FLAVOURS OF NUMBERS

100, 1100100, 64,25

all represents the number hundred in different numerical languages.

We count the minutes as 1,2,3...60 and mark it as one hour. Again we start counting the minutes from 1. So the minutes and seconds are having the base of 60 or radix 60. We count the inches 1,2,3 ....12 and mark it as 1 foot. It is having base 12.

In our day today life, we use numbers of base 10. (tenary numbers or decimal numbers)
We are used to this 10 number system and very comfortable with it. But a number system can have any base.

Unary numbers uses only one digits.

1-----l
2-----ll
3-----lll
4-----llll
You know using this unary numbers is highly difficult.

Next we have binary numbers using only two digits.
0,1,10,11,100
These numbers are widely used in all digital devices. the signal like voltage and current can either represent 0 or 1 and not anything in between. Hence the digital data cannot be corrupted and hence we gaga over digital devices.

Next we take up the numbers of radix 16 called hexadecimal numbers.

In this system we use alphabets also. As you can see, it is very compact. It can be represented by 4 binary digits. Hence hex. numbers are preferred notations in representing colours in a digital display.
Number system having bases 8 and 36 are also popular.

Tenary 10 means 10 (usual numbers)
binary 10 means 2
hex. 10 means 16.
Like words the numbers also have different shades and meanings depending on the context.

Devise your own number system to code the playing cards.

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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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