The formula for the sum of squares

Date: 23 Mar 2020 - Sezione: scienze/matematica/

The present essay is dedicated to the English-speaking friends. It is an answer to the question: “What is the formula for the sum of squares?” The question is ill-worded, and I assumed that it meant: “What is the the sum of the squares of the natural numbers from 1 to n?” On such assumption, I wrote an essay in two parts. The first part gives what I think to be the most elementary approach to finding the formula; the second part I give an intuitive manner to get to the same result, a child’s play with small cubes. In the first part I go into some details to explain a few elementary concepts, which are generally not underlined when (and if) the formula is discussed. For example I try to show why the formula is a third degree polynomial with constant term equal to zero. If one wants a more detailed explanation of a general formula for all sums of all powers of natural numbers from 1 to n, I suggest to have a look, for example, at and use Google Translate if you are not familiar with the Italian language.

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