PLEASE RUN TO STAY WHERE YOU ARE

There is a popular book by name 'who moved my cheese'. It is just little booklet. The central point in the book is: 'The block of cheese will be moved now and then, the cat should be always ready to go that extra mile'. Meaning: the world will change continuously, the people must adopt and update themselves continuously.

Let us take the example of music industry. Long, long ago, music means live concert only. Then it was recorded and played on a disc using vibrating needle. Next music was recorded on a plastic tape using magnetism. It was compact than a disc. Earphones came. It helped us to listen music without disturbing others. Next music was recorded on a CD using pits and pumps which were etched by laser. Pits and bumps represents zeros and ones using which music is coded. Now,music is digitized.
Next silicon chips (electronic memory) stored music. Now, 'apps' streams desired music to your smart phone. The 'app' also recommends songs based on your taste.
Cassette tape, record player, CD, DVD, walk-man all have gone. But FM radio is still surviving. Now we have 'radio like box' which has in store thousands of songs. Any song can be searched and played.
That is the rapid evolution of music industry. Many top players in the 'music arena' have their own app. What is next?

Knowledge increases with time in every field. Today a simple professional requires more knowledge than a man who was called expert 20 years ago.

Many carriers have gone. New jobs have born. Artificial intelligence, information technology, bio-technology, block chain will revolutionize the way we live. Tomorrow computer software (algorithm) will take decision about giving loan in a bank; will allot a college seat; will drive car.

People used to say; teacher is a learner throughout his life. Today, everybody is learner and learning is a life long process. Using a smart phone is a basic skill required today like reading and writing.

To retain your position in the society and in the office; to earn money, to get elevated.
Learning, re-skilling, specializing , adopting, all required.

Just remember, even our 'mornings' have changed. Usually, we are greeted with milk pocket, news paper and radio or TV programme. Today, we have milk pockets which stays fresh for 90 days, digital news papers,and whatsapp messages.

So do not fall behind, run till the end.
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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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