Archive for the ‘Uncategorized’ Category
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 […]
Why, when we round n+sqrt(n), do we never get a square?
Posted by: Gary Ernest Davis on: November 28, 2010
Jim Tanton (@jamestanton) Tweeted recently that for a positive integer , rounded to the nearest integer, is never the square of an integer. This certainly seems to be borne out by a few calculations (carried out in Excel, using the built-in “round’ function): n n+sqrt(n) round(n+sqrt(n)) 1 2 2 2 3.414213562 3 3 4.732050808 5 […]
