Real Mathematics – Strange Worlds #7

Mathematics is tough

Most of the people I meet tell me that they have never been good at mathematics. It is upsetting to hear such thing especially when they come from adults. Because even though they don’t realize it, these adults are having negative effects on kids.

Understanding mathematics is not easy. Doing it is not easy either. And as if these are not enough, kids hear how unnecessary it is to learn mathematics. It is not hard to find memes about the redundancy of trigonometry or algebra. I love memes by the way.

What should a 10-year old think when he/she hears that the thing you can’t do at school is not even useful after school? This student would distance him/herself from not only mathematics but all sciences until the end of time.

Worst thing is that this student (future adult) wouldn’t even have any idea about what he/she lost.

In almost every country there are huge masses who don’t know what mathematics is and how useful it would have been for them.

Perspective

One of the most crucial things one can gain from mathematics is having the ability of perspective. Whenever you are facing with a problem in life it would help you to solve that problem more quickly if you are capable of looking at thing from different angles.

Perspective is not only useful for solving problems. It helps one to understand other people’s feelings, thoughts, and state. Having perspective helps you to become an empathic person.

Actually having perspective relates to a habit. Mathematics can be very handy if you’d like to build a new habit for your mind. Personally I believe topology is cut out for it.

Engineer’s Problem

Points A-A’, B-B’ and C-C’ should be connected.

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A-A’: Electric system for the house.

B-B’: Gas system for the house.

C-C’: Water system for the house.

These three connections should not intersect with one another to avoid accidents such as fire. This is when the engineer is needed: Finding the right paths as electric system must be built first.

Engineer knows that there are 3 different paths for A-A’: Between B’-C’, B-C’ and C-B’. But there seems to be a big problem here. When engineer tries to connect any of those lines, it is impossible to connect B-B’ and C-C’.

How can the engineer solve this problem?

Beauty of Topology

Topology is very useful in case you can’t see a solution right away. In this amazing branch of mathematics we are allowed to deform objects. If so, then let us deform the shape of the problem in our imagination.

There would be no problem if B’ and C’ were replaced. This is the point where we’ll be using topology: If whole area of the shape was made of a kind of fluid, points B’ and C’ could be pushed away from their original places. And if we are allowed to push away these points, everything in between would have been pushed as well. This is why the connection between A-A’ would have been deformed as shown below:

You could imagine A-A’ as a string.

This deformed A-A’ path is engineer’s solution to the three connections problems.

IMG_6441

Then, if A-A’ connection is done first, B-B’ and C-C’ connections can be done as follows:

One wonders…

In the following picture you will be seeing a famous problem called “three utilities problem”.

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Now take a pen and a cup in your hands and try to find a way to connect three utilities to three houses.

M. Serkan Kalaycıoğlu

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