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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THE EARTH, A SUPER ORGANISM

JOIN MY COURSE: "Become a programmer in a day with python" A man called 'love lock' (what a name) proposed a theory called Gaia theory, named after Greek Goddess. It says, "Earth is a self-regulating organism like a human being. The organic life in it interacts with in-organic matter and maintains atmosphere, temperature and environment". Hence the earth is still suitable for the life to thrive. Imagine, in a particular place, there are lot of flowers. Some flowers are white and some are darkly coloured. We know, white reflects light and heat while dark absorbs the same. White flowers can thrive in hot climate. But dark flowers requires cold climate. The absorption and reflection balances and the environment reaches average, warm temperature at which both the flowers can co-exist. This is the essence of "Gaia" theory. On our earth, the oxygen constitute 20% of the atmosphere. The oxygen level is always mai

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

DISORDER IS THE "ORDER OF THE DAY"

Imagine a balloon full of air. The air molecules are moving randomly inside the balloon. Let us pierce the balloon with a pin. The air rushes out. Why should not the air molecules stay inside the balloon safely and ignore the little hole? That is not the way the world works. The molecules always "want to occupy as many states as possible". Hence the air goes out in the open to occupy more volume. The things always goes into disorder (entropy) and the disorder increases with time. The above statement is what we call "second law of thermodynamics". Consider a cup of coffee on the table. Suppose the heat from entire room flows to your cup of coffee, the coffee will boil and the rest of the room will freeze. Freezing means bringing things to order and arrangement. It violates the second law. Hence it will never happen. Hence heat must flow from high temperature to low temperature and not the other way. The air molecules in y

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