NO SIGN BOARDS IN THE OCEAN

Landmarks are called landmarks because they are found on the land. Then, how to navigate in the ocean. Today, we have electronic GPS devices with satellite connections. How seafarers survived in those days? That is why, they built light houses everywhere. Let us assume that there is a ship standing in the sea and there are two light houses L and M, on the land separated by 14 miles.

A sailor in the ship takes the bearing (angle) of the two light houses using a device. One light house is 30 degrees to the left of straight-on and another 15 degree to the right.
See the figure. The angles A and B are calculated as 76 degrees and 60 degrees using the properties of triangle.

Using trigonometry,
14 miles = d/tanA +d/tanB
14= d(cosA/sinA +cosB/sinB)
14 = d (sin(A+B)/sinAsinB
d=14(Sin76.sin60/sin (76+60) =16 miles.
The ship is 16 miles straight from the land. This method is called triangulation. It is used in survey, GPS systems etc.

During night in mid-sea, no landmark is visible. Sailors had to navigate using moon and stars. Say H is the angle between horizon and the moon. Then the ship is at a distance 60*(90-H) nautical miles from the place where the moon is straight overhead.
Astronomers published almanacs listing the positions of moon and stars to help navigators.

    By looking at the crescent moon, you can find the direction north or south.  From the tip of its horn on top (pointed end), draw a line to its second horn in the bottom. Extend the line, till it touches the horizon. That point is North, if you are in the southern hemisphere of earth and vice versa for others. This method is mostly correct and not perfectly correct.
    Seafarers explored, invaded, conquered, traded using this technique before the advent of sophisticated electronic devices. Salute the man's endurance.

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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 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. ...

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 ...

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