LARGEST PICTURE FRAME ON THE PLANET

Dubai has impressive skyline with many skyscrapers. How to add one more building that will stand out. Hence a design competition was held. A building design was selected. It is just a picture frame. It owns an award. The idea is: It will frame the landscape of old Dubai on one side and will frame the skyline of modern Dubai on the other side.

The construction took five years (2013-2018). Its height is 150 meters-equal to 45 story building. It is now standing majestically.

An experience:
     The entrance ticket is bit costly.
     After usual security check, we are allowed to enter one of the towers of frame. After short ride in escalator, we were shown some past Dubai. Then elevator took us to the top. We were given a short speech by a guide there. We got a clear 360-degree view of Dubai. The highlight is the glass bridge. One can walk on it and see 150 meters below. It is a thrilling experience. Some people fear to step on the glass, even though it is 100 percent safe. There you can take photograph, as if you were framed by Dubai frame. After viewing, the old and new Dubai on both sides, we go down through the other tower of the frame using an elevator. The elevator also has viewing glass.
    In the ground floor, we were shown a short movie clip which illustrates how the future Dubai is going to be. In future, there may be driver less cars, trains, flying taxis, tube rails and on and on.
     Finally, one leaves Dubai frame with different frame of mind. We understand "the change is only permanent". The man's quest and thirst will never end. Nature does not dominate in Dubai. But science, Engineering dominates. Man have achieved excellence in these fields in Dubai.

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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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