EVERYTHING WILL BE FREE AND ABUNDANT IN 2076

In this information era, many things have become cheaper and almost free. Access to movies, music, books, magazines, articles, information have become cheaper. Publishing and distribution of all the above have become free.

Voice calls and data are getting cheaper by the day. Remember the "telegram" days when we paid for each word to be sent. Now sending even video is free.

Mails are free. Storage for our documents are free. Creating tools like photo editor, video editor, drawing tools, music creators, blog tools etc, are free.

Today we have 3D printer in which molten plastic is used to mould objects of our choice. Plastic comb, footwear and a pet house have already been fabricated.

Experts forecast: In future we will have what is called "molecular assembler" controlled by a computer. It can fabricate food, drugs, cloths, tools etc., in your home itself. You can get anything on demand and further they will be cheaper. So we may move into the future of abundance and scarce free age.

Our economy is based on scarcity. It is driven by demand and supply. This scarce free era will have a great impact on economy. The meaning of money will attain in new dimensions.

Few years back, we paid thousands for new telephone connections and hundreds for the calls. To day they are almost free. We are now buying medicines for thousands. Tomorrow we may make our own medicines in our homes using cheap basic raw materials.

We do not know what the future has in store. Hence we should always be humble.

"Time, tide and change will wait for no man".

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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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