Let's make railways better

India is a very large country in terms of area and population. Also Indian railway has grown up by leaps and bounds since years. It is the biggest lifeline in our country as far as transportation is concerned. So it is obvious that we face lot of difficulties in getting tickets and reservations. Although in all these years our government has made these procedures faster and better, yet few more ideas can improve it. I have one such idea in my mind. and would like to share the same.

It is about platform tickets. In many cities people do not prefer standing in long queue just for platform tickets. Of course many are not willing to get, but then they are fined by the T.C. Also there are a class of people who wish to obey the rules but because of the queue they miss out. Railway is also loosing its income just due to lack of any facility regarding it. May be it is not a lot of amount for the railway but still it is not the matter of just money, somewhere discipline is also broken just for such silly reason.
So here is my suggestion if it could be possible. If we can have built up a machine which can give platform tickets as you enter a coin inside, just as we have in our public phone booths or weighing machines. This may save a lot of time of the passengers, visitors and ticket vendors. I think we should give it a thought.

"e" day

We celebrate "e" day, on 7th February (since e = 2.718281828459...). The number "e" is very special in math, in a similar way that "pi" is special.

One of the most amazing equations involving e is Euler's Formula:

e^ix = cos x + i sin x, where i = √(−1)

This formula makes the connection between the exponential function, trigonometry and the imaginary unit.

In the special case when x = π, we get

e^iπ + 1 = 0

This profound formula connects the numbers e, i, π, 1 and 0, with the fundamental operations plus (+) and equals (=).

Theodorus of Cyrene

Theodorus of Cyrene was a 5th century B.C. mathematician and was born around 100 years after Pythagoras. (Cyrene is now called Shahhat, in Libya.)

He apparently proved that the square roots of 2, 3, 5, 6 and so on up to 17 were all irrational, except the perfect squares 4, 9, 16. (Unfortunately we no longer have the proofs.) He also went on to construct these supposedly non-existent distances.

He proceeded as follows.

Start with a right triangle with equal sides 1, giving a hypotenuse of √2 (which of course was a problem, because this distance didn’t officially exist):

Then, extend a line with length 1 unit (using your 1-unit measuring stick) at right angles to the first hypotenuse as follows. This gives us the length √3 after we apply Pythagoras’ Theorem to the new triangle.

Do it again, and you now get the length √4 = 2. Theodorus had discovered one hypotenuse with a rational number length.

He kept going and found that the next one to have a "rational" length was √9 = 3.

He continued on to √16 = 4, constructed one more, √17, then stopped.

Starting from the right and with the thumb, we assign the values like so:

Thumb = 1

Index finger = 2

Middle finger = 4

Ring finger = 8

Baby finger = 16

A fist = 0

To make 13 in binary, you would need to keep raised the fingers that all add up to 13.

in this case we would keep up the ring finger (8), the middle finger (4) and the thumb

(1) as they all add up to 13.

Try doing 30.

You would hold up all fingers except for your thumb!

It’s really simple and allows you to count up to 31 on one hand!

To make the binary numbers bigger, simply follow the pattern onto the next hand,

Starting with the baby finger of your left hand:

Baby finger = 32

Ring finger = 64

Middle finger = 128

Index finger = 256

Thumb = 512

Incorporating both hands allows you to count to 1023!

What fingers would you hold up to get 444? ?

Albert Einstein’s Genius Routine

The genius of Albert Einstein has been attributed to intelligence increasing techniques he famously used. These were developed over 15-20 years in his life, so his progress was both slow and tedious. The basic things he did to increase his intelligence are detailed below

1. He would engage all his senses when it came to thinking.

In other words, he would think about the taste, smell, touch, sight and sound implications of what he was thinking. Obviously, this is extremely difficult to do in real life, because we don’t tend to think about problems in this way. However, the secret here is that over time, the different areas of the brain associated with the different senses would automatically become engaged without thinking about them to provide more brainpower. So where normally we would use 1-2 brain areas to think about something (e.g visual and logical), Einstein was using 7-8 areas (the senses which are automatically engaged, logical, creativity areas etc), therefore meaning he was literally using more of his brain to solve problems.

2. He made consistent use of visualisation in his thought experiments.

He would see the images in his mind and play about with them with the senses as above. The secret here is that when you see an image in a deep mental state, the subconscious and unconscious minds can take the image as being its own creation, and therefore use their own resources to determine a solution and develop the image. In other words, Einstein developed a strong connection to the subconscious and unconscious minds and used their great mental capacity to solve his problems.

3. He used to sleep a lot.

This is not just any sleep, but targeted sleep with specific goals in mind. Einstein used to sleep for 10-11 hours every night and when you sleep, you are in a subconscious and unconscious state of mind. The greater the depth of sleep, the more connected on awakening you become to parts of the subconscious and unconscious minds. For Einstein, this meant that his creativity, intuition and level of insight was completely abnormal and astronomical. His conscious mind was also made extremely sharp from the level of sleep. Therefore, he was able to have an extremely focused, and sharp mind alongside his strong subconscious connection, allowing him to solve difficult problems with ease.

What To Expect

Einstein’s strategy is simple to read on paper, yet extremely complicated to understand properly why it works. If you use Einstein’s strategy, it will be 5-10 years before you see any intelligence increase. It is therefore ineffective for the 21st century and the type of quick and fast gains you should be looking to accomplish. This is why I recommend using the modified Einstein’s version and combine it with research, so that you can increase your IQ dramatically within a 3-4 week period. The strategy is simple and much better than Einstein’s tedious and slow techniques.

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

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 = 12345678987654321

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

Sequential Inputs of 9

9 x 9 = 81

99 x 99 = 9801

999 x 999 = 998001

9999 x 9999 = 99980001

99999 x 99999 = 9999800001

999999 x 999999 = 999998000001

9999999 x 9999999 = 99999980000001

99999999 x 99999999 = 9999999800000001

999999999 x 999999999 = 999999998000000001

......................................

Sequential Inputs of 6

6 x 7 = 42

66 x 67 = 4422

666 x 667 = 444222

6666 x 6667 = 44442222

66666 x 66667 = 4444422222

666666 x 666667 = 444444222222

6666666 x 6666667 = 44444442222222

66666666 x 66666667 = 4444444422222222

666666666 x 666666667 = 444444444222222222

......................................

About prime numbers

Lines of primes

Prime numbers have fascinated mathematicians for centuries. A prime
number has exactly 2 factors – one and itself. The only even prime is
2, the rest are all odd.

The primes less than 100 are as follows:

2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97

There doesn’t appear to be a pattern in the distribution of primes.

How about the "gap" (spacing) between the primes? Is there a pattern
in that?

1 2 2 4 2 4 2 4 6 2 6 4 2 4 6 6 2 6 4 2 6 4 6 8

There doesn’t appear to be a pattern in the gaps, either.

Spiraling

Stanislaw Ulam was a Polish-American mathematician who was involved in
the Manhattan Project during World War II.

One day he was bored in a meeting and began to write numbers in a
spiral. He started like this, moving in a clockwise direction.

1 → 2 ↓
4 ← 3
The next round continued the "spiraling" pattern, as follows.

7 8 9 10
6 1 2 11
5 4 3 12
He kept going (it must have been a long meeting), then highlighted the
prime numbers and found something interesting.

73 74 75 76 77 78 79 80 81 82
72 43 44 45 46 47 48 49 50 83
71 42 21 22 23 24 25 26 51 84
70 41 20 7 8 9 10 27 52 85
69 40 19 6 1 2 11 28 53 86
68 39 18 5 4 3 12 29 54 87
67 38 17 16 15 14 13 30 55 88
66 37 36 35 34 33 32 31 56 89
65 64 63 62 61 60 59 58 57 90
100 99 98 97 96 95 94 93 92 91
Many of the primes appear to line up when arranged in such a sprial.

Let’s go much bigger and see what happens. We observe there are many
places where the primes form line segments, mostly at 45°, but
sometimes horizontal and vertical.

Why do we care about primes?

Apart from many other things, prime numbers are vital in the
development of encryption algorithms, used in generating secure
Internet transactions.
http://www.squarecirclez.com/blog/lines-of-primes/4260