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 A332501 #20 Mar 19 2025 05:54:17 %S A332501 2,7,2,5,7,3,7,0,5,6,7,9,9,9,2,5,2,4,9,6,7,4,6,3,8,5,8,1,2,9,6,5,6,3, %T A332501 8,6,5,1,5,4,5,8,2,9,2,8,9,8,1,7,0,8,0,9,8,2,1,4,0,4,8,7,6,2,1,1,7,5, %U A332501 0,4,6,3,2,1,5,6,4,3,0,5,4,6,2,7,0,7 %N A332501 Decimal expansion of the number u' in [0,2 Pi] such that the line normal to the graph of y = sin x at (u', sin u') passes through the point (3 Pi/4,0). %C A332501 Let S and C denote the graphs of y = sin x and y = cos x. For each point (u, sin u) on S, let S(u) be the line normal to S at (u, sin u), and let (snc u, cos(snc u)) be the point of intersection of S(u) and C. Let d(u) be the distance from (u,sin u) to (snc u, cos(snc u)). We call d(u) the u-normal distance from S to C and note that in [0,Pi], there is a unique number u' such that d(u') > d(u) for all real numbers u except those of the form u' + k*Pi. We call d(u') the maximal normal distance between sine and cosine, and we call snc the sine-normal-to-cosine function. %C A332501 The distance from (u',sin u') to its reflection in (3 Pi/4,0) is the maximal normal distance between sine and cosine. This distance is slightly greater than 1. See A332500. %F A332501 Equals (3/4)*Pi + d/2 = A177870 + A003957/2, where d is the Dottie number. - _Gleb Koloskov_, Jun 17 2021 %e A332501 2.7257370567999252496746385812... %t A332501 (* See A332500. *) %o A332501 (PARI) 3/4*Pi+solve(x=0,1,cos(x)-x)/2 \\ _Gleb Koloskov_, Jun 17 2021 %Y A332501 Cf. A332500, A086751, A332503, A177870, A003957. %K A332501 nonn,cons %O A332501 1,1 %A A332501 _Clark Kimberling_, May 05 2020