SOLIDIFYING THE CONCEPT OF NUMBERS

First, will understand, why we have numbers. Say, you are the manager of a restaurant. People sitting in the table order for 4 burgers. In the 'numberless world' , you will pass the order to the kitchen by calling out 'burger, burger, burger, burger'. We know saying 'four burgers' is easy. Four is a number. So, numbers are a shortcut for counting by ones'. Number is abstract form. Four may mean four butterflies or four stones. Numbers are concepts like beauty and intelligence.
Let us use pebbles to represent the numbers. Four can be arranged into 2*2 square form. Take 8. It can be represented by 8 pebbles arranged into 2*4 rectangular form. Many numbers can be represented by a square or a rectangle formed using pebbles. Examples 6,8,9,10,12,14....
But some numbers cannot be made into rectangle. Example 1,3,5,7,11..... These numbers which cannot subdivided into other numbers are called prime numbers. The prime numbers are 'atoms' of the number world. We can construct any number using them. How many prime numbers are there? Is there a limit for prime numbers? We do not know the answer.
Numbers should have base. We use numbers of base 10 (0.....9). Clocks use numbers of base 60. Computers manipulate binary numbers (0,1) of base 2. Base 16 numbers are also used in electronics. Even you can create your own system of numbers, if need be.
Let us solve one simple problem using pebbles to represent numbers.
Sum the numbers from 1 to 10. The answer is 55. No wonder. Let us solve it in a different way.

Put one pebble for number 1 in the first row. Put two pebbles for 2 in the second row. Repeat the process up to number 10. You will get a right angled triangle. That is half of a square, cut along the diagonal. Fill the missing 'half' with pebbles. You get 10*11 matrix of pebbles. Total elements (pebbles) in the square is 110. Half of it is 55. Hence the answer sum is 55. Hence if you picture and solidify the numbers, you can easily attack the numerical problems.
Numbers are the foundation on which Fort of mathematics is built.
-----------------------------------------------------------------

Comments

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 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. ...

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 ...

sciencecapsules

Search This Blog