MANY AVATHARS OF MONEY

Long ago, in the absence of money, exchange of goods was in practice. Next came coins made using precious metals like gold , copper. After the advancement of printing technology, paper money came into being and gained currency. Paper money is still holding forte.

Next we had plastic card with our information encoded in magnetic strips. Later the electronic chips were embedded in them. Plastic credit cards ushered in a cash free era. In the computer age money took digital form. That is electronic form. Our bank accounts, balances, deposits, everything were digitized. Instant transferring of money became a reality. Opening deposit accounts, getting credits, payments were a snap. The world was taken over by electronic commerce.

Then, electronic wallets in smart phones. Sending money from one phone to another was possible. It helped even small traders to go digital.

If the ball is passed from one child to another and to another, the children feel happy. Money should flow among the people to keep the economy healthy and people happy. Any system of money should aid easy flow . Digital money aids lot in this direction. Here we should recall "one man's expenditure is another man's income".

Latest avatar of money is cryptocurrency. Example bit coin. It is also a digital money but encrypted in computer coding. So it is purely based on mathematics. There are certain advantages in this type of money.

1. No central bank or government control this currency. You are the sole owner and nobody can freeze your account.
2. It is anonymous. No ID or documents required. Anybody can create a wallet address for the money like bit coin.
3. All transactions are recorded. No unaccounted black money. It is transparent.
4. Money transfers are instantaneous and low fees are levied.
5. It is getting popular day by day. But it is yet to get full legal status.

In spite of all the avatars, hot cash still reigns. Money's value is decided by demand and supply of goods. If the goods are available in plenty or if the goods are highly scarce, the money loose its value. Rapid scientific progress and free availability of all the goods may even make the money obsolete. what "form" money will take in future? The answer is anybody's guess.

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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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