SMALLER THAN THE SMALLEST

A needle point, we may be able to observe by naked eye. The bacterium is comparable to the needle point. It can be observed clearly using microscope. It"s size ranges from 0.5-5*10^-6 m (micrometer). There are good and bad bacteria. The diseases caused by bad bacteria can mostly be treated with the antibiotics. Also, the bacteria can be filtered out by 'reverse osmosis' etc,.

Next we have virus in the size of 20 to 400 nano meters( 10^-9 m). They are the smallest life on the planet. There are no good viruses. They cause common cold to AIDS. Their symptoms can only be treated. The body should have good immunity to survive.

Bacteria and viruses are made up of cells which in turn made up of molecules and atoms. The molecules are in the order of nano meter. So the nanotechnology means technology based on molecules.

One water molecule is made up of one hydrogen atom and two oxygen atom. Size of the atom is around 10^-10 m . Hydrogen atoms are the most abundant in the universe. They are also the simplest atoms just containing one proton and one electron. The size of the proton is about 10^-15 m.

Next, down the line; We come to electron which is the smallest thing we can play with. The radius of the electron is estimated to be 3*10^-15 m. The size of subatomic particles are not sharp. They are "fuzzy and wavy" according to physics.

Next the neutrino. This particles strike the earth continuously from the cosmos. They are the lightest. Their mass is less than one millionth that of electron. Since they are unimaginably small, they pass easily through all the materials including our body.

What is the smallest length we can measure? It is Planck's length or Planck's constant which is 1.6*10^-35 m. Below this classical physics breaks down. No instrument ever can be built to measure the length smaller than Planck's constant.

Planck's time is the time taken by the light photon to travel the Planck's length. It is 10^-43 second. It is the smallest interval of time we ever able to measure.

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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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