Tangram

The tangram  is a dissection puzzle consisting of seven flat shapes, called tans, which are put together to form shapes. The objective of the puzzle is to form a specific shape (given only an outline or silhouette) using all seven pieces, which may not overlap. It was originally invented in China at some unknown point in history, and then carried over to Europe by trading ships in the early 19th century. It became very popular in Europe for a time then, and then again during World War I. It is one of the most popular dissection puzzles in the world.[

Over 6500 different tangram problems have been compiled from 19th century texts alone, and the current number is ever-growing. The number is finite, however. Fu Traing Wang and Chuan-Chin Hsiung proved in 1942 that there are only thirteen convex tangram configurations (configurations such that a line segment drawn between any two points on the configuration's edge always pass through the configuration's interior, i.e., configurations with no recesses in the outline).

 

 

 

You can get more picture from google.

 

Activity to find the area of parallelogram

Multiplication of two numbers that differ by 2

Multiplication of two numbers that differ by 2

Note :This trick only works if you know the squares of numbers.

 

When two numbers differ by 2, their product is always the square of the number in between these numbers minus 1.

12 x 14 =   (13 x 13)  - 1 =  169 - 1 =  168
 

18 x 20 =   (19 x 19)  - 1 =  361 - 1 =  360

25 x 27 =   (26 x26)   - 1 =  676 - 1 =  675  
13 x 15 =   (14 x 14)  - 1 =  196 - 1 =  195

15 x 17 =   (16 x 16)  - 1 =  256 - 1 =  255

16 x 18 =   (17 x 17)  - 1 =  289 - 1 =  288

     

 

Angle sum property of Triangle

 

Ekādhikena Pūrvena,

Ekādhikena Pūrvena, ("By one more than the previous one") This  sūtra means that the prescribed arithmetical operation is either multiplication or division. Both are implied since we may proceed leftward and multiply (and carry-over the excess value to the next leftward column) or we may go rightward and divide (while prefixing the remainder). When dividing by a nine's family denominator, the digit to the left of the nine (previous) is increased by one to obtain the multiplier.

.Examples:

35×35 = ((3×3)+3),25 = 12,25 and 125×125 = ((12×12)+12),25 = 156,25

 

or by the sūtra, multiply "by one more than the previous one."

35×35 = ((3×4),25 = 12,25 and 125×125 = ((12×13),25 = 156,25

 

The latter portion is multiplied by itself (5 by 5) and the previous portion is square of first digit or first two digit (3×3) or (12×12) and adding the same digit in that figure (3or12) resulting in the answer 1225.
(Proof) 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. Examples:

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 sūtra 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.

The Vedic Mathematics Sutras

This list of sutras is taken from the book Vedic Mathematics, which includes a full list of the sixteen Sutras in Sanskrit,

The Main Sutras

1.       By one more than the one before.

2.       All from 9 and the last from 10.

3.       Vertically and Cross-wise

4.       Transpose and Apply

5.       If the Samuccaya is the Same it is Zero

6.       If One is in Ratio the Other is Zero

7.       By Addition and by Subtraction

8.       By the Completion or Non-Completion

9.       Differential Calculus

10.    By the Deficiency

11.    Specific and General

12.    The Remainders by the Last Digit

13.    The Ultimate and Twice the Penultimate

14.    By One Less than the One Before

15.    The Product of the Sum

16.    All the Multipliers

Square a 2 Digit Number Ending in 5

For this example we will use 25

• Take the "tens" part of the number (the 2 and add 1)=3
• Multiply the original "tens" part of the number by the new number (2x3)
• Take the result (2x3=6) and put 25 behind it. Result the answer 625.

Square of 35

• Take the "tens" part of the number (the 3 and add 1)=4
• Multiply the original "tens" part of the number by the new number (3x4)
• Take the result (3x4=12) and put 25 behind it. Result the answer 1225.

Square of 75

• Take the "tens" part of the number (the 7 and add 1)=8
• Multiply the original "tens" part of the number by the new number (7x8)
• Take the result (7x8=56) and put 25 behind it. Result the answer 5625.

 

To find the cube of numbers between 11 to 99

First learn the cubes of first 10 natural numbers

Lets Find the cube of 34

Step 1             Write the cube of 3 (tens place digit )

27

Step 2             Multiply the obtained cube by the ratio of unit place to tens place digit I;e 4/3 to get next
                       digits

(4/3)x27 = 36

                       Now you get next set of digits

27       36

Step 3           Multiply the obtained second set by the ratio of unit place to tens place digit again I;e 4/3 to    
                     get next digits

(4/3)x36 = 48

                    Now you get next set of digits

27       36        48

Step 4          Multiply the obtained third set by the ratio of unit place to tens place digit again I;e 4/3 to get
                    next digits

(4/3)x48 = 64

                   Now you get next set of digits

27      36      48      64

Step 5        Double the second set and third set digits as shown below and then add to get cube of number

                                                               12          15           6

                                                               27         36          48        64

                                                                   +      72           96

                                                             _______________________

                                                               39       123        150        64       ( Red digits are to be carry )

                                                              39       3        0       4

Thus Cube of 34 is 39304



Weights to Measure from 1 to 40 Kg

How can you measure  any weight between  1Kg  to 40Kg  using upto four weight without repeating any weight ?

  
Answer is  1Kg ,3Kg ,9Kg  ,27Kg 


With these 4 weights you can find any weight from 1 to 40  by  adding or subtracting

Is it not interesting !!!!!!!

Important Qutes

Pencil: I'm sorry.

Eraser: For what? You didn't do anything wrong.


Pencil: I'm sorry, you get hurt because of me. Whenever I made a mistake, you're always there to erase it. But as you make my mistakes vanish, you lose a part of yourself and get smaller and smaller each time.

Eraser: That's true, but I don't really mind. You see, I was made to do this, I was made to help you whenever you do something wrong, even though one day I know I'll be gone. I'm actually happy with my job. So please, stop worrying I hate seeing you sad.


"Our Parents are like the eraser, whereas we children are the pencil. They're always there for their children, cleaning up their mistakes. Sometimes along the way they get hurt and become smaller (older and eventually pass on) Take care of your Parents, treat them with kindness and most especially love them.

To calculate reminder on dividing the number by 27 and 37

Let me explain this rule by taking examples

consider number 64564276, we have to calculate the reminder on diving this number by 27 and 37 respectively.

Make triplets as written below starting from units place

64    564     276

now sum of all triplets = 64  +  564  +  276  = 904

divide it by 27 we get reminder as 13

divide it by 37 we get reminder as 16

Example.

Let the number is 2387850765

triplets are 2...387...850...765

sum of the triplets = 2+387+850+765 = 2004

on revising the steps we get

2        004

sum = 6

divide it by 27 we get reminder as 6

divide it by 37 we get reminder as 6

About Srinivasa Ramanujan

Well known mathematicians Professors G.H. Hardy and J.E. Littlewood compared Ramajuan’s mathematical abilities and natural genius with all-time great mathematicians like Leonhard Euler, Carl Friedrich Gauss and Karl Gustav Jacobi. The influence of Ramanujan on number theory is without parallel in mathematics. His papers, problems and letters would continue to captivate mathematicians in the future. He rediscovered a century of mathematics and made new discoveries. Srinivasa Ramanujan Iyengar (best known as Srinivasa Ramanujan) was born on 22 December, 1887, in Erode about 400 km from Chennai (formerly known as Madras). While at school, Ramanujan came across a book entitled "A Synopsis of Elementary Results in Pure and Applied Mathematics" by George Shoobridge Carr. This book had a great influence on Ramanujan’s career. G.H. Hardy (1877 – 1947), a prominent English mathematician wrote about the book: “He (Carr) is now completely forgotten, even in his college, except in so far as Ramanujan kept his name alive”. Ramanujan solved all the problems in Carr’s Synopsis. While working on Carr’s Synopsis, he discovered many others new formulae, and he began the practice of compiling a notebook. Between 1903 and 1914 he had compiled three notebooks. Much of Ramanujan’s mathematics comes under the field of number theory — a purest realm of mathematics. During his short lifetime, Ramanujan independently compiled nearly 3900 results (mostly identities and equations). He stated results that were both original and highly unconventional, such as the Ramanujan prime and the Ramanujan theta function, and these have inspired a vast amount of further research in the area of mathematics.

Interesting Facts in Sale and Purchase

Multiplication of 2 two-digit numbers where the tens digit of both the numbers are same and the unit digit of the two numbers sum to 10

Example.

To calculate 66 and 64:

 

In this tens digit is same and sum of unit digits is 10
Multiply 6 by 6+1. So, 6x7 = 42. Write down 42.
Multiply together the last digits: 6*4 = 24. Write down 24.
Thus  66 x 64 = 4224.

Example.
To calculate 57 and 53:

In this tens digit is same and sum of unit digits is 10
Multiply 5 by 5+1. So, 5x6 = 30. Write down 30.
Multiply together the last digits: 7x3 = 21. Write down 21.
Thus 57 x 53 = 3021.

 

 

To calculate reminder on dividing the number by 3

To calculate reminder on dividing the number by 3

Method:- first calculate the digit sum , then divide it by 3, the reminder in this case will be the required reminder

Example:- 12347528
let the number is as written above
its digit sum = 32 = 5
so reminder will be 2 when we divide 5 by 3 we get reminder as 2 so answer will be 2 

 

Example :- 25967785834
digit sum of the number is 64 = 10 = 1
reminder is 1

Example :- 50329845467
then digit sum = 53 = 8
when we divide 8 by 3 we get reminder as 2 so answer will be 2