groups usually contain 4 or 5 people at a good mix of ability levels. If you're a "C" student in math, then join a group that has 2 or 3 "A" or "B" students so that you can raise your level. Avoid joining a group full of students whose grades are lower than yours.[1]

Wednesday 15 November 2017

Ramanujan number




Wednesday, October 14, 2015


Mathematicians find 'magic key' to drive Ramanujan's taxi-cab number

A British taxi numbered 1729 sparked the most famous anecdote in math and led to the origin of "taxi-cab numbers." The incident is included in an upcoming biopic of Ramanujan, "The Man Who Knew Infinity," featuring Dev Patel in the lead role. Above is a still from the movie. (Pressman Films.)

By Carol Clark

Taxi-cab numbers, among the most beloved integers in math, trace their origins to 1918 and what seemed like a casual insight by the Indian genius Srinivasa Ramanujan. Now mathematicians at Emory University have discovered that Ramanujan did not just identify the first taxi-cab number – 1729 – and its quirky properties. He showed how the number relates to elliptic curves and K3 surfaces – objects important today in string theory and quantum physics.

“We’ve found that Ramanujan actually discovered a K3 surface more than 30 years before others started studying K3 surfaces and they were even named,” says Ken Ono, a number theorist at Emory. “It turns out that Ramanujan’s work anticipated deep structures that have become fundamental objects in arithmetic geometry, number theory and physics.”

Ono and his graduate student Sarah Trebat-Leder are publishing a paper about these new insights in the journal Research in Number Theory. Their paper also demonstrates how one of Ramanujan’s formulas associated with the taxi-cab number can reveal secrets of elliptic curves.

“We were able to tie the record for finding certain elliptic curves with an unexpected number of points, or solutions, without doing any heavy lifting at all,” Ono says. “Ramanujan’s formula, which he wrote on his deathbed in 1919, is that ingenious. It’s as though he left a magic key for the mathematicians of the future. All we had to do was recognize the key’s power and use it to drive solutions in a modern context.”

“This paper adds yet another truly beautiful story to the list of spectacular recent discoveries involving Ramanujan’s notebooks,” says Manjul Bhargava, a number theorist at Princeton University. “Elliptic curves and K3 surfaces form an important next frontier in mathematics, and Ramanujan gave remarkable examples illustrating some of their features that we didn’t know before. He identified a very special K3 surface, which we can use to understand a certain special family of elliptic curves. These new examples and insights are certain to spawn further work that will take mathematics forward.”

A close-up of the taxi-cab plate, in a scene from the upcoming movie, "The Man Who Knew Infinity." (Pressman Films.)

Ramanujan, a largely self-taught mathematician, seemed to solve problems instinctively and said his formulas came to him in the form of visions from a Hindu goddess. During the height of British colonialism, he left his native India to become a protégé of mathematician G.H. Hardy at Cambridge University in England.

By 1918, the British climate and war-time rationing had taken their toll on Ramanujan, who was suffering from tuberculosis. He lay ailing in a clinic near London when Hardy came to visit.

Wanting to cheer up Ramanujan, Hardy said that he had arrived in taxi number 1729 and described the number “as rather a dull one.” To Hardy’s surprise, Ramanujan sat up in bed and replied, “No, Hardy, it’s a very interesting number! It’s the smallest number expressible as the sum of two cubes in two different ways.”

Ramanujan, who had an uncanny sense for the idiosyncratic properties of numbers, somehow knew that 1729 can be represented as 1 cubed + 12 cubed and 9 cubed + 10 cubed, and no smaller positive number can be written in two such ways.

This incident launched the “Hardy-Ramanujan number,” or “taxi-cab number,” into the world of math. To date, only six taxi-cab numbers have been discovered that share the properties of 1729. (These are the smallest numbers which are the sum of cubes in n different ways. For n=2 the number is 1729.)

The original taxi-cab number 1729 is a favorite nerdy allusion in television sitcoms by Matt Groening. The number shows up frequently as an inside joke in episodes of “Futurama” and the “The Simpsons.”

But like much of Ramanujan’s discoveries, 1729 turned out to contain hidden meanings that make it much more than a charming mathematical oddity.

“This is the ultimate example of how Ramanujan anticipated theories,” Ono says. “When looking through his notes, you may see what appears to be just a simple formula. But if you look closer, you can often uncover much deeper implications that reveal Ramanujan’s true powers.”

Jeremy Irons portrays G. H. Hardy and Dev Patel plays Ramanujan in "The Man Who Knew Infinity." (Pressman Films.)

Much of Ono’s career is focused on unraveling Ramanujan mysteries. In 2013, during a trip to England to visit number theorists Andrew Granville and John Coates, Ono rummaged through the Ramanujan archive at Cambridge. He came across a page of formulas that Ramanujan wrote a year after he first pointed out the special qualities of the number 1729 to Hardy. By then, the 32-year-old Ramanujan was back in India but he was still ailing and near death.

“From the bottom of one of the boxes in the archive, I pulled out one of Ramanujan’s deathbed notes,” Ono recalls. “The page mentioned 1729 along with some notes about it. Andrew and I realized that he had found infinitely near misses for Fermat’s Last Theorem for exponent 3. We were shocked by that, and actually started laughing. That was the first tip-off that Ramanujan had discovered something much larger.”

Fermat’s Last Theorem is the idea that certain simple equations have no solutions – the sum of two cubes can never be a cube. Ramanujan used an elliptic curve – a cubic equation and two variables where the largest degree is 3 – to produce infinitely many solutions that were nearly counter examples to Fermat’s Last Theorem.

Elliptic curves have been studied for thousands of years, but only during the last 50 years have applications been found for them outside of mathematics. They are important, for example, for Internet cryptography systems that protect information like bank account numbers.

Ono had worked with K3 surfaces before and he also realized that Ramanujan had found a K3 surface, long before they were officially identified and named by mathematician André Weil during the 1950s. Weil named them in honor of three algebraic masters – Kummer, Kähler and Kodaira – and the mountain K2 in Kashmir.

Just as K2 is an extraordinarily difficult mountain to climb, the process of generalizing elliptic curves to find a K3 surface is considered an exceedingly difficult math problem.

Ono and Trebat-Leder put all the pieces in Ramanujan’s notes together to produce the current paper, illuminating his finds and translating them into a modern framework.

“Ramanujan was using 1729 and elliptic curves to develop formulas for a K3 surface,” Ono says. “Mathematicians today still struggle to manipulate and calculate with K3 surfaces. So it comes as a major surprise that Ramanujan had this intuition all along.”

Ramanujan is well-known in India, and among mathematicians worldwide. He may soon become more familiar to wider audiences through an upcoming movie, “The Man Who Knew Infinity,” by Pressman Films. Ono served as a math consultant for the movie, which stars Dev Patel as Ramanujan and Jeremy Irons as Hardy. (Both Ono and Bhargava are associate producers for the film.)

“Ramanujan’s life and work are both a great human story and a great math story,” Ono says. “And I’m glad that more people are finally going to get to enjoy it.”

Related:
Math shines with the stars in 'The Man Who Knew Infinity'
Doing math with movie stars
New theories reveal the nature of numbers 
Math theory gives glimpse into the magical mind of Ramanujan

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