sciencecapsules

         We know, just 2 numbers (x,y) are enough to mark a point in a graph sheet or in any surface.  Can we find the distance of the point from the origin just using these two co-ordinates?  Here the Pythagoras theorem comes to our help.  Since x and y co-ordinates indicate horizontal and vertical distance of the point from the origin, square both of them; add them and take square root.  We get the diagonal distance from the origin.                  r^2 = x^2 +y^2      Pythagoras theorem is the first topic in any math book.  It still reigns in math and physics world.  It's importance will never fade with time.      Suppose we want to find inner diagonal in a rectangular box, it can be found using the formula given below.  We should remember the box is a 3 dimensional one.    Diagonal^2 = Length ^2 + breadth^2+height^2      Hence Pythagoras theorem can be extended to 3 dimension or any dimension by just adding square of one more quantity.      5^2 =3^2+4^2  

First, a quick intro to sine wave. Y = sin(x)  or Y = A sin(2pi*n*t) A- amplitude n- frequency t - time      The above function describes (a graph) a simple and neat sine curve as the time progress.      Take two such waves and add them or superimpose one on the other(interference). Mathematically    Y = A sin(2pi*n*t)+ A sin(2pi*n*t)    Y = (A+A) sin( 2pi*n*t)     Here the amplitude doubles.  We get a bigger wave.     Now subtract both the waves. Y = A sin(2pi*n*t) - A sin(2pi*n*t)    = 0 The waves cancel each other. Figures are given above. Take two sine waves of slightly different frequencies and overlap them.      Y = A sin(2pi*n*t)+ A sin(2pi*(n+m)*t)     m = 1 or 2     If one draws a graph for the above function, a beautiful wave pattern results.  It is called beats.  Suppose, the two waves are sound waves and they overlap, beats arises.  Beats is periodic waxing and waning of the sound.  The wave pattern clearly indicates this.      Now we u

1.   E = mc^2      This equation does not require any introduction.  This equation says energy and mass are one and the same and one can be converted into another.  This formula is responsible for atomic energy.  Today's nuclear reactors and atom bomb arises from it.  This Einstein's equation will always occupy top pedestal in science. 2. ds >  0          This is the second law of thermodynamics.  The energy always flows from higher concentration to lower concentration.  For example, heat energy always flows from hot body to cold body.  Also the law means that disorder(energy) always increases.  This law made possible the invention of internal combustion engine. 3.       This is the Schrodinger's equation.  This function treats sub atomic particles as waves.  It gives probability and fuzziness to atomic particles .  Hence it gave birth to new science 'quantum mechanics'.  Laser, computers and quantum computing are possible only because of this equati