SCIENCE CAPSULES

           A convex surface (facing us) has positive curvature and a concave surface has a negative curvature.  A flat surface has zero curvature.  For example, a banana peel has positive curvature outside and negative curvature inside.      Take a paper and roll it as cylinder.  Length wise, you can draw a straight line.  Hence, lengthwise its curvature is zero.  But, across you can only draw circle or curve.  In this direction it has positive curvature.  If you multiply '+' and '0', you get 0.  Hence the curvature of cylinder at any point is 'zero'.  This is called "Gaussian curvature" of cylinder. Because of 'zero' curvature, you can roll a flat paper into cylinder and back.      Next take a sphere, all sides, it is curved convexly.  Hence at any point, it has positive  Gaussian curvature.  Hence spherical surface cannot be converted into flat...

           The great German mathematician Karl Fredrich Gauss devised a beautifully simple formula in 1800 to calculate the day of the week corresponding to any date.    N = D +E+F+G+(G/4)  Day of week = N mod 7.      Let us understand the formula with an example.  I want to find the day for the date "15 September 1959". Step 1. D = Day of the month - Here it is '15'         2. E = a number allotted by Friedrich for each month                Month               E                  Jan 1                0                  Feb 2               3                  Mar 3      ...

            In a town, there is a long street connecting bus station and train station.  A hotelier thought if he start a catering business at the middle of that street, he would be able to attract floating population from both the stations.  He started a hotel and flourished.  Some time later, another business men thought if he opens a Restaurant near bus-stand, he would get all the crowd from the bus-stand, but will loose all the people from railway station to the first established hotel.  So, starting his restaurant near the first hotel would be the optimum solution.  So the second business-man's thinking ran in the same lines as first business-man's.  Hence the second hotel came up near the first one.  Over the time, many business people thought in the same lines and many hotel came up near one another.  Slowly, the entire street was lined up with best hotels and the street was called 'Hotel street"....

          We are going to look at the second law of thermodynamics at another angle.      Ice melts to water; coffee cools down to room temperature; when a balloon is pierced, air rushes out; glass cup falls down, broken into pieces; acid and base combines to form salt and water.  The above actions and reactions takes place spontaneously .  Our common sense and intuition vouch for it.      Why the reverse should not happen?  Why not water turn into ice; why not air thrust itself into balloon; why not broken pieces join to form a cup; why particular direction for actions?  The second law answers.       An action will take place only when disorder or entropy increases in the surroundings or universe.  In short, change in entropy should be positive.      When the coffee looses heat, the room is slightly warmed up.  The air from balloon rushes out and di...

          Take a pop-corn bowl.  Fill it half with rice.  Take hand-full of peanuts.  Put on the rice.  Mix them well.  Now shake the bowl.  Slowly, all the nuts will come to the top and the rice  will settle at the bottom.  This is called ' Brazil nut effect or granular convection'.      Why this happens?  There are two reasons. 1. The system wants to lower the center of gravity and to occupy minimum energy level. 2. Small particles easily slip through the gaps between the larger particles and reach the bottom.      In the case of salt and sand. sand rises to the top. Suppose, you want to reverse Brazil-nut effect, there is a way.  Use a 'cone' shaped container.  In cone, smaller particles come to the top because the gaps or the space decreases as you go down.  The principle can be used for filtering particles according to size.     ...

  JOIN MY COURSE: "Become a programmer in a day with python"     Say, there are two persons Tom and Bob in a town.  Both attempted to rob a bank and caught.  During interrogation , the police give each an option.   That is , " if  you confess and your friend keeps silent,   you will go free and your friend will be behind the bars for a year.  If both of you prefer to keep mum, both may get one month  jail term.  If both of you confess, both will be sentenced for 6 months.  It is up to you to decide."   Hence both prisoners are put in a dilemma.  But it can be solved easily using math.  Let us get the help of matrix.      Let us reduce the situations to numbers - happiness score.                                                           ...

           A river flows from mountains to seashore - from top to bottom.  If the surface is even, it cannot flow, it will only stagnate.     Air flows from high pressure to low; heat flows from high temperature to low; current flow from  high voltage to low.  For an engine to work, heat source at high temperature and a sink at low temperature to receive heat must be available.      In all automobiles, engine is the source and environment is the sink.  That is why, in winter season, some two-wheelers are difficult to start.  Because the engine should be heated up before working.     Our body is a kind of engine.  It is slightly at higher temperature than the surroundings.No life in a cold body.      In the solar system, sun is the unique source at very high temperature and the rest of the planets in the system is the sink.  Sun keeps solar system working ...