SCIENCE CAPSULES

       VISIT:  STATISTICS LAB ONLINE   for interactive and animated experiments.        Arranging circles in a rectangle is always a problem.  If you arrange them as in figure(1), there will be a lot of wasted space.       But if you arrange it like figure (2), there will be less wasted space.  This is a hexagonal arrangement.  If oranges are arranged in this way and pressed, each orange will take a hexagonal shape.  Hence hexagonal-shaped objects can be neatly and efficiently packed.  That is why honey-comb cells have a hexagonal shape.  Some floor tiles have that shape.     But the hexagonal arrangement is always not the best.  If apples, oranges, mosambi are arranged in this way in a rectangular box.  There will be a lot of empty space in the beginning and at the end of the rows.   Hence they should be arranged as shown in figure (1).  12 oranges can eff...

      We have id number, license number, credit card number, our marks, our property, our temperature, our BP, all are digits, why?  They can be stored electronically in a small space. A thumbnail-sized chip can contain volumes and volumes of info. Data can be compressed easily. Compressed data can be transmitted easily. An email arrives in no time.  The digital info can be encrypted and decrypted easily. Due to encryption,  your credit card info. is safe.  The errors in the data can also be corrected. Suppose, there is a scratch in DVD, it will still play, hence, there are so many advantages for having info. in digital form.      But, some info. like audio, video is not available in digital form.  How they convert them into digital form. Let us find out. First, we should know what is analog data. Analog: Something physical with continuous change. Digital: Made of numbers.     A girl sings before a mic. It is analog. It is...

      Your son has secured the fourth rank in the class. There are twenty students in the class. Hence 15 students are below him or 80% of students are below him. Now, your son is said to at the "80th percentile". Percentile: The value below which a percentage of data falls. Formula: Percentile = (Number of values below "x"/total number of values)*100 In our case         =(16/20)*100         =80      Suppose, your son has scored 90% marks in math. But has percentile in math as 20. That means, only 20% of the students are below him. That is not impressive in spite of the high score . So percentile gives new meaning to data.      A total of 10000 people visited the shopping mall for over 12 hours.                Time (hours)                       people               ...

      'coin toss' is a famous experiment in probability theory. We always have a fifty percent chance of getting head or tail.      If you flip the coin 100 times, you may roughly get 50 heads. Suppose you do 100 flips 100 times, what will happen? Sometimes, you get 50 heads, other times 45 heads, or 55 heads, etc. Anyway, it is always around the central value '50' (50%).      Let us define 100 flips of the coin as one experiment and let us do 100 experiments. The experimental results are given below.        A = number of heads in every 100 flips or in one experiment            B =  number of times A in 100 experiments                                                                A           ...

        VISIT:  STATISTICS LAB ONLINE   for interactive and animated experiments.    Consider an egg. You can balance it on one of its ends. It won't last long. The slightest disturbance will topple it. The two tips of the egg are known as unstable equilibrium points. "Equilibrium" because you can balance the egg on them and 'unstable' because the egg will fall over at the slightest nudge. The points around the egg's body on which it balances robustly are called 'stable equilibrium' points.      Now consider a flat square (a cardboard piece). It has four 'stable equilibrium' points at the center of the sides. You can balance that square on these points. It also has four unstable equilibrium points at its corners. Similarly, a triangle has three stable and unstable equilibrium points. All ellipse has two stable equilibrium points in the centers of its long side and two unstable ones at the ends.     Can you find a two or th...

      VISIT: STATISTICS LAB ONLINE   for interactive and animated experiments.     Put a coin in a plastic tray. Consider both as a two-dimensional object. The coin can move within the tray but cannot escape from it. Suppose you lift the coin from the tray, it escapes from the boundaries of the tray. That is, you have moved the coin into the third dimension, that is why it escaped.      Now put a marble in a box. Both are 3D objects. You cannot move the marble outside the box without damaging the walls of the box. But, if you move the marble into the 4th dimension, the container walls cannot stop its movement(as in the coin and tray- case) and the marble will easily escape from the containment of the box. Similarly, one can escape from the jail, if be could move into the fourth dimension.      Einstein said, that besides three dimensions(length, breadth, depth) the time can be considered as the fourth dimension. We are abl...

     John lives in a warm country. He has just 30 square meters of land. He can plant cocoa and pineapples. How much of pineapple and cocoa he has to plant in his plot to get maximum profit? This is a classical problem. It can be solved with graphs.     Let x stand for the amount of cocoa and y for the amount of pineapple. When john harvests the crops, he will get a unit return of 3 dollars on the cocoa and of 2 dollars on the pineapples. His total return p will be  p = 3x+2y       ----(1)     The profit p, we want to maximize. Planting comes with a cost. The unit cost of cocoa seed is 2 dollars and of pineapple, the seed is 1 dollar. Also, 4 dollars is required to cultivate both the crops in his land.     Hence, the total cost c of growing the two crops is       c = 2x+y+4   -----(2)      John has only 50 dollars in the bank. That is the first constraint. We write it mathe...