MATHS MAGIC

HARIKRISHNA

IX-B

                                                                                

Sneak some spelling into this math problem.

1.  Select any number. Write it out as a word; six hundred and six.

2.  Count the letters (but don’t count spaces or the hyphen); 13.

3.  Write down the number of letters as a word; thirteen.

4.  Count the letters in that word; 8.

Count the letters of that word; eight. The answer will always work down to “4.” So, 5 (letters in eight), five, 4!
Do this trick on a calculator with a 10-digit display or work it out on paper.

1.  Choose any number 1 through 9; 8.

2.  Multiply that number by the magic number – 123,456,789; 8 x 123456789 = 98,765,432

3.  Multiply the answer by 9; 98,765,432 x 9 = 8,888,888,808.

4.  The answer will be a 10-digit number, with nine of the digits the same as the number chosen in step 1.

The answer here will always work out to 1.

1.  Ask another person to choose a number from 1 to 10 without revealing this number; 3.

2.  Have them double the number; 3 + 3 = 6.

3.  Add 2 to the result; 6 + 2 = 8.

4.  Divide that number by 2; 8 divided by 2 = 4.

5.  Subtract the original number from the answer in step 4; 4 – 3 = 1.

6.  The answer is always 1.

It seems like magic that the answer always works out to 9.

1.  Enter into a calculator any number that consists solely of the number nine repeated; 9,999.

2.  Multiply it by any number; 9,999 x 25 = 249,975.

3.  Write down the number on paper.

4.  Add the individual digits in the answer; 2 + 4 + 9 + 9 + 7 + 5 = 36

5.  Add the answer digits together. If the answer isn’t 9, repeat adding the new answer digits until the result is 9

JOKES….JOKES……

JOKES….JOKES……

·       A math student is pestered by a classmate who wants to copy his homework assignment. The student hesitates, not only because he thinks it's wrong, but also because he doesn't want to be sanctioned for aiding and abetting.
His classmate calms him down: "Nobody will be able to trace my homework to you: I'll be changing the names of all the constants and variables: a to b, x to y, and so on."
Not quite convinced, but eager to be left alone, the student hands his completed assignment to the classmate for copying.
After the deadline, the student asks: "Did you really change the names of all the variables?"

·       Teacher: "Who can tell me what 7 times 6 is?"
Student: "It's 42!"
Teacher: "Very good! - And who can tell me what 6 times 7 is?"
Same student: "It's 24!"

·       Why do mathematicians, after a dinner at a Chinese restaurant, always insist on taking the leftovers home?
A: Because they know the Chinese remainder theorem

·       Teacher: What is  2 k + k?
Student: 3000!

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·       Q: What do you get if you divide the cirucmference of a jack-o-lantern by its diameter?
A: Pumpkin Pi!

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·       Q: Why do you rarely find mathematicians spending time at the beach?
A: Because they have sine and cosine to get a tan and don't need the sun!

·       Pi to i: Get real! 
i i to Pi: Get rational!

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 NUMBERS

                                                Ganga  K S

                                                         IX B

 0,1,2,3,4,5...................

NUMBERS THE FIRST STEP OF

MATHEMATICS

  Have BEEN A HELPFUL DEVICE

IN EVERY SUBJECT.

FROM ARYABHATA TILL NOW

WE USE NUMBERS 

IN OUR DAY TO DAY LIFE.

WE USE NUMBERS AS

OUR FRIENDS WHEN 

PLAYING,CALCULATING.....

EVERY WHERE THERE IS A NUMBER

AS A PART OF OUR LIFE

IT DOES NOT HAVE AN END
IT GOES 

ON AND ON........JUST COUNT...... 0,1,2,3,4,5 .......

MATH PUZZLES………………

….  Anjali.J.VIIIA

1. Light Bulb
A light bulb is hanging in the first floor of the room. There are three switches in the ground floor room. One of these switches belongs to that light bulb. The light bulb is not lit and the switches are in off state. There is only one chance to visit the room. How can it be determined which of these switch is connected to the light bulb.

Solution:
First turn ON the first switch and leave it for few minutes. Then turn OFF the first switch and ON the second switch. Now enter the first floor room. If the light bulb is lit, the second switch must be connected to it. If it is not lit, it might the first or the third switch. Now touch the light bulb, it is hot it will be the connected to the first switch. Nor if it is cold, then it should be the third one.

2. Eleven Apples Puzzle: 

Question: 
Miss Anne has eleven kids in her class. She has a bowl containing eleven apples. Now Miss Anne want to divide the eleven apples to the kids, in such a way that a apple should remain in her bowl.
How can Miss Anne do it?

Solution:
Ten kids will get each one apple. The eleventh kid will get the apple with the bowl.

3. Two Fathers Puzzle:

Question:
Two fathers took their sons to a fruit stall. Each man and son bought an apple, But when they returned home, they had only 3 apples. They did not eat, lost, or thrown. How could this be possible?

Solution:
There were only three people. Son, his father and his grandfather.

4. Handshakes Puzzle: 

Question:
Jack and his wife went to a party where four other married couples were present. Every person shook hands with everyone he or she was not acquainted with. When the handshaking was over, Jack asked everyone, including his own wife, how many hands they shook. To his surprise, Jack got nine different answers.
How many hands did Jack's wife shake?

Solution:
Because, obviously, no person shook hands with his or her partner, nobody shook hands with more than eight other people. And since nine people shook hands with different numbers of people, these numbers must be 0, 1, 2, 3, 4, 5, 6, 7, and 8.
The person who shook 8 hands only did not shake hands with his or her partner, and must therefore be married to the person who shook 0 hands.
The person who shook 7 hands, shook hands with all people who also shook hands with the person who shook 8 hands (so in total at least 2 handshakes per person), except for his or her partner. So this person must be married to the person who shook 1 hand.
The person who shook 6 hands, shook hands with all people who also shook hands with the persons who shook 8 and 7 hands (so in total at least 3 handshakes per person), except for his or her partner. So this person must be married to the person who shook 2 hands.
The person who shook 5 hands, shook hands with all people who also shook hands with the persons who shook 8, 7, and 6 hands (so in total at least 4 handshakes per person), except for his or her partner. So this person must be married to the person who shook 3 hands.
The only person left is the one who shook 4 hands, and which must be Jack's wife. Jack's wife shook 4 hands.

5. Gold Puzzle: 

Question: 
There are three boxes in a table. One of the box contains Gold and the other two are empty. A printed message contains in each box. One of the messages is true and the other two are lies.
The first box says "The Gold is not here".
The Second box says "The Gold is not here".
The Third box says "The Gold is in the Second box".
Which box has the Gold?

Solution:
As the message contains one truth, the third says that the gold is in the second box, if it is to be true, then the first box message will also become true. So Gold cannot be in second and third boxes. Gold is in the first box.

Strange Properties of 666

Strange Properties of 666

"The Number of the Beast"

                          
 Sudhy P S - XII B

The last book of the Bible, Revelation, brings up the number 666 as being the number of the beast connected with the end of this age and the coming of the Messiah. You will find the direct reference in Chapter 13, verse 18 of Revelation. Besides that cataclysmic reference, the number 666 has quite a few very interesting properties.

666 = 3^6 - 2^6 + 1^6

666 = 6^3 + 6^3 + 6^3 + 6 + 6 + 6

(Mike Keith mentions that there are only five other positive integers that exhibit this property...find 'em!)

666 = 2^2 + 3^2 + 5^2 + 7^2 + 11^2 + 13^2 + 17^2

666 = 1 + 2 + 3 + 4 + 567 + 89 = 123 + 456 + 78 + 9 = 9 + 87 + 6 + 543 + 21

Moreover, 666 is equal to the sum of the cubes of the digits in its square (666^2 = 443556, and the sum of the cubes of these digits is 4^3 + 4^3 + 3^3 + 5^3 + 5^3 + 6^3 = 621) plus the sum of the digits in its cube (666^3 = 295408296, and 2+9+5+4+0+8+2+9+6 = 45, and 621+45 = 666).

Incredibly, the number 666 is equal to the sum of the digits of its 47th power, and is also equal to the sum of the digits of its 51st power. That is,

666^47 = 5049969684420796753173148798405564772941516295265
4081881176326689365404466160330686530288898927188
59670297563286219594665904733945856

666^51 = 9935407575913859403342635113412959807238586374694
3100899712069131346071328296758253023455821491848
0960748972838900637634215694097683599029436416

and the sum of the digits on the right hand side is, in both cases, 666. In fact, 666 is the only integer greater than one with this property. (Also, note that from the two powers, 47 and 51, we get (4+7)(5+1) = 66.)

Mr. Keith also points out that if we assign numerical values for the letters of the alphabet starting with A = 36, B = 37, and so on, we find that the letters in the word

SUPERSTITIOUS = 666 !!!

                            

From contributor James Watt comes the following: "Here are some other neat things about 666 I seem to have discovered (since I never found any reference anywhere else). 6+6+6 =18 and 18 x 37 = 666. 
Similarly, 4+4+4 = 12. 12 x 37 = 444. etc. In Roman numerals (and the Greek equivalents), which John would have used to write them, it is DCLXVI, the exact sequential descending order of Roman Numerals.
Now 1/81 = .012345679012345679012345679.... Notice the 8 is missing. 1+2+3+4+5+6+7+9 = 37.
The other 'number of the beast' is called the vulgate number. It is 616. If 'vulgar' Roman numerals are used in ascending order, vulgate Roman numerals 616 is IVXCD. The'L' is missing."

From contributor Matt Westwood comes this interesting fact: "666 is also the total of all the numbers in a 6x6 magic square. That is, it's the 36th triangle number, being <math>sum_{k=1}^{36} k</math>." He also goes on to mention "In one of the many branches of Hermitic magic that I once studied, the magic squares of the various sizes were talismans for the various planetary influences: 3x3: Saturn, 4x4: Jupiter, 5x5: Mars, 6x6: Sun, 7x7: Venus, 8x8: Mercury, 9x9: Moon. A more recent book on the subject tried to convince that 11x11 was Neptune, or something, but this is far from profound: there exists a simple algorithm for creating *any* odd-order magic square with consecutive natural numbers starting from 1. Although I did find it profound at the time that I won a raffle ticket with the number 369 (the number of the 9x9 square) on the very day I moved into a new house. Add or subtract n from every digit of any magic square, and it remains magic of course."

Amazing prime numbers

                                                    -  Sneha Devan XIB -

Here are few amazing prime numbers, these prime numbers were proved by the XVIII^th century.

31, 331, 3331 ,33331 ,333331, 3333331 ,33333331.

angel number 412

 Rules

   Step 1  

               Select any whole number. 

   Step 2  

               If it is an even number, divide by 2; if it is odd number multiply by 3 and add 1. 

   Step 3  

               Repeat the process mentioned in step 2 until you get the loop value 4, 2, 1 in 

               repetition. 

Example

  Whole number is 15. 

  15 is an odd no; so (15 × 3) + 1 = 46 

  46 is an even no; so 46 / 2 = 23 

  23 is an odd no; so (23 × 3) + 1 = 70 

  70 is an even no; so 70 / 2 = 35 

  35 is an odd no; so (35 × 3) + 1 = 106 

  106 is an even no; so 106 / 2 = 53 

  53 is an odd no; so (53 × 3) + 1 = 160 

  160 is an even no; so 160 / 2 = 80 

  80 is an even no; so 80 / 2 = 40 

  40 is an even no; so 40 / 2 = 20 

  20 is an even no; so 20 / 2 = 10 

  10 is an even no; so 10 / 2 = 5 

  5 is an odd no; so (5 × 3) + 1 = 16 

  16 is an even no; so 16 / 2 = 8 

  8 is an even no; so 8 / 2 = 4 

  4 is an even no; so 4 / 2 = 2 

  2 is an even no; so 2 / 2 = 1 

  1 is an odd no; so (1 × 3) + 1 = 4 

  4 is an even no; so 4 / 2 = 2 

2 is an even no; so 2 / 2 = 1 




So the loop 4..2..1 goes on and on.

Tip : The angel number 421 is the smallest prime formed by the two powers in logical order from right to left. 

HISTORY OF TRIGONOMETRY

 Ansua XI C

The history of trigonometry goes back to the earliest recorded mathematics in Egypt and Babylon. The Babylonians established the measurement of angles in degrees, minutes, and seconds. Not until the time of the Greeks, however, did any considerable amount of trigonometry exist. In the 2nd century bc the astronomer Hipparchus compiled a trigonometric table for solving triangles. Starting with 7½° and going up to 180° by steps of 7½°, the table gave for each angle the length of the chord subtending that angle in a circle of a fixed radius r. Such a table is equivalent to a sine table. The value that Hipparchus used for r is not certain, but 300 years later the astronomer Ptolemy used r = 60 because the Hellenistic Greeks had adopted the Babylonian base-60 (sexagesimal) numeration system.

In his great astronomical handbook, The Almagest, Ptolemy provided a table of chords for steps of y°, from 0° to 180°,that is accurate to 1/3600 of a unit. He explained his method for constructing his table of chords, and in the course of the book he gave many examples of how to use the table to find unknown parts of triangles from known parts.

                                Indian astronomers had developed a trigonometric system based on the sine function rather than the chord function of the Greeks. This sine function, unlike the modern one, was not a ratio but simply the length of the side opposite the angle in a right triangle of fixed hypotenuse. The Indians used various values for the hypotenuse.

Late in the 8th century, Muslim astronomers inherited both the Greek and the Indian traditions, but they seem to have preferred the sine function. Trigonometric calculations were greatly aided by the Scottish mathematician John Napier.

                                     Finally, in the 18th century the Swiss mathematician Leonhard Euler defined the trigonometric functions in terms of complex numbers. This made the whole subject of trigonometry just one of the many applications of complex numbers, and showed that the basic laws of trigonometry were simply consequences of the arithmetic of these numbers.

AryabhatTa

Bijeesh A B - VI C -

Aryabhata was the great Hindu Mathematician. He lived from 475 AD to 550 AD. He wrote on arithmetic including undo this heading arithmetic and geometric progressions, quadratic equations, and indeterminate equations. His work often called Aryabhatiya consists of a collection of astronomical tables and the Aryastasata which include the Ganita, a note on arithmetic, the Kalakriya on time and its measure and the Gola on the sphere. Aryabhata was one of those ancient scholars of India who could stand with pride among the greatest scholars even of the modern age.

Puzzle

   1)There is a number which is very peculiar. This number is 3times the sum of its digits. Can you find the number?

 2) Write the biggest number that can be written with four one’s?

3) Can you write 1789 in roman numbers?

 4) What is the sum of first 70 odd numbers?

5) Find the value of:

                                   CCLXV+CXVI+XIII+VI=?

Beginning of algebra

 It is said that algebra as a branch of mathematics began about 1550 BC, that means more than 3500 years ago, when people in Egypt started using symbols to denote unknown numbers .Around 300 BC, use of letters to denote unknown and forming expressions from them was quite common in India. Many great Indian mathematicians Aryabhata, Brahmagupta, Mahavira and Bhaskara II and others, contributed a lot to the study of Algebra.

Branches of mathematics

The branches of mathematics in which we study about numbers is called arithmetic. The branch in which we learn about figures in two and three dimensions and their properties is called geometry. The branch in which we use letters along with numbers to write rules and formulas in general is called algebra.    

Answers for the puzzleS

1Ans) 27

            2+7=9

            9x3=27

2Ans) 285311670611

3Ans) MDCCLXXXIX

4Ans) 4,900 (70x70)

5Ans) CD  
  
                        CLXV              265

                      C XVI               166

                                 XIII                 13                        

                  VI            +       6    
  

           Ans          CD               400  

                                                          

Math’s Interesting Facts

                                                                                                                  ANILA

                                                                                                                      IX-B

·         The word "mathematics" comes from the Greek máthēma, which means learning, study, science.

·         What comes after a million, billion and trillion? A quadrillion, quintillion, sextillion, septillion, octillion, nonillion, decillion and undecillion.

·         Different names for the number 0 include zero, nought, naught, nil, zilch and zip.

·         The = sign ("equals sign") was invented by 16th Century Welsh mathematician Robert Recorde, who was fed up with writing "is equal to" in his equations.

·         Googol (meaning & origin of Google brand) is the term used for a number 1 followed by 100 zeros and that it was used by a nine-year old, Milton Sirotta, in 1940.

·         The name of the popular search engine ‘Google’ came from a misspelling of the word ‘googol’.

·         Abacus is considered the origin of the calculator.

·         12,345,678,987,654,321 is the product of 111,111,111 x 111,111,111. Notice the sequence of the numbers 1 to 9 and back to 1.

·         Plus (+) and Minus (-) sign symbols were used as early as 1489 A.D.

·         An icosagon is a shape with 20 sides.

·         Trigonometry is the study of the relationship between the angles of triangles and their sides.

·         If you add up the numbers 1-100 consecutively (1+2+3+4+5...) the total is 5050.

·         2 and 5 are the only primes that end in 2 or 5.

·         From 0 to 1,000, the letter "A" only appears in 1,000 ("one thousand").

·         'FOUR' is the only number in the English language that is spelt with the same number of letters as the number itself

·         40 when written "forty" is the only number with letters in alphabetical order, while "one" is the only one with letters in reverse order.

·         Among all shapes with the same perimeter a circle has the largest area.

·         Among all shapes with the same area circle has the shortest perimeter .

·         In 1995 in Taipei, citizens were allowed to remove ‘4’ from street numbers because it sounded like ‘death’ in Chinese. Many Chinese hospitals do not have a 4th floor.

·         In many cultures no 13 is considered unlucky, well,there are many myths around it .One is that In some ancient European religions, there were 12 good gods and one evil god; the evil god was called the 13th god.Other is superstition goes back to the Last Supper. There were 13 people at the meal, including Jesus Christ, and Judas was thought to be the 13th guest.

Some beautiful examples with multiplication

12345679 x 9 = 111111111;

12345679 x 8 = 98765432

An interesting fact about primes
Mathematicians of XVIII^th century proved that numbers 31; 331; 3331; 33331; 333331; 3333331; 33333331 are primes. It was a big temptation to think that all numbers of such kind are primes. But the next number is not a prime.
333333331 = 17 x 19607843