sciencecapsules

      Join our free course-Build your personal expert with python.                               Today, we can count friends through Facebook.  And our friends seem to have more friends. why?     A person who does not have any friend will also not be your friend.  A person who makes friends with everyone will also make friends with you.  That is, if a man has more friends, he is more likely to make friends with you .  If he has fewer friends, he may not be your friend.  That is why those who make friends with you would already have more friends.     Your friends will have more contacts and interactions with others.  Hence infectious diseases will easily spread through them. So your friends seem to have more illnesses than you.     Today, we are struck by the pandemic.  The Hindu dated 24-08-2020 says, "with 3 million cases, COVID -19 unlikely to abate soon.  Only a vaccine can prevent infections and help bring out herd immunity".      But we cannot vaccinate all the 120 cror

                             ADVT:  SMARTWATCHES IN AMAZON       The Pixar company made many successful animation movies. The toy story was the beginning.  The toy story series was a huge success.         The toys should have smooth curves and surfaces. From roughly drawn lines, they created smooth curves. We are going to see how they made it. The process is called subdivision surfaces.     Study the following figures. Here a triangle is converted into a smooth curve. SUB-DIVISION RULES 1. Insert two new vertices at 1/4 and 3/4 distance on each edge. 2. Remove the old vertices (corners) 3. Connect the new vertices. 4. Repeat the process until you get a smooth curve.   In the end, sharp corners are cut, and we get a smooth curve. A toy's face, nose, fingers, etc. can be made this way. Remember, points make up curves. Curves make up surfaces. Surfaces turn into a 3D toy. Catmull and Clark devised this algorithm. A FEW MORE EXAMPLE Artists simply create a jag ged version of what they

                                                                                      ADVT:  SMARTWATCHES IN AMAZON         We always worry about our flaws.  If one's nose does not have a perfect shape, he worries a lot. But, do you know, in spite of our flaws, many people still love us.    The matchmaking site "OK Cupid" conducted one experiment.  The site used a 'five-star rating' system, for attractiveness.  OkCupid wanted to find out how this attractiveness score relates to the number of messages received from interested persons.  So a sample of 500 women all between the age of twenty and twenty-seven and all living in the same city, was monitored over the course of a month and the data analyzed.     During the study, one "Ms.Attractive" had an average attractiveness score of 3.4 and the other Ms. Controversial had an average attractiveness score of 3.3.  You would expect these two ladies to receive a similar amount of online attention, but there was

                                        ADVT:  SMARTWATCHES IN AMAZON             A virus is born, multiplies, spread and on the way, it does some destruction.  Let us find out how various viruses behave.      A person with flu may be infectious for five days (infectious period-- I), during which time they will infect about four people (spread factor-- S).  One will infect four people, four will infect 16 people.  16 will infect 64 people and so on. Hence 4 is spread factor in the case of flu.    In the following table, various infectious disease, their infectious period, and spread factors are given. Disease                   infectious period      spread factor                                          I                                  S HIV                               4 years                            3 Smallpox                     25 days                            4 Flu                                  5 days                           4 Measles                         14 days 

                                                    ADVT:  SMARTWATCHES IN AMAZON       Suppose, a family has two or three children.  Will they have the same birthday?  It happened in Great Briton.  In 2010, Jennifer and Briss Allah were expecting their third child.  They were also preparing to celebrate the birthday of their two children, Adam and Najla on 7th October.      While Mum Jennifer was blowing up balloons for the upcoming celebrations, she felt something in her stomach and realized that her contractions had begun.  She could not believe it.  The unthinkable was about to happen.  The family's third child, Sami, was also born on 7th October. The "daily mail" proclaimed,' Happy birthday to you ... and you... and you too. Couple's three children born on the same date'.    An event such as this occurring is mindboggling. But statistically, it can happen.  Let us see the little math behind it. The probability of first    child born on any day      = 1  T

                   ADVT:  SMARTWATCHES IN AMAZON      Consider this quadratic equation X^2+X = 12 we can solve this equation using pictures The area of the green square is x*x = x^2.  The area of the red rectangle is x*1 =x. The total area, according to the equation is x^2+x =12.      Split the red rectangle into two equal halves.  The width of each is 0.5.  The total area remains the same.     Move one halved rectangle to the bottom of the square as shown in the figure.    Fill up the extra corner square.  Its area is 0.5 *0.5 = 0.25.  Now the total area becomes 12.25.  The above figure is the perfect square.  Hence length *length also gives the area.   Therefore, we can write. (x+0.5) * (x+0.5) = 12.25 or (x+0.5)^2 = 12.25 or x+0.5 = square root of 12.25. x+0.5 =3.5=3+0.5 so, x = 3 we got the answer     Other quadratic equations may be solved in this way.  Even quadratic formula for x can be derived using pictures -try yourself. x^2 can be visualized as a square. x^3 as cu

                                               ADVT:  HOME PROJECTOR IN AMAZON          Some years ago, British illusionist Derren Brown performed a feat that you might call a miracle.  In front of a camera, using a fair coin, he flipped ten consecutive heads.  The footage was not edited, there was no sleight of hand.  The general public was baffled.    Later, Brown revealed his secret. He knew that the probability of throwing ten consecutive heads is 1/1024.  (Law of large numbers)  probability of getting one head =1/2 Probability of getting ten consecutive heads. 1/2*1/2*1/2*1/2*1/2*1/2*1/2*1/2*1/2 =1/1024          This means that once in every 1024 attempts you would expect to get 10 consecutive heads.  Derren Brown tossed a coin for nine hours and filmed it continuously.  He initially broadcasted just the last minute of footage, giving the viewer the impression that he had flipped ten consecutive heads on his first attempt.  Today, this process can easily be simulated in compu

                        ADVT:   HOME PROJECTOR IN AMAZON      How human population or bacteria population grows?  Two may become four. Four may become eight and so on.  Here the offspring gives rise to more offsprings.     How the nuclear bomb explodes?  One nuclear fission becomes two due to ejected neutrons.  Two becomes four fissions and so on.  This chain reaction is left uncontrolled then it results in a huge explosion.  Here fission causes fission.  How the plant and tree grow?  From seed, stem shoot out.  Then it branches out.  Next, it clads with leaves.  More leaves, more photosynthesis.  Then it yields flowers, fruits, etc.  Here, we observe the rapid growth of plant cells.     Why do not we learn from nature?  Why do not we use the money to make money?  Why do not we use the interest to get more interest?  That is compound interest, the magic. In compound interest, money grows rapidly towards the end.                  " Compound interest is the addition of interest t

                         ADVT:  HOME PROJECTOR IN AMAZON                    Draw the 1cm line and extend it by another cm.  It just becomes double (2cm).  Now draw a square having each side 1cm.  It is area is 1square cm.  Now, double each side.  The area will become 2*2 =4 sq.cm.  When the sides are doubled, the area increases four times.   Make a cube having a 1cm length in all directions. Its volume is 1 cubic cm. Double each side. Now its volume is 2*2*2 =8 cubic cm.  The volume has increased by 8 times. That is scaling. That is the dimension. SOCIAL DISTANCING:     If you are in a queue (one dimension) of people spaced about 0.5 meters apart, then the number of people standing within twenty meters is about 20/0.5 =40.    But if you are in a two-dimensional crowd of people again spaced about 0.5 meters apart, then the number of people in the square of 20 meters length(each side) is 20/0.5*20/0.5 =1600.  If a flock of birds, flying in three dimensions is spaced about 0.5 meters

                                   ADVT:   HOME PROJECTOR IN AMAZON     The clock's face has 12 elements. Let us assume that it forms a group G. 1. Add any two numbers in the clock's face. 2'0clock +3 hours =5'o clock 2+3=5, 5+4=9, But 9+5=14 =2. Adding any two numbers will always give another number in group G. Hence the 'group' satisfies 'closure' property. 2. 3'oclock +12 hours =3'oclock     9'oclock+12 hours =9'oclock. so   A*12=A If you add any element 'A' in the group to 12, the result is always 'A' The '12' is called the 'identity' of the group. 3. Take 5, add 12-5 (7) to it.     5+7 =12 we get the identity. 7 or 12-5 is said to be the inverse of '5'.  Hence, for every element 'a' of the group, there is another element b, so that a+b =identity. Element b is called the 'inverse' of a.  In our case b=12-a. 4. Group elements also exhibit 'associativity'

                        ADVT:   HOME PROJECTOR IN AMAZON    1. CODE    Double the number as follows       1,  2,  4, 8      = 2^0,  2^1,  2^2,  2^3 Now reverse them as  8 4 2 1 Now code as follows 8    4   2   1 0    0   0   0   represents  0 0    0    0  1   represents  1 0    0   1   0   represents  2 0    0   1   1  represents   3 0     1   0   0  represents 4  0     1   0   1  represents  5 .....    ....  ...   ....      ...... .... .....     ....     ..      ...... 1   1   1    1   represents 15 8 4 2 1 code can represent up to 15. But 0 to 9 is enough to represent all numbers.             8  4  2  1             8  4  2  1          8  4  2  1 345  =   0  0  1 1(3)        0  1  0  0(4)     0  1  0  1(5) this code is used in digital gadgets. 2. Weights:     In those days, weighing stones were used by traders.  To measure up to 255 kg, the following weights are enough. 1,2,4,8,16,32,64,128          (doubling way) To weigh 153 kg, use 128+16+8+1 =153 You can try any other weight. 3.