sciencecapsules

           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 one.  Take an orange.  Peel its skin.  Put on the floor.  stomp on it.  It will not be

           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              2                  Apr  4              5                  May 5              0                  June 6              3                  July   7             5                  Aug 8               1                  Sep 9                4                  Oct 10              6                  Nov 11             2                  Dec 12             4     in our case E

            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".  The town also became city.      That is, why we see many

          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 disturb the order in surroundings.  The broken pieces have more disorder than a full cup.  That is the reason for the directio

          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.      The plowing of a field always brings up new stones and boulders due to 'granular convection'.      Gravity is

  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.                                                                                  happiness score Jail term-   0 month                                                        4 Jail term -  1 month                                                        3 Jail term -  6 months 

           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 and hence the earth ebbs with life(photosynthesis, rain, etc).    So we learnt that, ups(source) and downs (sink) are

  BRAIN :      When you 'think' there is electrical activity in the brain.  It can be taken out using electrodes,amplified and can be used to control a robotic arm.  So doing things at the speed of thought is possible. SPINAL CORD:      Even today, people are getting artificial replacements of spinal cord.  It will be improved further.  It may aid paralytic patients to walk again in future.  LUNGS:      "Extra corporal membrane oxygenation" ECMO, a artificial lung which can be carried in a backpack is already available.  It functions like real lung and stays outside the body. KIDNEYS:      We know, dialysis machines does the work of kidneys from outside the body.  Also kidney transplant are taking place- but the wait is long.  Research to make artificial kidney is in progress. GENES:      Creating genetically modified human being is possible.  But it has so many ethical issues. 'Cloning' is the starting points in this direction.  We do not kno

        Why the flowers have 3 or 5 petals?  Why we do not have circular or square mobile screens?  Why the galaxies are spiral? 1. GOLDEN NUMBERS 1 1 2 3 5 8 13 21  34  ....      The above sequence is called Fibonacci sequence.  Here, any number is the sum of preceding two numbers.  The nature follows this series everywhere.  Many flowers have 3 or 5 petals.  Mostly 3 leaves are arranged spirally in a stem.  Also pineapple scales follow 21 and 34 pattern. 2. GOLDEN RATIO:      In the above series,  divide 3 by 2, you get 1.5.  As the series progresses, dividing any number by the preceding number, you get the stable ratio 1.61803.. .. an irrational constant.      If you divide length by the breadth of mobile screen or length and breadth of credit card, mostly you will get this ratio.  This ratio  appeals to our eyes.      Bone lengths from tip of the finger to the elbow and facial features follow this ratio. 3. GOLDEN ANGLE:      Divide the total angle

         Once upon a time, a man climbed a high mountain.  He went through the floating clouds.  He turned opposite to the sun, there appeared a giant man with the multi-color halo around his head.  He shivered.  Now the science explains this phenomenon.  It is called the 'brocken spectre' named after a mountain peak.  Also called 'solar glory'.      The giant man is nothing but his own distorted shadow.  The sun light passed through the raindrops in the cloud. Refraction, prismatic effect and interference of sun light creates Rainbow coloured halo around the shadow's head.      This glory can be seen while travelling in a airplane. The plane's shadow will be cast on the clouds surrounded by the 'glory'.  Please occupy middle of the aircraft to watch it. Conditions: 1. The glory will always appear opposite to the sun like a rainbow. 2. Clouds,mist, water sheet must be present. 3. The observer must be present above the clouds.  Hence it

          A technique called 'hashing' is used here.  Let us see what it is ?      Below, I have given four passwords -deliberately simple.       1. 7168       2. 1234       3. 5555       4. 7613      Since there are a total of four passwords.  Divide each passwords by 4. 1. 7168/4 =1792; reminder 0 2. 1234/4 =308 ; reminder 2 3. 5555/4 = 1388; reminder 3 4. 7613/4 =1903; reminder 1      The reminders are the keys or fingerprint or message digest.      The websites only stores these keys.  The 'hashing' procedure may be kept secret.  The keys are normally of same length-like one digit.      When you type your password, the password is converted into the key using 'hashing'.  The generated 'key' and the stored key in the website are compared.  If they match exactly, you are allowed entry.  If a site follows a good hashing algorithm, your passwords need not be saved. (Note:  We may get same key for two or more passwords called col

        We take in glucose through the food.  We take in oxygen through breath.  Both react to produce water,carbon-di-oxide and energy.  The energy keeps us active and healthy.  This is the opposite reaction of photosynthesis.      Oxygen atom has six electrons.  Any atom which has eight electrons feel satisfied and complete like "Houseful show".  This is called 'octet' rule in chemistry.  Hydrogen has only one electron.  An oxygen bonds with two hydrogen atoms and share its electrons.  As a result, the oxygen gets eight electrons and H 2 O -water is formed.  This is how water is formed in the energy giving glucose reaction.      Since oxygen is always short of two electrons.  It is highly reactive.  It easily removes electrons from other suitable atoms.  This is called  'oxidation'.      A small percentage of oxygen in our body combines with one hydrogen atom and forms OH radical.  It is short of one electron.  It is electron hungry.  It alwa

         The books are always the source of knowledge for the mankind.  The historical town of Alexandria is known for its great library.  Whenever a ship arrived at the port of Alexandria, people searched for the books.  Those people loved the books so  much.       we have seen hand-written magazines circulating in hostels, class-rooms etc, a few decades ago.  Printing industry brought in big revolution in the distribution of books and magazines. Harry potter books are hugely sold-a recent revolution.  The great epics like ' war and peace', gone with wind' started their journey in book format.  We cannot imagine subjects like, math, physics, chemistry without books.      Those days, books were sold in small and big shops in towns and cities.  They had limited number of books on some subjects in their shelves.  We had to select from them.  That is no big deal or choice.      Than, the online shop 'Amazon' made its 'debut'  by selling printed books