A383082
The number of distinct straightedge-and-compass constructions that can be made with a total of n lines and circles.
Original entry on oeis.org
1, 3, 3, 16, 205, 5886, 542983
Offset: 0
For n = 0, the a(0) = 1 diagram is the one consisting of two points.
For n = 1, there are a(1) = 3 possible constructions:
1) a line between (0,0), and (1,0),
2) a circle of radius 1 centered at (0,0),
3) a circle of radius 1 centered at (1,0).
For n = 2, there are a(2) = 3 possible constructions:
1) a line between (0,0), and (1,0) and a circle of radius 1 centered at (0,0), which marks the point (-1,0);
2) a line between (0,0), and (1,0) and a circle of radius 1 centered at (1,0), which marks the point (2,0);
3) two circles, both of radius 1, centered at (0,0) and (1,0), which marks the points (1/2,sqrt(3/4)) and (1/2,-sqrt(3/4)).
For n=3, see the a(3)=16 diagrams in the link.
A383083
The number of distinct straightedge-and-compass constructions that can be made with no lines and n circles.
Original entry on oeis.org
1, 2, 1, 4, 44, 1084, 91192
Offset: 0
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.
Original entry on oeis.org
2, 2, 6, 14, 147, 5743, 900487
Offset: 0
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).
A383273
Triangle read by rows: T(n,k) is the number of ruler-and-compass constructions consisting of n-k lines and k circles with 0 <= k <= n.
Original entry on oeis.org
1, 1, 2, 0, 2, 1, 0, 0, 12, 4, 0, 0, 45, 116, 44, 0, 0, 232, 1565, 3005, 1084, 0, 0, 1627, 34114, 166556, 249494, 91192, 0, 0, 21547
Offset: 0
n\k | 0 1 2 3 4 5
----+--------------------------
0 | 1
1 | 1 2
2 | 0 2 1
3 | 0 0 12 4
4 | 0 0 45 116 44
5 | 0 0 232 1565 3005 1084
6 | 0 0 1627 34114 166556 249494 91192
T(2,1) = 2 because there are two ruler-and-compass constructions with a line and a circle:
A circle centered at (0,0) through (1,0) and a line through (0,0),(1,0).
A circle centered at (1,0) through (0,0) and a line through (0,0),(1,0).
T(2,2) = 1 because there is one ruler-and-compass construction with two circles:
A circle centered at (0,0) through (1,0) and a circle centered at (1,0) through (0,0).
Showing 1-4 of 4 results.
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