Enigma 229: Five-point circle
12 October 2014
Posted by on
From New Scientist #1375, 15th September 1983 [link]
I’ve been trying to draw the smallest possible circles with a precise number n of lattice-points on their circumferences. Here are my results for n=4 and n=8. Each has its centre at a point (½, ½), and the radii are ½√2 (about 0.707) and ½√10 (about 1.581).
I find the problem trickier when n is odd. What is the radius of the smallest circle with exactly five lattice-points on its circumference, please? And where will its centre be?
The original article seems to have miscalculated ½√10.
Note: I am still waiting for a phone line to be connected at my new house, so I only have sporadic access to the internet at the moment. The latest estimate is that I’ll have a connection by the end of October 2014.