HOW MANY SECURITY CAMERAS YOU REQUIRE?

We have a museum housing valuable antiques. We have a gallery of highly priced or priceless paintings. We have a mall of many showrooms. How to guard them all? How many guards we require? How many CCTV cameras required? A bit of math will help here.

Suppose an exhibition has triangular stalls. Each stall can be guarded by one man because he can easily have a look at the three walls. Hence the formula is,
No. Of guards = whole number part of No. of walls / 3

We know a square hall or rectangular hall with four walls can also be looked after by a single man. Many art galleries and museums have many corners turning at right angles (90 degrees). These galleries can be divided into rectangular halls.
Hence No. of cameras required = whole number part of (1/4 * no. of corners)

Suppose, a mall is made up of a number of rooms. And two rooms have a common door. Then a man standing at the door can watch two rooms at a time. For example, a train may have one guard for every two compartments.
No. of watchman required = 1/2* number of rooms.

A polygon (like a pentagon) shaped hall which has corners outside can be watched by a single person. A star like a shape which has corners inside requires more manpower.
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THE EARTH, A SUPER ORGANISM

JOIN MY COURSE: "Become a programmer in a day with python" A man called 'love lock' (what a name) proposed a theory called Gaia theory, named after Greek Goddess. It says, "Earth is a self-regulating organism like a human being. The organic life in it interacts with in-organic matter and maintains atmosphere, temperature and environment". Hence the earth is still suitable for the life to thrive. Imagine, in a particular place, there are lot of flowers. Some flowers are white and some are darkly coloured. We know, white reflects light and heat while dark absorbs the same. White flowers can thrive in hot climate. But dark flowers requires cold climate. The absorption and reflection balances and the environment reaches average, warm temperature at which both the flowers can co-exist. This is the essence of "Gaia" theory. On our earth, the oxygen constitute 20% of the atmosphere. The oxygen level is always mai

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

DISORDER IS THE "ORDER OF THE DAY"

Imagine a balloon full of air. The air molecules are moving randomly inside the balloon. Let us pierce the balloon with a pin. The air rushes out. Why should not the air molecules stay inside the balloon safely and ignore the little hole? That is not the way the world works. The molecules always "want to occupy as many states as possible". Hence the air goes out in the open to occupy more volume. The things always goes into disorder (entropy) and the disorder increases with time. The above statement is what we call "second law of thermodynamics". Consider a cup of coffee on the table. Suppose the heat from entire room flows to your cup of coffee, the coffee will boil and the rest of the room will freeze. Freezing means bringing things to order and arrangement. It violates the second law. Hence it will never happen. Hence heat must flow from high temperature to low temperature and not the other way. The air molecules in y

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