cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-1 of 1 results.

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

Views

Author

Peter Kagey, Apr 16 2025

Keywords

Comments

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.

Examples

			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.
		

Crossrefs

Showing 1-1 of 1 results.