ELECTRONIC SPACE

Do you think we have abundant storage for information?. Let us find out.
We know 0 and 1 are called binary digit or bit. With one bit we can represent two numbers 0,1. With two bit we can represent 4 numbers.

Binary Decimal
0 0 0
0 1 1
1 0 2
1 1 3
With 32 bit, the maximum, positive value we can represent is 2147483647.

Those days we had only 32 bit computer system. To maintain time, the computer has to count seconds, hours and days. The old computer can count up to that above number. Than it had to start from zero.

Once, in USA air-traffic control room, the people failed to notice the computer count had reached the maximum. So they had not reversed it to zero. The time in those computers came to a stop. And the air traffic was thrown into disarray for a few hours.

Today, we have 64 bit, 128 bit computer systems. And we have fairly enough electronic space.

Now we are able to appreciate why clocks are circular? The needles can go round and round and from beginning again and again. A clever use of physical space.

The digital picture quality goes on increasing. HD - high definition. UHD - ultra high definition. Hence we require more and more electronic space or electronic memory. The smart phones RAM (Random access memory) goes on increasing. Once we measured memory in mega bytes; To day in Gigabytes; Tomorrow in tetra bytes. 300 hours of video are uploaded in youtube every minute. Imagine how much memory they require in their servers.

We created more data in the past 2 years than in all of preceding history. We are now facing storage problem. The human DNA stores more efficiently than the electronic memory.

Scientists say, they can store ( if experiment is successful) . 215 petabytes of data (215 million giga bytes) in a single gram of DNA. In principle, we could store every bit of data ever created by humans in a single room. Hope we will see that day.

Think of those prehistoric days when people passed every bit of information from generation to generation only through oral communication and the storage was only their brains. We have come a long way.
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LISSAJOUS FIGURES

Definition: "When a particle is subjected to two sine wave motion or two oscillatory motion at right angles, the particle describes lissajous figures". We know sine wave motion and circular motion is basically same. Hence we draw two circles A and B perpendicular to each other. The circle B rotates twice faster than circle A. That is, frequency of circle B is two times than that of A. A particle at the intersection of two circles is subjected to two sine wave motion A and B at 90 degree simultaneously. The particle will describe figures depending on the frequency and phase of A and B . In our case, the ratio of frequency is 1:2 and the two waves are in phase. To draw lissajous figures : A moving point in both the circles are chosen. Here we should remember; during the time taken by the circle A to complete one rotation, circle B completes two. Hence the points are marked on the circles according to their speed. Then straight lines

THE PARABOLA

A jet of water shooting from a hose pipe will follow a parabolic path. What is the so special about parabola. Y= x^2 Draw a graph for the above equation. It will result in a parabola. This parabola is also called unit parabola. Any equation involving square will yield a parabola. Example: Y = 2x^2 +3x+3 (also called quadratic equation) X= 2 and -2, both satisfies the equation 4 = X^2. Parabolic equations always have two solutions. Any motion taking place freely under gravity follows parabolic path. Examples: An object dropped from a moving train, A bomb dropped from flying plane, A ball kicked upwards. If a beam of light rays fall on the parabolic shaped mirror, they will be reflected and brought to focus on a point. This fact is made use of in Dish Antenna, Telescope mirrors, etc. Inverted parabola shape is used in the construction of buildings and bridges. Because the shape is able to bear more weight. A plane

CASINO'S GAME

Let us find out how the casino survives with mathematics. Say, your friend invite you for a game of dice. You must bet (wager) 2 dollars. If you roll 'six' you will get back 8 dollars. The game will go on for 30 rounds. All sounds good. The probability of rolling 'six' is 1/6. Since the game will be played for 30 times, the 'expected win' is 30*1/6 = 5. That is, you are expected to win 5 rounds out of 30. Hence your gain will be 5 * 8 =40 dollars. ok. This also implies that you will loose 25 rounds. Hence your loss will be 25*2 =50 dollars. Your net gain will be gain-less = 40-50 = -10 dollars. For 30 rounds, the loss is -10 dollars, Hence, for one round =-10/30 = -1/3 dollars. There will be a loss of -1/3 or 0.33 dollars per round. It is not a fair game. Let us make a simple formula to calculate 'Pay out per round\. The probability for a win = p The pay-out in case of win = V No. of rounds = n The expect

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