WHY THE MOVIE IS SHRINKED IN TV AND MOBILE

Take an A4 paper. Measure length and breadth. It will be 297 mm and 210 mm. 297/210 gives 1.414. This is the square root of 2. We can also say, the A4 paper has the ratio 1:1.414. For any A series paper, we always get this ratio. We know, if you cut the A4 paper into halves, we get two A5 papers. If you double -up the A4 paper, we get an A3 paper. This is the concept of A series paper.

Why should we maintain a fixed ratio? Suppose you want to photocopy the contents in the A1 paper to A5 paper using Xerox machine. The contents will exactly fit in the small A5 page. This is because of the constant ratio of A series papers. If we do not maintain the ratio, the contents will either over-fit or underfit. That is, either some contents will be left out or blank space will appear.

When a movie is telecast in the TV or streamed in the mobile, a black space appears at the top and bottom of the screen. It is because of mismatch of ratios. Mobile and TV screens have an aspect ratio of 16:9. But a movie is shot in the aspect ratio of 2.35:1. That is the reason.

Tele serials are shot in the ratio 16:9. Hence they are clearly displayed on the screen. In the case of picture and movie, landscape and rectangle always have the appeal.

Old TV had the ratio 4:3 or 16:10. 16/10 gives 1.6 which is the golden ratio given by Fibonacci sequence.

Note: All the countries have flag and flag-code. The flag-code specifies the aspect ratio. Many countries and India have the ratio 3:2 and standard sizes. A national flag should strictly adhere to the ratio and the code.
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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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