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

Author

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

Keywords

• nonn
• hard
• more

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.

Examples

			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).
		

Links

• Peter Kagey, Illustration of a(3)=6.
• Peter Kagey, Illustration of a(4)=44.
• Peter Kagey, Illustration of a(5)=1000.

Crossrefs

Cf. A241600, A250001, A383082, A383083, A383273