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.
A383085
The number of points in the Euclidean plane that can be determined via a straightedge-and-compass construction using no lines and n or fewer circles.
Original entry on oeis.org
2, 2, 4, 10, 52, 1704, 214135
Offset: 0
A383086
The number of distinct distances between points in the Euclidean plane where the points are constructed via a straightedge-and-compass construction using n circles and no lines.
Original entry on oeis.org
1, 1, 2, 4, 35, 2480
Offset: 0
For n = 0 and n = 1, the only number that is constructible is 1, the distance between the two initial points.
For n = 2, we additionally can construct sqrt(3): draw two unit circles, centered at each of the two starting points. These unit circles intersect in two places, which are a distance of sqrt(3) apart.
For n = 3, we additionally can construct 2, and 3.
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).
A383744
The number of distinct straightedge-and-compass constructions that can be made with a total of n lines and circles up to rigid motion.
Original entry on oeis.org
1, 2, 2, 6, 44, 1000, 90585
Offset: 0
For example the following two constructions are considered the same:
(1) Draw a circle centered at (0,0) through (1,0), and then draw a line through (0,0) and (1,0).
(2) Draw a line through (0,0) and (0,1) and then draw a circle centered at (1,0) through (0,0).
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