# Squares Definition and 2 Discussions

In Euclidean geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, π/2 radian angles, or right angles). It can also be defined as a rectangle in which two adjacent sides have equal length. A square with vertices ABCD would be denoted

{\displaystyle \square }
ABCD.

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1. ### B Is ##\sum^n_{k=0} 2k+1 = n^2## useful? Has it been found already?

I was looking at the tiles of my home's kitchen when I realized that you can form squares by summing consecutive odd numbers. First, start with one tile, then add one tile to the right, bottom, and right hand corner (3), and so on. Can this be applied somewhere? And has someone found it already?
2. ### I Absolute difference between increasing sum of squares

Given are non-negative integer variables ##x##, ##y## and ##z##. I am trying to deduce the absolute difference between a certain value of ##C=x^2+y^2+z^2## and the very next smallest increase in ##C## possible. I'd like to do this so I can (dis)prove the following: Whether small absolute...