Square of integer is quite easy, childlike stuff. But there is no harm in seeing a known thing in different lights. Experimenting on any thing is always fun, at least initially. So, while reading some stuff on semiconductor physics I came to think about viewing square of integer in different perspective. Following is the description what went in my head.(adsbygoogle = window.adsbygoogle || []).push({});

Assume,xandyrepresents occurrence of two distinct actions. Also, assume thatxandyare related in such a way that ifxoccurs 2 times,yoccurs 4 times, ifxoccurs 3 times,yoccurs 9 times. In other words,y=x^{2}

Square is a special case of multiplication. We can say or write that,y=x*x.

Now, if we forget about Mathematics in its present form, it is quite easy to understand a fact that occurrence of some actionAcan cause occurrence of another actionBin such a way thatBwill occur as many times asAoccurs. Or in simple Mathematical term, we can write (occurrence ofB) = (occurrence ofA) or simplyB=A.

But it is bit hard to grasp a fact likey=x*x. How it may happen that occurrence ofAcauses occurrence ofBas many times of occurrence ofAasAactually had occurred itself. It seems like some other thing is also happening apart fromAand that unknown thing is influencing the occurrence ofB, too.

If we writey=x*zandz=x, it also yields same result asy=x*xdoes if we assume z as the occurrence of a third thing in such way that its occurrence is influenced byx, andzitself influences occurrence ofy.

So,y=x^{2}may signify the following fact.

Occurrence ofxcauses occurrence ofzin such a way thatzoccurs as many times asxoccurs.

And occurrences ofyis dependent onxandzin such a way thatyhappens as many times asxoccurs ifzwas not there at all oryhappens as many times aszoccurs ifxwas not there.

So, if we find a situation in measurement where we find a relation involving square of something, we can think (as there is no harm in thinking) that may be we are missing one influential factor. And unknown factors drive human crazy :)

Since square of integer is discussed, its worth mentioning viewing square of 1 with different eye. Fory=x*x=x*z, it means ifxhappens 1 time,zalso happens 1 time andyhappens 1 time. Well, it is more weird than to understand 3^{2}=9 with the light of above way of thinking. Though I am not entirely convinced myself, but I think we can view 1^{2}=1 fact in the following way.

Making relation between occurrence ofxandywill involve some sort of measurement. Measurement is just comparing something with some another thing or simply called unit. But before measuring something you need to first observe the occurrence of something. Without first observing something it is hard to be enthusiastic to go for measuring that thing. 1 may represent the very start or basis or unit of measuring of that observed thing. So, we can think that “if x=1 then y=1” may represent that very beginning of measurement.

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# Square of Integer

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