A383084 -id:A383084 - cp's OEIS frontend

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

Peter Kagey, Apr 16 2025

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.

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

Cf. A383083, A383084.

A383087 The number of distinct distances between points in the Euclidean plane where the points are constructed via a straightedge-and-compass construction using n lines and circles.

Original entry on oeis.org

1, 1, 3, 5, 73, 6628

Offset: 0

Peter Kagey, Apr 16 2025

We say that a real number is a constructible number if it is the distance between two points that can be determined from a straightedge-and-compass construction.

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 points.

			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) and 2.
To 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.
To construct 2, draw a unit circle along with the line connecting the starting points. The line marks two points that are opposite of each other on the unit circle.
For n = 3, we additionally can construct 3 and 4.

Cf. A383082, A383084, A383086.

cp's OEIS Frontend

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.

Views

Author

Keywords

Comments

Links

Crossrefs