MIRACLE WILL HAPPEN IN YOUR LIFE

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Some years ago, British illusionist Derren Brown performed a feat that you might call a miracle. In front of a camera, using a fair coin, he flipped ten consecutive heads. The footage was not edited, there was no sleight of hand. The general public was baffled.

Later, Brown revealed his secret. He knew that the probability of throwing ten consecutive heads is 1/1024. (Law of large numbers)

probability of getting one head =1/2
Probability of getting ten consecutive heads.
1/2*1/2*1/2*1/2*1/2*1/2*1/2*1/2*1/2 =1/1024

This means that once in every 1024 attempts you would expect to get 10 consecutive heads. Derren Brown tossed a coin for nine hours and filmed it continuously. He initially broadcasted just the last minute of footage, giving the viewer the impression that he had flipped ten consecutive heads on his first attempt. Today, this process can easily be simulated in computers and results can be verified. This proves that persistent effort will make a miracle happen.

Suppose you want to buy 65 inches OLED TV. At the moment, you do not have the required money. But you keep on exploring various models of the TV and its prices. You also continuously explore your financial situation and EMI schemes. One fine morning, you get a solution and the TV will arrive at your doorstep.
This process can be applied to buy a diamond necklace, get a good job, or enroll in a good college.

A miracle happens, when you try, try, and try without losing patience.
Thomas Edison tried 1000 materials before finding tungsten filament for the bulb. It gave light to the world for nearly 100 years.
The great Tamil poet Thiruvalluvar says,

"Even if God fails to help, your perseverance will yield fruit".

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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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