If I have an infinitely large grid made of perfect squares aligned in the exact same way as normal squared paper, if I start at any arbitary point, and draw concentric circles, where I start on the corners of squares, and draw round 360 degrees, will the circle, no matter how large, only ever pass exactly (not just to good precision, but exactly) 4 corners of squares. I appreciate I probably haven't explained it well so i've attached a diagram. it takes ages to do though so only the first few are shown, you should get the idea I think.
If your interested, i'm doing this to work out the RDF of a uniform lattice
Non-urgent, non-exam-related geometry question Watch
- Thread Starter
- 15-01-2010 03:03
- 15-01-2010 10:20
If your circle has radius 5, won't it pass through (3,4)?
- 15-01-2010 10:50
- 15-01-2010 11:08
Taking the centre of the circles as the origin, doesn't the circle passing through (1,3) pass eight corners? In fact, if you imagine the radius as the hypotenuse of a right-angled triangle, as tgodkin suggested, then any time the circle passes through a corner where the shorter sides of the triangle are different lengths it will pass through eight points.
E.g.: a circle drawn through (1,3) would also pass (3,1), (3,-1), (1,-3), (-1,-3), (-3,-1), (-3,1), (-1,3).
However, a circle passing through a point where one of the coordinates is 0 [e.g. (2,0)] or where the absolute value of the x and y coordinates is the same [e.g. (2,-2)] will only pass through four corners.
I might have misunderstood your question, but hopefully that helps.Last edited by Meridian_Star; 15-01-2010 at 11:12.