DISTANCE: LIGHT YEARS TO MICRONS

The observable universe has atleast 2 trillion galaxies in it. The light takes 93 billion years to travel from one end to the other.

We are living in a galaxy called milky way. Our nearest neighbour called Andromeda galaxy is 2.5 million light years away.

Alpha centuri is our nearest star besides our sun. We can reach that star, if we travel in the speed of light for 4.25 years.

The farthest planet in the solar system is Neptune, the diameter of its orbit can be taken as the width of the solar system. The diameter is about 9 billion km.

The sun is about 150 million km from earth. The distance from the moon to the earth is only 384400 km.
The international space station which is orbiting the earth; in which men lives and does experiments, is at the height of 408 km from the surface of the earth. The height of the mount Everest is 8488 m or just 8 km.

The average height of man is between 5 to 6 feet.(180cm) We are lilliputians in the world of cosmos. But we are giants in the world of atomic particles.
Three grains of table salt stacked together adds upto 1 mm in length. Hence each grain length is 0.3mm.
The size of virus range from 20 nano meter to 250 nano meter. (10^-9 m = 1 nano meter)
A virus is hundred times smaller than bacteria. It can only be seen by electron microscope.

Everything in this universe is made up of atoms. They are million times smaller than the human air. The sizes range from .1 to .5 nano meter.
The nucleus which is present inside an atom occupies only a width of 10^-15 m. The nucleus occupies only a tiny space in the atom. Atom is mostly empty with electrons revolving here and there. Similarly inter-planetary space is mostly empty with planets revolving here and there. We can now understand that all the matters in the universe can easily be contained in an atom. That atom pregnant with universe was present before the big-bang-the birth of universe.

The longest distance can be measured using the time taken by the light waves to travel. The very tinyest distance can be measured by using the electron waves in an electron microscope.

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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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