Archive for November 2010
When is an integer a square?
Posted by: Gary Ernest Davis on: November 30, 2010
This post came out of a conversation with James Tanton (@jamestanton) about squares of integers being exactly the integers not represented by rounding for an integer (see here for background). To say that rounding yields an integer is to say that: ……………………………. (*) Subtracting from the inequalities in (*) and squaring – as we can […]
Geodesic paths and their daughters (on a rectangular grid)
Posted by: Gary Ernest Davis on: November 30, 2010
Walks on a grid On the rectangular grid shown below we can imagine walking from the red spot to a yellow spot, by taking unit steps up, down, left or right, to adjacent spots: There are many ways to walk from the red spot to the purple spot shown below, but only 2 of those […]
