sciencecapsules

         In this essay, let us take some time to wonder about our own planet.      As for as we know, this is the only and lonely planet which sustains life.  When it is looked from the moon, it appeared like beautiful blue marble.  It has little habitable land and more ocean waters.  It shelters wide spectrum of plant and animal life.  It is not like a moon which is a boring and barren land.  It has oceans, dessert, rivers, waterfalls, valleys, farms, vineyards, mountains, forests, lakes and so on.      The earth yields flowers of many colours, designs, and smell.  We can grow sugar cane and hot hot chilli side by side.  It is wonder that the same earth yield so much variety, spice, colours, and tastes.      All the 100 plus  elements in the periodic table can be mined out of earth's surface.  It yields so much iron and hydrogen but little gold and uranium.      Man has discovered, invented and designed variety of buildings, wonders like taj mahal, effile tower, gadg

         Age of universe is said to be about 13 billion years.  It can be estimated using the Radio-activity in a piece of rock.  The entire universe was said to be contained in an atom 13 billion years ago.  An explosion occurred (big bang) and the entire universe was thrown out and started spreading.  The universe continuous to expand even today.      Age of the earth is around 4.5 billion years.  It is born out of sun and belongs to the solar family.  It  has undergone so many changes since its birth.  Even old continents have gone and new continents have formed.      The first man had appeared around 2.5 million years ago.  The first single cell life appeared in the ocean and evolved into intelligent human beings according to Darwin's  theory.      The mutations and environment necessity made us.  We are now dominating the world in using its resources.      Pyramids were built 4500 years ago around 2500 B.C.  Such a large structure built so long time ago; before ma

         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

            Take 4 pieces of triangle shape.  Join and make a closed form.  You get a prism or pyramid form.  It has some properties. 1.  All the faces are triangle (same polygon) 2. Three triangle meet at every corner.  (same number of polygon meet at each vertex) 3. At each vertex, the three internal angles[angle between sides] are 60+60+60=180 degree.  It is always less than 360 degree. 4. They always satisfy Euler's formula No. of faces+No. of vertices- No. of edges = 2    4               +   4                - 6                       =2 This shape is called tetrahedron.  It belongs to platonic solids, named after philosapher plato.  Platonic solids have  the above properties.  There are only five platonic solids in our three dimensional world. 1. Tetrahedron:  3 triangles meet at every corner. 2. Octahedron:  4 triangles meet at every vertex. 3. icosahedron:  5 triangles meet 4. Cube:  3 squares meet 5. dodecahedron:  3 pentagons meet.       Platonic solid

       The observable universe has atleast 2 trillion galaxies in it.  The light takes 93 billion years to travel from one end to the other.      We are living in a galaxy called milky way.  Our nearest neighbour called Andromeda galaxy is 2.5 million light years away.      Alpha centuri is our nearest star besides our sun.  We can reach that star, if we travel in the speed of light for 4.25 years.      The farthest planet in the solar system is Neptune, the diameter of its orbit can be taken as the width of the solar system.  The diameter is about 9 billion km.      The sun is about 150 million km from earth.  The distance from the moon to the earth is only 384400 km.      The international space station which is orbiting the earth; in which men lives  and does experiments, is at the height of 408 km from the surface of the earth.  The height  of the mount Everest is 8488 m or just 8 km.      The average height of man is between 5 to 6 feet.(180cm)  We are lilliputians

      Imagine car moving in a plane surface.  It is moving on a 2-dimensional surface.  Hence it can move in two directions(x and y).  In other words, the car can have 2 transnational motions.  How about rotations?  It can only turn left or right on the surface. It has only one rotational freedom.  Hence one steering wheel is enough to turn the car.      Imagine an air-craft flying in a 3-dimensional air space.  It can have 3 transnational motions (x,y,and z).  It can also rotate about all the three x,y and z axes.  Hence the air-craft also has three rotational freedom.  ( In 3 dimensions only, the number of rotational freedom and the number of transnational freedom equals).      So, an air-craft needs a three steering wheels.  Three wheels are not practically possible.  Hence the joy-stick was invented.  The mechanism of joy-stick is the same as that used in computer games. The stick can move up and down; can move side ways, can rotate.  All the three rotational motions can

   In this game,  You are given only three alphabets M,I,U.  That means, the following are the only valid strings.      MU      UIM      MUUMUU      Rules of the game 1. If you possess a string whose last better is I.  You can add on a U at the end. 2. Suppose you have Mx.  Then you may add Mxx to your collection.  'x' being string in the system. Examples:      From MIU, you may get MIUIU      from MU, you may get MUU      From MUM you may get MUMUM 3. If III occurs in one of the strings in your collection, you may make a new string with U in place of I1I. Examples:      From UMIIIMU, you can make UMUMU      From MIIII, you can make MIU 4. If UU occurs inside one of your strings, you can drop it.     From UUU get U     From MUUUIII, get MUIII          At any point, you can apply any rule which you think as the best for the given situation. Goal :  Produce MU from the starting string MI using the above rules.      Can you make it?  What rule, you w

       We see parabolic antenna everywhere, in mobile towers,  in TV reception at home.  Parabolic mirrors are the main component in space telescope.  Let us see why they bring rays or waves to focus.      In the above figure, the light rays are reflected by the  parabolic mirror and meet at the point F called focus.  Light rays are reflected according to the law of reflection.  The law of reflection works based on the principle that a wave always takes the path of least time.      In the same figure, below the horizontal line, all the rays travel  equal distance before meeting at the focus F (1).  Also all the rays take equal and least time (2).  Only one point F satisfies the above two conditions for all the rays.  Hence all the rays ultimately meet at the focus.  This is the principle for all the focusing devices and also for all the waves likes electromagnetic waves, heat waves, sound waves and light waves.      Let us see another interesting example of focusing.  T

          We know our earth is enveloped by gas atmosphere.  The atmosphere stick to the earth because of gravity.  The moon has weak gravity.  Hence no atmosphere on it.  As the earth rotates, the atmosphere also rotates along with it.  Suppose, you are lifted up in the atmosphere by a balloon, you will be dragged along with the atmosphere and the earth.  As the fish live in water atmosphere, we live in gas atmosphere.  Both cannot breath outside.      Air has the bouyancy like water.  Hence an airplane can glide and float like a ship on the water.  Many times we can see gliding birds.      Sunlight scattered by the atmosphere gives the illusion of blue sky.  No blue sky in the night.  Our atmosphere has 78% of nitrogen.     We inhale oxygen and give out carbon-di-oxide. The plants use carbon-di-oxide for photosynthesis and release oxygen.  This cycle keeps the Eco-system going.  The lungs of a city are parks.      When the air molecules strike a surface, pressure arises.  

1. E = m*c^2 for physics     e^i*pi + 1 = 0 for math      The most important, useful and beautiful formula. 2. e = 2.71... Euler's constant.     i = Root of (-1)     pi = 3.14....     0,1 = integers.      The formula relates all the important five constants in mathematics . Note that all the constants lie around zero. 3. i is the imaginary number and used in complex algebra.  Pi is connected with circle and hence belongs to geometry. e is a exponential function.  It is also the base  of natural logarithm .  0,1 are integers --Arithmetic      Hence the formula connects four diverse fields. 4.    The formula also uses three important mathematical operations.        1. Addition (reverse is subtraction)        2. Multiplication (reverse-division)        3. exponentiation (reverse-root) 5. Meaning - little math     e^i*pi +1= 0     e^i*pi = -1 can be written as e^i*pi = cos pi +i*sin pi = -1              -1 + 0 = -1              -1 = -1 Hence proved.

       We know, when a ray of light travels from air to water, it bends according to snell's law.  Why should it bend?  Why should it follow snell's law?      Say, you are coast guard.  Some one cries for help from the sea.  You want to reach the person as quickly as possible.  Here you have to travel in two media.  1. You have to run in the land (fast). 2. You have to swim in the sea (slow).  Hence you need to find the path of shortest time.  So you will choose to run a maximum distance on the sand; will reach a particular point on the edge of water; than will swim towards the person in distress.      That path will never be a straight line but looks bent.      Similarly, a ray of light travels faster in air, but slower in water and glass.  Hence the light takes a bent path while crossing from air to glass.  This is the principle of least time.  Also called Fermat's principle. (Note:  When a ray hits a water surface normally (at 90 degree), it will not bend

     Draw a right angled triangle of angle 30 degree as shown in the figure.  Let the length of the hypotenuse be 1 unit.      We know sine 30 = opposite/hypotenuse = opposite side/1 unit      Hence sin30 is the length of the opposite side which is 0.5 unit.  Hence sin30=0.5 similarly cosine30=cos30=adjacent /hypotenuse =.87 unit    This ratios sin30 and cos30 holds good for any smaller or larger triangles.  We can find any side of the triangle using these ratios.      We can find the sine and cos values for angles from 0 to 90 degree in this way.  Also they are available in ready table form.  This 'sin and cos' concept is also extended to the angles 91 to 360 degree,  Here, we have to incorporate positive and negative signs suitably (refer).  Now, tan x = sin x/cos x =  opp/hyp/ adj/hyp = opp/adj       When 'sin' is divided by 'cos' ,   the ratio of opposite side/ adjacent side is obtained.  We call it 'tan'. (tangent)     Say, you

         First, we will learn the three logic operations widely used in the Digital electronic circuits. 1. Operation 'AND'      If A=1 AND if B=1, the operation 'A AND B' will also yield 1.  That is, if either one of them OR both is zero, A AND B will yield No result(0). 2. Operation 'OR'      If either A OR B =1; then operation A OR B will output1. 3. Operation 'NOT'      NOT A   means A is simply reversed. (A=1 changes to 0 and vice versa).      Three electronic circuits were built to execute the above operations.  The DeMorgan's laws tells us that just one circuit is enough to execute all the three operations.  Let us see how. Law I :  NOT ( A AND B ) = NOT A   OR  NOT B Law II : NOT ( A OR B ) = NOT A    AND  NOT B Laws says that AND operation can be converted into OR operation with the help of NOT.  Similarly 'OR' can be turned into 'AND'      Let us now select only 'AND' operation.  Combine

   Take a torch light, switch it on in a dark room.  A cone  of light starts from it and falls on the wall. 1. Hold the torch straight, a circular patch of light falls on the wall. 2. Tilt the torch's face slightly downwards, you can see a elliptical patch of light. 3. Tilt the face upwards,now parabola is visible. 4.Tilt the face still more upwards, hyperbola appears.(double curve)  Here the light cone is sliced off by the wall at various angles and the different shapes appear.  All these curves are called conics.      All these conics can be created by a single equation. AX^2+BXY+CY^2+DX+EY+F = 0    Here X and Y are graph-coordinates.  A,B,C,D.E and F are constant numbers.  By feeding suitable values to the constants, one can create any curve belonging to the conic family.  Conics are observed in many motions.      The electrons in the atoms and the planets in the solar system orbits in a circular or elliptical path.      Any body moving under gravity fol