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A mathematical theorem of relationship



I suddenly awaken from my idle sleep, hiding out from another 300 words that I have to finish for tomorrow's essay. And then came to my mind this graph, asymptotic graph of friendship. y = 1/x



 An asymptot curve of y=1/x,

where:
y=quality or quantity of the relationship
x=time

You see, friendship, at least mine, always ended up in an asymptotic period where you and your friend(s) are hardly even seen each other, nor care about each other. For example, take this so called loyal friend of mine. We were very close from kindergarden up until junior high. Whenever there was me, there was her by my side. But when we parted school, our friendship did part as well. Well, it didn't end like totally zero--although tends to be approaching it, thus made the relationship asymptotic to zero. At the beginning, sure we were bonded to each other very closely, but in the end, that relationship ceased near to nothing.

What about love relationships? Well, I suppose the same thing happens also, somewhat a relationship tends to be declining in both quality and quantity overtime. Maybe there would be an argue that some kind of relationship maybe plotted to a sinusoidal kind of chart, but I tend to be in a pessimistic perspective for both friendship and love relationships since none of those ended up quite satisfactory or up and down: they tend to be decline overtime. The only sinusoidal relationship I had is maybe my relationship with my family.


A sinusoidal curve of y = sin x.
where:
y=quality or quantity of the relationship
x=time

Is there any arguments or supporting factors that made this theorem real? Yes perhaps there is. The frequency of seeing each other again contributes to the quality of the relationship, in my opinion may be implemented on both love and friendship. Though somehow in love there still another factor that contributes to the quality of a relationship, which could be called as boredom factor. Even though you see each other constantly, there always almost 99.99% of possibilities that the relationship's quality be declined overtime.

Can there be a way to somehow switch all the graphs into at least a sinusoidal ones? since obviously, we can't expect some perfect relationship that could be plotted by the graph of y=x, where gradually the quality and quantity of the relationship incline positively, although started as both negative.

An idealistic relationship graph of y=x
where:
y=quality or quantity of the relationship
x=time

Could my theorem be wrong? Could somehow friendship and love lasted for a lifetime?
At least for now, all I can say is: not a chance.


______________


credits of graph:

asymptot: http://www.freemathhelp.com/asymptotes.html
sinusoidal:http://www.intmath.com/trigonometric-graphs/1-graphs-sine-cosine-amplitude.php
y=x : http://www.sparknotes.com/math/algebra2/inequalities/section1.html
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