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.

1, 2, 2, 6, 44, 1000, 90585

Offset

0,2

Comments

A straightedge-and-compass construction starts with 2 points marked on the plane, traditionally (0,0) and (1,0). One can use a straightedge to draw a line between two marked points or a compass to draw a circle centered at a marked point through another marked point. New points occur at the intersections of lines or circles with lines or circles.

In this sequence, two constructions are considered the same if you can rotate, reflect, or translate one to get the other.

Links

Table of n, a(n) for n=0..6.

Peter Kagey, Illustration of a(3)=6.

Peter Kagey, Illustration of a(4)=44.

Peter Kagey, Illustration of a(5)=1000.

Example

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).

Crossrefs

Cf. A241600, A250001, A383082, A383083, A383273

Sequence in context: A032117 A137244 A284707 * A174589 A326942 A247943

Adjacent sequences: A383741 A383742 A383743 * A383745 A383746 A383747

Keyword

nonn,hard,more

Author

Peter Kagey and N. J. A. Sloane, May 08 2025

Status

approved