TURNING MINUS INTO PLUS

We know, minus multiplied minus yields a plus. It is difficult to explain the logic behind it. But there is a fun way to explain. If you are my enemy(pardon me), your enemy is my friend. That is enemy's enemy is a friend.
We will see some real life examples. If you owe a bank 3 dollars, it is indicated in your account as the - 3 dollars. If 3 dollars is due to you, from bank it is indicated as +3 dollar.

So, Owe = -
due = + (for our understanding)

The bank credits some money to your account. It is a positive operation. The bank debits some money from you. It is a negative operation.

So, credit = +
debit = -

Suppose, the bank debits 2 times from your account. Each time 3 dollars that you owe to the bank. This operation can mathematically written as

2 debts * 3 dollar -owe = amount
-2 * -3 =+6
only if you credit real 6 dollars, the account will get the old balance again. That is why minus times minus is a plus.

In physics, the signs indicate mainly direction.

When a body is moving up against the gravity , the g = 9.8 is taken as negative. When it is falling down, 'g' is positive.

When a current is going clockwise direction in a circuit, it is positive current. When the current goes anti-clockwise, it is negative.

Suppose in an electrical circuit, battery sends a current in anti-clockwise direction. Here both current and battery's voltage are negative.

-voltage*-current
-v*-I=vI= electrical energy.

The workdone and electrical energy in the circit must be positive. Hence '-' * '-' = ''+' holds good again.

The minus and plus makes things clear and life easier.

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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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