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Showing posts from July, 2015

One more formula for Squares of Integers

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Even though I have left formal math behind several years ago (though somewhat later than it had left me behind!), I have always had a fascination for numbers, some of which has been applied in original musical concepts I have popularised over the years including Seamless Korvais.

This topic is completely off the music charts as it attempts to chart a different course in pure math in a fairly populated area - Squaring numbers. Doubtless there are several time-tested and elegant approaches to this including the most well known algebraic formula of (a+b)^2 and others based on pattern recognition.  I found another approach staring me in the face this afternoon, literally in my half-sleep state.

I roused myself to action and tested the concept. Itseems to hold good from negative infinity to positive infinity and I decided to not get too greedy and ask for more but share it with heads wiser than mine in the field.  So here goes (in fairly simplistic, rather than formal terms)...


Explanation…