STRENGTH OF PASSWORD

First, let us take a 4-digit PIN. Let us also assume that a man is attempting to steal it. To get the first digit right, he has to try all the 10 digits (0--9) and 'one' will be correct. So the chance of getting correct first digit, is 1/10. The ' Multiplication rule in probability' says that the chance of getting all the four digits right is 1/10*1/10*1/10*1/10 = 1/10000. It means, if he makes 10000 tires, at one instant he will get the correct PIN. But the bank allows only 3 tries and limited time. So the PIN is safe as long as you keep it safe.

Now our financial transactions depends on the password. Let us see, how to strengthen the password.

Let us consider a 7 character password which can take alphabets and numerals. The total number of characters is 26+10= 36. The chance of getting any one character right is 1/36. As usual, the chance of getting all the seven characters right is 1/36*1/36*1/36*1/36*1/36*1/36 *1/36 = 1/36^7 = 1/ 78364164096. So the chance getting correct password is almost negligible. If you increase the length of the password and add more special characters to the password, its strength increases. It is difficult to break it.

The mathematics behind the PIN and the passwords is strong. So handle them with confidence and care. An example : STRONG password @2018.

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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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