File:Boyt.jpg

Approximation of the shape of the sledge runner by with the hundredth iteration of sin ;

$y=\sin^n(\pi/2)-\sin^n(x)$

with single adjusting parameter $n\!=\!100$. Super sin and the Abel sin functions, id est, SuSin and AuSin, are used to evaluate the high iteration of sin.

C++ generator of curve
using namespace std; typedef complex z_type;
 * 1) include 
 * 2) include 
 * 3) include 
 * 4) define DB double
 * 5) define DO(x,y) for(x=0;x<y;x++)
 * 1) include
 * 1) define Re(x) x.real
 * 2) define Im(x) x.imag
 * 3) define I z_type(0.,1.)


 * 1) include "ado.cin"
 * 2) include "arcsin.cin"
 * 3) include "susin.cin"
 * 4) include "ausin.cin"

DB sinni(int n, DB x){ DB s=x; int m; DO(m,n)s=sin(s); return s;}

z_type sinn(z_type n, z_type z){return susin(n+ausin(z));}

int main{ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d;

FILE *o;o=fopen("boy.eps","w"); ado(o,318,30);
 * 1) define M(x,y) {fprintf(o,"%6.4f %6.4f M\n",0.+x,0.+y);}
 * 2) define L(x,y) {fprintf(o,"%6.4f %6.4f L\n",0.+x,0.+y);}

fprintf(o,"1 1 translate\n 100 100 scale\n"); fprintf(o,"1 setlinejoin 2 setlinecap\n"); for(m=0;m<4;m++){M(m,0) L(m,.2) } for(n=0;n<3;n++){M( 0,.1*n) L(M_PI,.1*n)} fprintf(o,".004 W 0 0 0 RGB S\n"); M(M_PI/2.,0); L(M_PI/2.,.2) M(M_PI,0); L(M_PI,.2) fprintf(o,".003 W 0 0 0 RGB S\n");

n=100; p=sinni(100,M_PI/2);

M(0,p) DO(m,315){x=.01*(m+.1);y=sin(x); y=p-sinni(100,x); L(x,y); } fprintf(o,".01 W 0 1 0 RGB S\n");

fprintf(o,"showpage\n"); fprintf(o,"%c%cTrailer\n",'%','%'); fclose(o); system("epstopdf boy.eps"); system(   "open boy.pdf"); //for macintosh getchar; system("killall Preview"); // For macintosh }

Latex generator of labels
File boy05.pdf should be loaded from http://mizugadro.mydns.jp/t/index.php/File:Boy04.jpg to the working directory in order to compile the Latex document below]]

\documentclass[12pt]{article} \usepackage{geometry} \usepackage{graphics} \usepackage{rotating} %\paperwidth 3230pt %\paperheight 1700pt \paperwidth 2460pt \paperheight 1180pt \topmargin -100pt \oddsidemargin -72pt \textwidth 3200pt \textheight 1700pt \newcommand \sx {\scalebox} \newcommand \rot {\begin{rotate}} \newcommand \ero {\end{rotate}} \pagestyle{empty} \begin{document} \hskip 140pt \sx{10}{\begin{picture}(248,116) %\put(4,9){\includegraphics{sinplo1}} %\put(0,0){\sx{1.6}{\includegraphics{Boy_on_snow_sled,_1945}}} \put(-16,0){\rot{1}\sx{.14}{\includegraphics{boy05}}\ero} \put(14,9){\includegraphics{boy}} \put(3,28){\sx{1.}{$y$}} \put(0,16){\sx{1.}{$0.1$}} \put(0, 06){\sx{1.}{$0$}} %\put(-7, 06){\sx{1.2}{$-2$}} \put(13,0){\sx{1.}{$0$}} \put(113,0){\sx{1.}{$1$}} \put(163,0){\sx{1.}{$\pi/2$}} \put(213,0){\sx{1.}{$2$}} %\put(313,0){\sx{1.}{$3$}} \put(224,0){\sx{1.}{$x$}}

\end{picture}} \end{document}