sciencecapsules

    Is it always A*B =B*A? yes.  4*3= 3*4.  It is elementary.  The multiplication said to obey "commutative law" in math.  It can be easily proved. Draw the dots as given below.                                                      0  0  0                                                      0  0  0                                                      0  0  0                                                      0  0  0      It is 4*3 matrix -(4 rows and 3 columns).  Totally 12 dots.  Just rotate the page by 90 degrees.  We get 3*4 matrix.  But the total dots are 12 only.  Hence A*B=B*A.      Say, you are shopping for a pair of jeans.  The price is 50 dollars.  But there is 20% discount.  And you have to pay 8% tax also.  A smart salesman may tell you "I will add the tax first and apply 20% discount on the total so that you will get more savings.      Now we will do the calculation the salesman way,               price 50 dollars               8% of tax 4

      "The greatest shortcoming of the human race is our inability to understand the exponential function". said a great physicist.      This can be illustrated by a simple story.  Once a king a offered a reward to a poet.  He asked the poet what he desired to have?  The poet replied,"chess board filled up with grains".  The king exclaimed,"what"?.  The poet said, "I want a chess board filled up with grains in this way.  Put one grain on first square, two on second square, four on third square.  Every time double the number of grains and fill up all the 64 squares".  Anyway, the king ordered the servants to carry out the poet's wish.      Half way through the process the numbers exploded.  The king realized the reward could not be fulfilled even if he used all the grains in the kingdom. That is the power of exponential function.  Here the function is  Y =2^x,   2^0=1, 2^1=2,  2^2=4,  2^3=8.......2^64= 1.8 followed by 19 zeros    

        We have so many style of fonts in any language.  They are easily scalable.  Their file size is very small in kilo bytes.  How is it possible?  Let us explore the interesting idea that create fonts.      We know how to plot a point in a graph and how to draw straight line.  Two points are enough to make a st.line.  Every line has a slope  m.  Slope is found by dividing the ,rise, of the line by 'run' of the line.  The 'rise' is change in Y-coordinate between two points.  The 'run'is change in X-coordinate. Let the point be X1, Y1 Than the equation of a line is Y-Y1 =m(X-X1) our case:      Slope of the line given in the figure is m = rise/run = 8 - 3/6-1 = 5/5=1 using slope and one point we can write the equation of a line slope = m=1 point = (X1,Y1) = (6,8) so Y-8 = 1(X-6) Y-8 = X-6 Y=X-6+8 Y=X+2.  This is the equation of the line.  The short segment of line can be written as Y=X+2, from X=1, to 6 Hence, to draw line, we do not nee

       A table of numbers is a matrix example:    1 2 3                    4 5 6                    7 8 9 A image is made up of number of dots or points or pixels (picture elements).  The rows of dots can be represented as matrix. example 111 112 114 ...                200 210 215 ....                98 97 96 ...                -- --     --  ...                --  --    -- ...     It is a representation of grey scale image. Here, each dot is given some value from 0 to 256.  0 means dark, or black, 256 is bright or white.  Hence, we have converted an image into set of numbers in matrix I.      If we multiply each number in the matrix by a factor like 1.5, (called scalar multiplication), the values will increase and the image will brighten up.  If you multiply by 0.6, the image would be dimmed.  Now, we are able to control the image with mathematical operations.  The scalar multiplication is written as 1.5 I or 0.6 I. COLOUR IMAGE      Using three primary colours na

         Why your washing machine spins rapidly to dry your clothes?  Let us find out      Think a rotating body.  A force called centripetal force must act to keep the body in rotation.  That is a constant force but its direction keeps-on changing circularly.  So the acceleration is always present in a rotatory motion.  More speed means more acceleration and more force[F = ma].      We know, ' acceleration' due to gravity is 9.8m/s^2.  A force which give rise to 9.8 m/s^2 acceleration is called one 'g' force.         Centripetal force acts from the body towards the centre.  An equal reaction force[centrifugal force] acts from the centre towards the body and tries to push the body away. Hence by spinning a body at the right speed, one can create the centrifugal force of any 'g' value.      The spinning earth gives rise to centrifugal force.  That force pushes the earth from inside and makes it bulging.  Hence earth looks more like an apple then like

        How some sites like "okcupid" find your 'match' or 'would be', mathematically.  We will see that algorithm in simple language.      The site or the app asks a number of simple questions.  One can choose and answer the questions.  The more you answer, the more likely you will get a match.  While answering, three things should be done.  1. Attach some importance to the question. 2. Give what answer you expect for the question from other person. 3. Answer the question yourself.  Let us see an example. SCORES FOR IMPORTANCE Irreverent - 0 A little important - 1 Some what important - 10 Very important - 50 Mandatory - 250 Let us take 2 questions 1. Does my height matter for you? 2. Do you earn a five figure salary? Let us assume that 'you' and your would be partner 'x' answer these questions.     Now, we have to view the scores in your point of view and in X's point of view.           IN YOUR EYES     For the

         Here, let us explore various sources of light. A point to remember;      Normally, there are two processes which yield light.      1. When the charges vibrate(ions, electrons) light waves[electromagnetic waves] are emitted      2. When high energy electrons return to the low energy state, the excess energy is released as light.       But, in this article, we will simply say, when the atoms are agitated, light is given out.    1. Oil lamps and candles:          Here, oil and wax burn using atmospheric oxygen.  It is a combustion process.  Heat generated in the process agitates the vapour atoms around the wick.  Hence light is emitted. 2. Incandescent lamps:      The tungsten bulb is the first electric lamp.  Electric current is sent through the tungsten filament; Heated to very high temperature; tungsten atoms are agitated and emit light.  A bulb surrounds the filament to keep away the oxygen.  Hence, no burning here.  It is the first incandescent lamp. 3. Fl

     A small body circling around a big heavenly body is known as sattellite.  Natural satellites are moons.  Our earth has only one moon, where as Jupiter has 69 moons, saturn has 53, Uranus has 27 ,.... Man has made many artificial sattellites and put them into orbits.      Any satellites has four main parts. 1. Solar power system 2. Control for its attitude. 3. Transmitter and Reciever 4. A payload to collect information such as camera or particle detector.     The space is said be above 100 km from earth's surface.  A rocket carries satellites and launch it in its orbit.  The rocket must have more than 11.2 km/second speed.  Then only it can escape the earth's gravitational pull, else it will fall back.  That velocity is called 'escape velocity'.  Then the satellite must be given proper push (force, velocity) by the rocket in the orbit.  That orbital velocity is about 8 km/second.  If the speed is more, the satellite will go away from the earth.  If it is les

     Say, you are travelling in a boat in a sea on a clear day.  There is no dust, mist,or hills.  You get a clear picture of environment.  You see horizon.  We say, horizon is the line where the sky meets the land. or the point where your straight line vision is blocked by earth's curvature.  Now the question is , how far you can see? You see the horizon with your eyes and your eyes are situated at 'your height' from the sea level.  Let it be H.  Let 'R' be the radius of the earth and 'D' be horizon distance from you.  With this data, we have constructed a right angled triangle as shown in the figure. APPLYING PYTHAGORAS THEOREM       R^2+D^2 = (R+H)^2  SIMPLIFYING, D = ROOT OF(2RH)    putting radius of the earth R as 6.4*10^6 meters, we get D= square root of 2*6.4*10^6*H meters suppose your height is 1.8 meters D= 4800 meters or 3 miles. Your horizon is at the distance of 3 miles.  Hence horizon goes further and further as you climb up and