Hardy's 6 wishes

In the 1920s, the British mathematician G H Hardy wrote a postcard to his friend, listing 6 New Year’s wishes :

1. Prove the Riemann hypothesis.

2. Score well at the end of an important game of Cricket.

3. Find an argument for the non-existence of God that convinces the general public.

4. Be the first man at the top of Mount Everest.

5. Be the first president of the USSR, Great Britain and Germany.

6. Murder Mussolini.

Mathematics and Sex

The great think about liking both Math & Sex is that, I can do either one while thinking about the other. (Steven E Labdsburg, 1993)

-1 is equal to +1

We all know,     a = √a * √a = √(a*a)

Which implies,     -1 = √(-1) * √(-1) = √{(-1)(-1)} = √1 = 1

Of course, it can't be true.

Then what could be wrong?

We define,     a = √a * √a     or,     √ab = √a * √b

But it is valid only when at least one of     a & b     is non-negative.

The Palindromic Numbers

        1 * 1         =         1

       11 * 11        =        121

      111 * 111       =       12321

     1111 * 1111      =      1234321

    11111 * 11111     =     123454321

   111111 * 111111    =    12345654321

  1111111 * 1111111   =   1234567654321

 11111111 * 11111111  =  123456787654321

111111111 * 111111111 = 12345678987654321

The Pyramid of Numbers

                                1 = 1                 = 1²

                            1+2+1 = 2+2               = 2²

                        1+2+3+2+1 = 3+3+3             = 3²

                    1+2+3+4+3+2+1 = 4+4+4+4           = 4²

                1+2+3+4+5+4+3+2+1 = 5+5+5+5+5         = 5²

            1+2+3+4+5+6+5+4+3+2+1 = 6+6+6+6+6+6       = 6²

        1+2+3+4+5+6+7+6+5+4+3+2+1 = 7+7+7+7+7+7+7     = 7²

    1+2+3+4+5+6+7+8+7+6+5+4+3+2+1 = 8+8+8+8+8+8+8+8   = 8²

1+2+3+4+5+6+7+8+9+8+7+6+5+4+3+2+1 = 9+9+9+9+9+9+9+9+9 = 9²

Amazing Power Relationship

Our number system has many unusual features built into it. Here is one of them discovered by Carl Friedrich Gauss (1777 – 1855).

81 = (8+1)² = 9² 
or 4,193 = (4+1+9+3)³ = 17³

Now enjoy the list.

81 = 9²

512 = 8³

4,193 = 17³

5,832 = 18³

17,576 = 26³

19,683 = 27³

2,401 = 7⁴

234,256 = 22⁴

390,625 = 25⁴

614,656 = 28⁴

1,679,616 = 36⁴

17,210,368 = 28⁵

52,521,875 = 35⁵

60,466,176 = 36⁵

205,962,976 = 46⁵

34,012,224 = 18⁶

8,303,765,625 = 45⁶

24,794,911,296 = 54⁶

68,719,476,736 =64⁶

612,220,032 = 18⁷

10,460,353,203 = 27⁷

27,512,614,111 = 31⁷

52,523,350,144 = 34⁷

271,818,611,107 = 43⁷

1,174,711,139,837 = 53⁷

2,207,984,167,552 = 58⁷

6,722,988,818,432 = 68⁷

20,047,612,231,936 = 46⁸

72,301,961,339,136 = 54⁸

248,155,780,267,521 = 63⁸

20,864,448,472,975,628,947,226,005,981,267,194,447,042,584,001 = 207²⁰

Amazing Number Patterns

Just watch the first & last digits of the multiples.

999,999 *  1 = 0,999,999

999,999 *  2 = 1,999,998

999,999 *  3 = 2,999,997

999,999 *  4 = 3,999,996

999,999 *  5 = 4,999,995

999,999 *  6 = 5,999,994

999,999 *  7 = 6,999,993

999,999 *  8 = 7,999,992

999,999 *  9 = 8,999,991

999,999 * 10 = 9,999,990

Only for Boys

We all know that every day is a special M############ Day. So to celebrate every M############ Day, here’s a li’l poem.

My M############ Addiction
(unknown author)

Feeling gently for my gland,

Clutching with an eager hand,

Now it feels so small and thin,

Yet playing softy with the skin,

Makes it grow hard and thick,

How I need this erect d###!!

I'm in no hurry, I have all day,

To let my mind slip away,

Into my world of m############,

Where ###k's my master,

And I'm its slave,

It's what I want, it's what I crave.

Rubbing gently rubbing slow,

I slide the skin to and fro,

As the hours pass by,

I get so high,

I explode like a thousand guns,

The s##### bursts out and runs and runs.

I'm now at peace, I’ve soothed my brain

Yet soon I’ll have to m######### again.

Truth

The word ‘True’ is not a true word and there is no true meaning of it. (Pritam Saha)

Get Crazy

The global average efficiency of vehicles is 5 km to a liter. Japan & Western Europe manage an average of up to 11 km.

Believe It or Not

An average person’s eyes are closed for about 30 minutes a day while awake, due to blinking.

Global Warming

If you avoid 25 km of driving every week, it would eliminate about 226 kg of CO₂ emissions a year!

Beautiful Number Relationship

Notice the consecutive exponents.

135 = 1¹ + 3² + 5³

175 = 1¹ + 7² + 5³

518 = 5¹ + 1² + 8³

598 = 5¹ + 9² + 8³

Now, take it to one place further.

1306 = 1¹ + 3² + 0³ + 6⁴

1676 = 1¹ + 6² + 7³ + 6⁴

2427 = 2¹ + 4² + 2³ + 7⁴

The next ones are really amazing.

Notice the relationship between the exponents and the numbers.

3435 = 3³ + 4⁴ + 3³ + 5⁵

438579088 = 4⁴ + 3³ + 8⁸ + 5⁵ + 7⁷ + 9⁹ + 0⁰ + 8⁸ + 8⁸

(We’ve considered here 0⁰ as 0. But, in fact, it’s undetermined.)

What is Anger?

Anger is one letter short of Danger!

Round Off Decimal Numbers

1. If the 1st discarded digit is less than 5, we’ve to leave the remaining digits unchanged.

(e.g. Round off 2.534 to 2 decimal place. The answer is 2.53)

2. If the 1st discarded digit is greater than 5, we’ve to add 1 to the last retained digit.

(e.g. Round off 3.268 to 2 decimal place. The answer is 3.27)

3. If the 1st discarded digit is exactly 5 and there are more non-zero discarded digits, we’ve to add 1 to the last retained digit.

(e.g. Round off 3.2653 to 2 decimal place. The answer is 3.27)

4. If the 1st discarded digit is exactly 5 and all other discarded digits are zero, we’ve to add 1 to the last retained digit if it’s odd and we’ve to leave the last retained digit unchanged if it’s even.

(e.g. Rounding off of 3.265 to 2 decimal place is 3.26 and rounding off of 3.275 to 2 decimal place is 3.28)

* The rule 4 is only applicable in Numerical Analysis. Otherwise add 1 if the 1st discarded digit is 5.

Dravid, the Wall

Sachin is God …

Sourav is God on the off side …

Laxman is God in the 4th innings …

But when the doors of the temple are closed, even the God is behind the Wall.

Dravid made 69 (79) on his last appearance in the blue shirt on Friday.

Collective Nouns

A culture of Bacteria, a quiver of Cobras, a smack of Jellyfish & a plague of Locusts!!

Multiples of 1089

Let’s look at the first nine multiples of 1089 :

1089 x 1 = 1089

1089 x 2 = 2178

1089 x 3 = 3267

1089 x 4 = 4356

1089 x 5 = 5445

1089 x 6 = 6534

1089 x 7 = 7623

1089 x 8 = 8712

1089 x 9 = 9801

Now try to find out the symmetricity of the multiples.