MINIATURIZATION AND MOORE'S LAW

Think of old radio sets made of tube valves. Transistors replaced valves and the radio shrunk to pocket size. Then electronic circuits were replaced by silicon chips. Hence the radio set shrunk further and embedded in smart phone today.

The miniaturization is more pronounced and visible in electronics. but the phenomena happens in all the fields.

Fans, lamps,(CFL, LED), motor pumps, grinders, car engines, fordable umbrella, contact lenses, button cells, phones, speakers(ear phone), clocks, machines and tools and what not. Everything has shrunk.

ADVANTAGES OF MINIATURIZATION
1. It is affordable.
2. Space saving , raw material saving
3. less energy, less pollution.
4. It is portable
5. highly efficient.

MOORE'S LAW
"The law is the observation that the number of electronic components in a silicon chip (integrated circuits) doubles approximately every two years".
The law has been guiding electronic industry for a long time. It is the driving force of technological change, productivity and economic growth.

We experience the Moore's law in our hands. The smart phone has become thin, but its performance has increased many folds. We are able to enjoy a full length movie on the phone screen with great clarity and sound quality.

FUTURE
In the field of nano-technology, machines and tools will be constructed using molecules. For example; nano-car will carry the drug in our veins through the blood stream and will deliver it in the proper location in the body. So miniaturization or even 'microzation' is welcome.

IN A LIGHTER VEIN: If we have broad mind, small cars and compact house is enough for us and good for the environment. The micro blogging site twitter is more popular and read than Tolstoy's great epic 'war and peace'.

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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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