EVOLUTION OF BOOK

The books are always the source of knowledge for the mankind. The historical town of Alexandria is known for its great library. Whenever a ship arrived at the port of Alexandria, people searched for the books. Those people loved the books so much.

we have seen hand-written magazines circulating in hostels, class-rooms etc, a few decades ago. Printing industry brought in big revolution in the distribution of books and magazines. Harry potter books are hugely sold-a recent revolution. The great epics like ' war and peace', gone with wind' started their journey in book format. We cannot imagine subjects like, math, physics, chemistry without books.

Those days, books were sold in small and big shops in towns and cities. They had limited number of books on some subjects in their shelves. We had to select from them. That is no big deal or choice.

Than, the online shop 'Amazon' made its 'debut' by selling printed books. Now the consumers can search through millions of books; select a little and buy from anywhere. The book selling moved to another level.

Next came, E readers, Tablets, smart phones etc. The books were digitized-made into electronic form. The books can be bought and down loaded immediately. Hundreds of books can be stored in the device or in the cloud. It saves the space in a home and no book-shelf to gather dust.

In the electronic devices, the font size, brightness can be adjusted. One can get the meaning of a word online immediately and read without light without glare in 'Night mode'. E books are boon to elders and somewhat cheaper. Above all, one can carry a library in their pockets. The latest is audio books. one can listen to the books for hours while walking, cooking, driving. The 'speed of reading' can be adjusted. Now, any one is able to consume lot of books.

In the electronic era, there are some new concepts like 'Renting a book'. returning a book, exchange of books, instant publishing, subscribing to unlimited e books or audio books, buying high pierced books through EMI. Truly, a golden period for book lovers.

It is going to be exciting to see, 'what is next' in the evolution of books.
Long live books.
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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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