THRUSTING SEVEN SEAS INTO A GRAIN OF SALT

Our sun is a ball of fire. Its flares are extending to thousands of kilometers. It is in the middle life and produces such a enormous energy. It is a small star and all the stars are similar to our sun.

When a star is living it produces light and heat energy through nuclear fusion. That is, by combining hydrogen atoms into helium atoms. When the star runs out of the nuclear fuel, it will die. During the death of a big star, its outer shell will blast off with such a brightness that it will be visible throughout the galaxy even in daytime. This phenomenon is called 'supernova'. Next, star's inner core will get compressed due to gravity. That is, star will collapse under its own weight. It will collapse into a mathematical point called "gravitational singularity". All the mass is concentrated in that point. Hence it will have zero volume, infinite density and enormous gravity.

The influence or the gravitational field of the singularity will extend to certain radius or to a certain circular area around the point mass. The boundary of that area is called 'event horizon'. Anything, even light that reaches event horizon will be sucked in by huge gravity and will never return. This dead star is called "black hole". No light returns, so it is black. Everything falls inside, so it is a hole.

A star with the mass of our sun may become a black hole of 3 km radius. A star with the mass of earth may become palm sized black hole{hypothetical}. Our sun will never become a black hole because it is a small star.

At the center of our milky way galaxy, there is a super massive black hole with the mass of 4 million suns. Our universe is born from such a singularity.

If you read somewhere that a mountain can be converted into an ant, it may not be a 'cock and bull' story.

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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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