Skip to main content

THE CATCHMENT AREA FOR YOUR BUSINESS

      In a medical emergency, you always want to rush to the nearest hospital. A city has a number of hospitals. Suppose we have a map showing each hospital catchment area (for anyone in that region, that hospital is closer than any other) that will be highly helpful. How do you make that map?

    It can be easily done. But doing it manually is difficult. With a computer algorithm, we can easily create a map.

     Start with two hospitals at points A and B on the city map. Draw a line that connects them. Find the midpoint of that line and then draw a line that passes through that midpoint and is perpendicular to the line from A to B. That line divides the city into two regions. One region having A contains all the points closer to A than to B. The other contains all the points closer to B than to A.


 ADVT: TODAY'S DEALS IN AMAZON

Now, look at the third hospital, at point C. Repeat the above process to the hospitals at A and C, you get a second line of separation. Repeat for B and C, you get the third line of separation. Erase the unnecessary extensions of the lines, you get the following figure.


    We will continue to do for all the hospitals in the city. We get the picture given below. This kind of division of the map into regions is called a "Voronoi" diagram. It is named after the Russian mathematician Gregory Voronoi (1868-1908)

     We will see one striking use of this diagram. In the 1950s, a Cholera outbreak occurred in London, killing 10% of the population. One physician by name John snow thought that cholera came from contaminated water supplies. He convinced others of his theory by first making the number of deaths at each address on the map. He then also identified the "catchment area" of a particular water pump at 40 Broadwick street. Points within the catchment area were closer to the broad street pump than any other pump. It turned out that almost all the deaths marked on the map lay inside the catchment area of the Broad Street pump.

     This demonstrated clearly that contaminated water was indeed the cause of cholera. Today the spot where the pump once stood is marked by a memorial and there is a pub right next to it named in John snow's honor.

    There are two ways to create a Voronoi diagram. We can either use crow flying distance (straight distance) to mark catchment areas or walking distance along streets and alleys (Manhatten distance) to carve out catchment areas. John snow used 'Manhatten distance".

    You can make a Voronoi diagram for your business and similar businesses in the city. It will be helpful in designing a better marketing strategy. Wikipedia lists so many uses for Voronoi diagrams.

    Brilliant mathematical ideas are a joy forever.  

Comments

Post a Comment

Popular posts from this blog

THE EARTH, A SUPER ORGANISM

     JOIN MY COURSE: "Become a programmer in a day with python"       A man called 'love lock' (what a name) proposed a theory called Gaia theory, named after Greek Goddess.      It says, "Earth is a self-regulating organism like a human being.  The organic life in it interacts with in-organic matter and maintains atmosphere, temperature and environment".  Hence the earth is still suitable for the life to thrive.      Imagine, in a particular place, there are lot of flowers.  Some flowers are white and some are darkly coloured.  We know, white reflects light and heat while dark absorbs the same.  White flowers can thrive in hot climate.  But dark flowers requires cold climate.  The absorption and reflection balances and the environment reaches average, warm temperature at which both the flowers can co-exist.  This is the essence of "Gaia" theory.      On our earth, ...
3 comments
Read more

DISORDER IS THE "ORDER OF THE DAY"

         Imagine a balloon full of air.  The air molecules are moving randomly inside the balloon.  Let us pierce the balloon with a pin.  The air rushes out.  Why should not the air molecules stay inside the balloon safely and ignore the little hole?  That is not the way the world works.  The molecules always "want to occupy as many states as possible".  Hence the air goes out in the open to occupy more volume.   The things always goes into disorder (entropy) and the disorder increases with time.  The above statement is what we call "second law of thermodynamics".      Consider a cup of coffee on the table. Suppose the heat from entire room flows to your cup of coffee, the coffee will boil and the rest of the room will freeze.  Freezing means bringing things to order and arrangement.  It violates the second law.  Hence it will never happen.  Hence heat must flow from high ...
Post a Comment
Read more

CASINO'S GAME

           Let us find out how the casino survives with mathematics.      Say, your friend invite you for a game of dice.  You must bet (wager) 2 dollars.  If you roll 'six' you will get back 8 dollars.  The game will go on for 30 rounds.  All sounds good.      The probability of rolling 'six' is 1/6.  Since the game will be played for 30 times, the 'expected win' is 30*1/6 = 5.  That is, you are expected to win 5 rounds out of 30.  Hence your gain will be 5 * 8 =40 dollars.  ok.  This also implies that you will loose 25 rounds.  Hence your loss will be 25*2 =50 dollars.  Your net gain will be gain-less = 40-50 = -10 dollars. For 30 rounds, the loss is -10 dollars, Hence, for one round =-10/30 = -1/3 dollars.  There will be a loss of -1/3 or 0.33 dollars per round.  It is not a fair game.     Let us make a simple formula to calculate  'Pa...
4 comments
Read more