A383084 The number of points in the Euclidean plane that can be determined via a straightedge-and-compass construction using n or fewer lines and circles.
2, 2, 6, 14, 147, 5743, 900487
Offset: 0
Examples
For both n = 0 and n = 1, the a(0) = a(1) = 2 points are the initial points: (0,0) and (1,0). For n = 2, the a(2) = 6 points are the two above points along with (-1,0), (2,0), (1/2,-sqrt(3)/2), and (1/2,sqrt(3)/2): (-1,0): formed by intersecting the line between (0,0) and (1,0) with the circle of radius 1 centered at (0,0). (2,0): formed by intersecting the line between (0,0) and (1,0) with the circle of radius 1 centered at (1,0). (1/2,-sqrt(3)/2), and (1/2,sqrt(3)/2): formed by intersecting the circle of radius 1 centered at (0,0) with the circle of radius 1 centered at (1,0).
Links
- Peter Kagey, Illustration of the a(5)=5743 points.
