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WHAT WE LEARN FROM PACKING ORANGES IN A BOX

     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 efficiently be arranged in a box in this way.  That is why 12 - dozen - came into being.
    Suppose, you arrange oranges in3D space.  You have to arrange them in a pyramid shape.  That is done in all the fruit shops.
     A mobile phone is also called a cell phone.  Because space is divided into cells and each mobile tower covers a cell.  That is, each tower spreads signals in a 'circular area' of a certain radius.  A number of towers will cover a large area or a city.  Here, in the arrangement circles (towers), we do not want any gaps.  The signals should seamlessly spread and cover a large area.  Hence hexagonal arrangement is the best.  Here the circle may overlap.
    Even the triangle is the polygon(3 sides).  They can be packed well. But they are not as efficient as circles.  The circle is the one that covers the largest area for a given perimeter.  If the number of sides of a polygon is increased without limit, the polygon will end as a circle.  Hence, if the circle is not suitable for a given situation, go for the highest order polygon. 




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