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...

           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 ...

  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...

        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.   ...

         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...

          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 ar...

        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 bod...

         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 ch...

           How far and how clearly we can see? The star we see in the night sky is single or double?  The answer :  " We can at the most distinguish things that are 30 centimeters apart at a distance of 1 kilometer".  This result from the following formula   Angular dispersion of human eye A = 1.22*L/d  L - wave length of light  d - diameter of aperture of pupil of the eye.      We get A as 0.0003 radian. = 0.0003/1 = 0.0003 km/1 km  = 30 cm/1 km.        What is the angular dispersion? Why this restriction to human eye?  To explain that, we have to go to the physics principle-dispersion-diffraction.      Let us say, water flow from a lake through a narrow channel to another lake.  Once the water exists the channel it will spread out [Dispersion].  That is the nature of all  fluids.  But a stream of arrows or bullets passing t...

         Some where in the mountains, a river originates.  It flows down to the low-lands and into the sea.  It flows because of the slope and the gravity.  River appears to run on a plane ground.  But there is always a slight slope.      If one of the banks of a river is weak, the river burrows in and curves.  The curved flow of water hits the opposite bank and curves again. It repeats on and on.  That is why, all the rivers follow snake like path.      The river suddenly turns creating a whirlpool; it some times falls down creating waterfalls; it smashes on boulders and rocks; it splits up creating island; it finally enters ocean where again there is clash between land mass and waters.  Consequently river split up into several branches creating delta region.  Such a hard journey. The river's journey is similar to the human life.      The river is like conveyor...

        Look at the mirror.  If you do not like what you see, break it (take it lightly).  Again, in  each piece, your face appears.  Again break them all.  In all the pieces, your face appears and smile at you.  This is the way nature works.         Look at a tree.  Every branch is the replica of the tree.  And every sub-branch also.  You can see the pattern of tree in each leaf.  There is redundant information.  Nature uses redundancy to protect life forms.  DNA is present in each cell of life forms.  That is why, plants,can be grown not only from seeds but also from stems, roots and even leaves.      Hologram that is found in all the Id cards, credit cards etc. yields 3D picture.  "Optical interference pattern" is recorded in the hologram.  If you cut the hologram into pieces, one can get same 3D picture from each piece but smaller ...

          There are only 26 symbols in English.  Shakespeare has used only these symbols and written great dramas. To venture into math and accountancy, we need 10 more symbols (numbers).  For science and technology, we still needed more symbols.  And we borrowed them from Greek and Latin.  Also, we require punctuation for clarity.  That is human weakness, we need more and more symbols to understand a concept or a message.  But the nature has coded all the information using only four symbols (chemicals) in the DNA.  But only two symbols are enough to represent any info. in today's machines and digital devices. ACOUSTIC - MORSE CODE      In those days, Morse code were used for instant and emergency communications (Telegram).  Morse code consists of only 2 symbols dot and dash.  Dot means a sound signal of short duration.  Dash means a sound signal of lon...

          You cannot gain one thing without losing another.  No thorn, No rose.  That is the philosophy of life and as well as science.      Take a flowing air or water.  As the speed increases, the pressure should drop.  Or if the pressure rises, the speed will go down.  That is Bernoulli's principle employed in air-planes etc.      Consider falling stone, or water falls.  Here, as potential energy goes down, kinetic energy will pick up.      Next, Electric transformer, voltage can only be increased at the cost of current or vice versa.      Take gear systems, either force or speed can be increased.  Both cannot be increased together. whenever there is oxidation [lose of electrons, say,  at negative of battery], there must be reduction [gain of electrons at positive]       The principle of entropy, says that, if "o...

           Why the gas stove gives out blue flame?  Let us explore.       Origin of light:      When the charges (electrons, ions) vibrates, oscillating electric field is created.  Oscillating electric field subsequently gives rise to oscillating magnetic field.  Now the electromagnetic wave is born.  It will start to spread out. If the wave's frequency falls within the visible range, it is light.      Invisible Infra-red:      All the bodies in this world or in this universe have some temperature  above absolute zero kelvin.  Hence, atomic particles[charges] in these bodies execute vibrations due to heat.  They will start emitting electromagnetic waves[light waves]. If their temperature is less than 1000 k,  the frequency of waves will fall in infra-red range.  Humans, animals, trees, houses ...   always emit IR radiations.  He...

          We inhale oxygen and exhale carbon-di-oxide.  Plants take in carbon-di-oxide and give out oxygen during photosynthesis.  That is how, nature recycles the air.      Water flows through the rivers to the sea.  It is evaporated from the oceans to form clouds.  The clouds pour down as rain.  The fresh, pure water is not created out of nowhere.  Water is only recycled by the nature.  We buy, brand new, fresh water bottle.  It is neither new or fresh.  But, it is already used thousands and thousands of time.  It is smartly recycled by the nature and is given to us as fresh.      We eat the yields from the plants and trees.   Human and animal waste is the fertilizer for plants.  The entire Eco-system  goes on recycling.  Man is not able to create a closed Eco-system which recycles itself yet.      Even we are recycled....

              Stopping a car running at 60 kmph all of a sudden is equal to elephant falling from a third floor and hitting the ground.  Lot of energy has to be dissipated.  Engine is constructed in front portion of the car so that it can absorb the impact in case of the crash.  The front of the car should not be rigid.  It should absorb and dissipate the energy by crumbling and deforming .  The bumper is also used to absorb energy during the crash.  Besides, there are air bags in front of the passengers.      During an impact, there is a large deceleration (negative acceleration).  The loose and soft organs in the body cannot withstand such a force and energy.  Hence so many safety measures are built in a car.      Engine is at the front and the boot is at the back in every car to withstand the unexpected collision.  Wash rooms are kept at the two ends of ...

         We know reflection without which we cannot even see our own face.  Now let us explore the how and why of reflection.      The reflection obeys the law that "angle of incidence = angle of reflection ' (fig) why?  The light ray coming from the source hits on the mirror and bounce back.  For this process, the shortest and quickest path the ray can take leads to the law of reflection.        We see mirage in the hot summer on the roads.  It is also a kind of reflection.  Mirage appears because, the light ray takes quickest path to reach our eyes.      The brain always tells us about the position of the object using the path of light coming from it.  In a mirror reflection, the light rays seems to be coming from backside of the mirror.  Hence, we get the illusion that  the objects are situated behind the mirror.      A convex mirro...