It's True. Isn't it?

Mathematics may not teach us about how to add happiness or subtract sadness. But it does give us one great hope that all the problems have atleast a single solution.

Have you heard about this before?

HOW WOULD YOU NAME A SIXTY ONE DIGITS NUMBER SUCH AS THIS: 7, 346, 648, 004, 560, 986, 215, 348, 444, 286, 445, 305, 146, 039, 140, 046, 960, 678, 582, 256, 003 ?

SEVEN VIGINTlLLION, THREE HUNDRED FORTY SIX NOVEMDECILLION, SIX HUNDRED FORTY EIGHT OCTODECILLION, FOUR SEPTENDECILLION, FIVE HUNDRED SIXTY SEXDECILLION, NINE HUNDRED EIGHTY SIX QUINDECILLION, TWO HUNDRED FIFTEEN QUARTER DECILLION, THREE HUNDRED FORTY EIGHT DUODECILLION, FOUR HUNDRED FORTY FOUR UNDECILLION, TWO HUNDRED EIGHTY SIX DECILLION, FOUR HUNDRED FORTY FIVE MONILLION, THREE HUNDRED AND FIVE OCTILLION, ONE HUNDRED FORTY SIX SEPTILLION, THIRTY NINE SEXTILLION, ONE HUNDRED FORTY QUINTILLION, FORTY SIX QUADRILLION, NINE HUNDRED SIXTY TRILLION, SIX HUNDRED SEVENTY EIGHT BILLION, FIVE HUNDRED EIGHTY TWO MILLION, TWO HUNDRED FIFTY SIX THOUSAND AND THREE.

Source: Shakuntala Devi (1984), "The Book of Numbers".

Way to locate prime numbers

Do anybody know how to find out the prime numbers from the whole list of available natural numbers?

I have found out one of the easiest ways to locate primes. It is called as SIEVE OF ERATOSTHENES and the most effective method of locating primes, this procedure separates the primes out of the set of all whole numbers. The whole numbers can be arranged in different columns starting with number one. But the correct method is to start arranging the number from two. Then the primes are circled and all multiples of 2 are crossed out. Next the number 3 is circled and all the multiples of 3 are crossed out. Next the same thing is done to 5 and 7. The remaining numbers are the primes.

Prime Numbers from 1 to 100

Prime Numbers listed using only odd numbers

Mathematicians call this procedure a SIEVE because it is a way of filtering the primes from the other whole numbers.

What Mathematicians do?

If you ask mathematicians what they do, you always get the same answer. They think. They think about difficult and unusual problems. They do not think about ordinary problems: they just write down the answers.

Uniqueness of numbers!!

Numeric Palindrome with 1's

1 x 1 = 1

11 x 11 = 121

111 x 111 = 12321

1111 x 1111 = 1234321

11111 x 11111 = 123454321

111111 x 111111 = 12345654321

1111111 x 1111111 = 1234567654321

11111111 x 11111111 = 123456787654321

111111111 x 111111111 = 123456789876543 ­21

Sequential Inputs of numbers with 8

1 x 8 + 1 = 9

12 x 8 + 2 = 98

123 x 8 + 3 = 987

1234 x 8 + 4 = 9876

12345 x 8 + 5 = 98765

123456 x 8 + 6 = 987654

1234567 x 8 + 7 = 9876543

12345678 x 8 + 8 = 98765432

123456789 x 8 + 9 = 987654321

Sequential 1's with 9

1 x 9 + 2 = 11

12 x 9 + 3 = 111

123 x 9 + 4 = 1111

1234 x 9 + 5 = 11111

12345 x 9 + 6 = 111111

123456 x 9 + 7 = 1111111

1234567 x 9 + 8 = 11111111

12345678 x 9 + 9 = 111111111

123456789 x 9 + 10 = 1111111111

Sequential 8's with 9

9 x 9 + 7 = 88

98 x 9 + 6 = 888

987 x 9 + 5 = 8888

9876 x 9 + 4 = 88888

98765 x 9 + 3 = 888888

987654 x 9 + 2 = 8888888

9876543 x 9 + 1 = 88888888

98765432 x 9 + 0 = 888888888

Without 8

12345679 x 9 = 111111111

12345679 x 18 = 222222222

12345679 x 27 = 333333333

12345679 x 36 = 444444444

12345679 x 45 = 555555555

12345679 x 54 = 666666666

12345679 x 63 = 777777777

12345679 x 72 = 888888888

12345679 x 81 = 999999999

What is the value of Zero (Not mine)?

What is the value of 0/0?

(a)I first thought the answer will be 1. Because "I have been thought the number when divided by itself" will be 1.

(b)Then i thought the answer will be zero because when the numerator is zero during division, the answer will invariably be zero.

(c)I also thought that the answer will be ∞ because anything divided by zero will be equal to infinity.

What do you think will be the correct answer for the above question?

Power of 2!!

During the first year of our engineering degree, we will mostly like have very little or limited connection to our department or to our faculties. While we are entering into the second year or third semester of our engineering degree, we have been warned by our seniors about one of our professors and received several tips from them. The famous tip I received was:

"Please keep your heads down. Do not try to answer any of his questions even if you know the answer. It will lead only to disaster from there."

I am not the kind of guy who will keep his mouth shut if i know the answer. Some of them got cobwebbed by his questions in third semester. I thought my turn will take some time. Yes, it did take time. I have survived the third semester without much damage.

But in fourth semester, my day has arrived. He was teaching about a 8-bit microprocessor in our class and he asked some question. The answer for this question will be 2¹⁶. But he is not satisfied with the answer 2¹⁶ and he wanted the numerical value of it.

Everyone is alert to the situation and noone wants to answer this question. But he is like Ghazni Muhammad and will not fall back till he gets what he want. So he changed his question and asked "What is the value of 2⁸" since it is a 8-bit processor. Since I am one of those 'geniuses' who will answer the question even the monstrous questions if it is of mathematical genre. I answered as "256". In that moment I realized I might be in for some trouble. But I have decided to take him down since it falls under my area of interest. 

Prof: 2⁹
Me: 512

Prof: 2¹⁰
Me: 1024

Prof: 2¹¹
Me: 2048

I can hear couple of people whispering the answer to their neighbour alongside me even though they are afraid to confront him. But it has gradually disappeared once the speed of the questions are increased by him.

He has increased the speed of the questions exponentially and my answer also reached him exponentially faster. The answers have reached him within the fraction of a second. It started to look out like we both are having a verbal battle out there. Our classmates started looking at each other like how you would normally watch the movement of tennis ball between two players in a tennis match if you are seated anywhere behind the umpires' chair or near the net.

Prof: 2¹²
Me: 4096

Prof: 2¹³
Me: 8192

Prof: 2¹⁴
Me: 16384

Prof: 2¹⁵
Me: 32768

Prof: 2¹⁶
Me: 65356

To much of his delight, I have responded the most important question with the wrong answer. I said "65356" instead of the correct answer 65536. It is enough for him to do what he can do best. i.e. Teasing the student who answers the question. He has literally mocked at me for not knowing this answer. But none of them in our class laughed at me and hence he marched on and on. I believe he definitely don't know the answer for the next powers of 2 but still he carried on because he wanted to embarrass me.

Prof: 2¹⁷
Me: 131072

Prof: 2¹⁸
Me: 262144

Prof: 2¹⁹
Me: 524288

Prof: 2²⁰
Me: 1048576

Prof: 2²¹
Me: 2097152

Prof: 2²²
Me: 4194304

Prof: 2²³
Me: 8388608

Prof: 2²⁴
Me: 16777216

Finally I believe he ran out of the gas and moved onto the next topic. At this moment in my life, I believed that I am really special with numbers. Do you all agree with me on this?

Note: He also came for our Microprocessor lab. More on that later.

With Love,
Anand

Sequential Inputs of numbers with 8

Sequential Inputs of numbers with 8

1 x 8 + 1 = 9

12 x 8 + 2 = 98

123 x 8 + 3 = 987

1234 x 8 + 4 = 9876

12345 x 8 + 5 = 98765

123456 x 8 + 6 = 987654

1234567 * 8 + 7 = 9876543

12345678 * 8 + 8 = 98765432

123456789 * 8 + 9 = 987654321

Mathematics

What is Mathematics?

This question will arise in each and every individual's mind at least once in their life. I also had this question when I was a small child. I have asked this question to several people but they could not be able to answer this question with concrete definition like we can define any other subject. It made me to be so curious about this subject and that what made me as one of those math freaks. Since no one is not sure about the definition, I have made my own definition and here's how it goes:

"Mathematics generally has no accepted definitions. It is the abstract study of quantity, structure, space, change, and many other topics."