SMART PHONE FROM SAND

Your smart phone mainly made up of pure sand-silicon. Yes, It is true. Mostly life forms are carbon based. But the electronic gadgets are silicon based (Today). Life forms are made of cells. But electronic goods are made of 'transistors'.

What is transistor? It has three parts Emitter, base and collector. We can give input signal (voltage) to any pair (eg: base and emitter) and get output voltage from another pair(emitter and collector). One can control output voltages using tiny input signals. Hence amplification is possible in it. Transistor can be used as a switch (ON and OFF ) . Hence Binary numbers (0 and 1 ) can be stored and manipulated by transistors. Transistors are found in thousands or even in millions in many electronic devices. Computers, internet, smartphone, Automobile electronics, Medical electronics, all made possible because of tiny transistors. Today transistors are hair-thin. Transistor is mainly made of silicon(sand), little boron and a little phosphorus. Transistor act by controlling the flow of electrons. Transistor can also be compared to a value in a water pipe. Before the invention of Transistor, vacuum tubes were used. They were bulky and consumed lot of electrical energy. (Long back, A crude computer was constructed using vacuum tubes ,switched on and the entire city voltage dropped).

The main electronic elements like transistor, Resistor, capacitor, inductor can be made using silicon. Hence it is possible to construct or fabricate entire electronic circuit on a thin silicon wafer. That is microchip. Today complex circuit with millions of electronic components is fabricated on a nail sized silicon wafer. Hence today's electronic gadgets are compact, powerful and cheap. Think, how many gadgets the smartphone made extinct.

Tomorrow, the transistor could be a few atoms thick. DNA may replace silicon memory, High level quantum physics will play some role in electronics.
Anyway, clever use of sand, invention of transistor, design of microchip brought in information and technological revolution.
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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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