WHY WE HAVE TWO EYES?

Photos lack depth perception. The above photo clearly illustrates that. Because the photos are shot with a single eye or lens

. We have two eyes separated by a distance of 2.5 inches. The two eyes see the same scene or object in two different angles. Hence two slightly different images fall on the retina of the eyes. Brain process these images and gives the depth perception or third dimension.

Thousands of years back, we required two eyes for hunting and to escape from wild animals. Today, we require depth perception for crossing a busy road!! Only using two eyes, we can estimate the distance of approaching vehicles and take a decision to cross the road.

Consider the birds like chickens and pigeons. They have two eyes, one on the left side and the other on right side of the head. Hence they get a 360-degree view of the world. It will help them to easily escape from predators. But there is a price to pay. They lack binocular vision like us and lose depth perception. To overcome this drawback, the birds always bob their heads. When they move the heads up and down, they get two images. These images are processed by the brain and give them 3D -effect.

Similarly, two ears give us depth perception in sound. You can tell where the 'cry for help' is coming from, front or back, left or right.

Meanwhile - enjoy 2.0 -3D.
Some people say we do not use the depth perception as much as a caveman (like Tarzan hoping from tree to tree). Hence, evolution may wipe out our two eyes. Instead, we may get a single eye at the centre of the head.
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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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