Abstract Confusions

Complexity is not a cause of confusion. It is a result of it.

Category Archives: Graph Theory

Math Games for Children

Games are the sure shot fun way to teach some thing. And math is one of the top-notch skills one needs to own for being successful in any career. Imagine if playing games hone your mathematical skills. As a kid I grew up learning few board games which helped me to understand the most basic math operations – counting, addition and division (subtraction and multiplication thereof).

Very recently, I tried teaching math principles to my nephew but found difficult without the help of games. The most important thing I did was to run to a store to get him a board game. So, if you don’t want to spend those long boring hours and make teaching fun, try few of these games.

Snakes and Ladders

This is a simple game. Most of adults would have played it. Two or more players can play this game. This board game has hundred squares numbered from 1 through 100. And a player wins if he starts from 1 and reach 100. Each player has to toss a die and move their playing piece according to the output of the die.

ladders-snakes-board-game-screenshot

Snakes and Ladders - A Chance game in 100 squares

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Instant Insanity – A Graph Theoretic Wonder

Instant insanity is one the many games involving sound mathematical principles. In particular it involves graph theory to solve. One of the mathematics most powerful tool – representation theory is used. As you are aware of, what looks like a strange problem is transformed into totally a unrelated problem in another field because of the hidden relations / transformations. Often these relations transform into a treasure trove of knowledge and excitement.

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Six Degrees of Separation

How many times you met some stranger and he turns out to be one of your friend’s friend or friend’s – friend’s friend? How many times you meet some one in airport or in rail journey and he turns out to be your school mate or college mate? Many of us might this kind of meetings most often.

So, this post is about the mystery behind such happenings.

Meet Mr Shah

One such incident to reckon. Couple of weeks before, I met Fowzul’s hubby – Mr. Shah on beach. At first he is a perfect stranger to me. All I know was, he studied in a same college where I studied but left it before me joining it. Then when he spoke about his friends, we both came to know that we have common friends. So, it turned out like enquiring about the friends in common.

The question we have now is – “Is it possible to know any given stranger through known people?”, if so, how many such people you need to know to know “the stranger?”. Hold your breath, the answer is a mere six. And that is the maximum number of people for that. That is, you need to know, exactly six people to know any one in the world.

You & A Stranger

Let me put it more specific. Consider a farmer in remote Chinese village. Now, you need find your way to get connected to him with six or less people. There are many examples for these in popular culture and mathematical culture.

Kevin Bacon number is one such very popularly known and discussed. Bacon acted as the famous scientist in “Hollow Man” movie. He once said, he can relate to any actor in the world.

In mathematics, Paul Erdos – a famous mathematician who collaborated with so many people and produced graph theoretical paper had a number named after him. It is known as Erdos number.

Erdos number - An example

Erdos number - An example

Now, how amazing is it? we don’t have a proof for this anyway.