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.
%I A383087 #8 Apr 18 2025 21:54:10 %S A383087 1,1,3,5,73,6628 %N 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. %C A383087 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. %C A383087 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. %e A383087 For n = 0 and n = 1, the only number that is constructible is 1, the distance between the two initial points. %e A383087 For n = 2, we additionally can construct sqrt(3) and 2. %e A383087 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. %e A383087 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. %e A383087 For n = 3, we additionally can construct 3 and 4. %Y A383087 Cf. A383082, A383084, A383086. %K A383087 nonn,more,hard %O A383087 0,3 %A A383087 _Peter Kagey_, Apr 16 2025