ATOMS OF MATHEMATICS

Consider this,

6= 2 * 3
9 = 3* 3
12 = 2* 2* 3

The kind of numbers like 6, 9, 12 are called composite numbers because they can be broken down into smaller numbers.
But numbers like 2, 3, 7, 11 cannot be split up into whole numbers. They are divisible by 1 and by themselves only. These numbers are called prime numbers. They behave like "atoms" in the number system. We can build other composite numbers using them in an unique way. For example, 28 can be expressed as 7 * 2* 2. This is the only way to write 28 using primes.
Another example:6545448 = 2^3*3^5*7*13*37

The list of prime numbers below 100 is given below.
2, 3, 5, 7, 11, 13, 17, 19, 23 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
There are 25 primes between 1 and 100. But only 14 primes between 900 and 1000. There is no formula to find the prime numbers. There is no pattern in the appearance of primes. Yet, the umber of prime numbers are limitless. The largest known prime is 2^24036583-1.

There is rough formula to calculate the number of primes up to N.
Number of primes = N/log N (log of base e)
This formula is also called prime number theorem.

There is one prime use for prime numbers.
Multiply to 2 large primes and release the product. It is very difficult to extricate the 2 primes from the product and the process will consume lot of computer time.(try to get back 2 primes from 8633- a toy problem)
This principle is used in public key cryptography(sending secrets in open channels). Example: Credit card transaction.

Final note: I said the prime number 5 is unbreakable. Please allow me to correct myself now. 5 can be split up into integer complex numbers as follows.

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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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