Home> urticator.net Search About This Site > Domains Glue Stories Computers Driving Games Humor Law Math > Numbers Science Powers and Fractions Notes About Squares Decimal Expansions (Section) > Number Maze Primes Divisibility Intrinsic Nature of Primes Other Topics Other Topics (2) The Next Block
|
Minimal BlocksSuppose we define an ordering on the points of the plane by saying that (x1,y1) ≤ (x2,y2) if and only if x1 ≤ x2 and y1 ≤ y2. The ordering is only partial, i.e., doesn't apply to all pairs of points, but then when it does apply we can probably all agree with the result. Under that ordering, a set of points won't necessarily have a minimum, but it will have a minimal set, a set of points such that every other point is larger than at least one of them. Here's the minimal set for the points that are centers of 3×3 blocks.
Actually, that's only half the minimal set … you can get the other half by reflecting about the line y = x. Next, here are the coordinates, reflected to fit the convention that x < y.
Which of these is the “real” first block is a matter of taste. However … if we measure using the function min(x,y), the first block is the first one I found, but under any other reasonable measure—max(x,y), x+y, sqrt(x2+y2)—the first block is (1275,1309). Finally, here are three nice non-minimal blocks that I happened to notice.
|
See AlsoNext Block, The Odds and Ends @ July (2004) |