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.

2, 2, 4, 10, 52, 1704, 214135

Offset: 0

Author

Peter Kagey, Apr 16 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). In the constructions counted by this sequence, only the compass is used. Circles can be drawn at any marked point through any other marked point, and new points are marked where circles intersect.

Links

• Peter Kagey, Illustration of the a(5)=1704 points.
• Wikipedia, Mohr-Mascheroni theorem

Crossrefs

Cf. A383083, A383084.