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 A381380 #39 Apr 10 2025 08:04:42
%S A381380 2,7,2,7,0,5,4,7,7,3,8,1,2,0,4,8,9,8,8,4,3,5,1,5,5,6,7,9,0,2,0,2,5,9,
%T A381380 8,4,2,8,3,4,6,4,7,7,1,9,9,0,3,1,3,8,7,4,0,0,3,1,0,7,1,1,8,9,3,9,5,3,
%U A381380 9,5,1,4,0,1,3,6,7,1,4,8,4,8,4,4,9,4,0,4,0,1,1
%N A381380 Decimal expansion of the area of a ruled surface formed by moving a segment of length sqrt(6), the ends of which lie on the diagonals of opposite faces of a unit cube oriented at right angles to each other.
%C A381380 A segment of constant length continuously sliding its endpoints along two intersecting straight lines defines a ruled surface -- a linoid. Here we consider a linoid defined by a segment of length sqrt(6)/2 sliding along two intersecting diagonals of opposite faces of a cube with edge 1. The surface of a linoid is given by the equation 2*x^2/(z - 1/2)^2 + 2*y^2/(z + 1/2)^2 = 1.
%C A381380 The surface of a linoid consists of four congruent surfaces. The area of one of them is calculated using integrals and multiplied by 4.
%C A381380 The name of the figure "linoid" was introduced by the author in the related article, see link.
%H A381380 Nicolay Avilov, <a href="/A381380/a381380.jpg">Construction of a linoid</a>
%H A381380 Nicolay Avilov, <a href="https://elementy.ru/problems/2516/Obem_linoida">Volume of a "linoid"</a> (in Russian).
%F A381380 Equals sqrt(2)*Integral_{t=0..Pi/2} Integral_{z=0..1/2} sqrt(5 + 24*z^2 + 24*z*cos(2*t) + cos(4*t)) dz dt.
%e A381380 2.72705477381204898843515567902...
%K A381380 nonn,cons
%O A381380 1,1
%A A381380 _Nicolay Avilov_, Feb 22 2025
%E A381380 Terms corrected by _Jinyuan Wang_, Feb 23 2025