File:CihplotT.png
Original file (1,267 × 1,059 pixels, file size: 87 KB, MIME type: image/png)
Explicit plot $y=\mathrm{Cih}(x)=\cosh(x)/x$.
The minimum is realized at
- $x=H\approx 1.199678640257734$ ;
- $J=\mathrm{Cih}(H)\approx 1.50887956153832$
C++ generator of curve
File ado.cin should be placed to the working directory in order to vompile the C++ code below.
#include <math.h> #include <stdio.h> #include <stdlib.h> #define DB double #define DO(x,y) for(x=0;x<y;x++) using namespace std; #include <complex> typedef complex<double> z_type; #define Re(x) x.real() #define Im(x) x.imag() #define I z_type(0.,1.) #include "ado.cin" //#include "acip.cin" #define M(x,y) fprintf(o,"%6.4f %6.4f M\n",0.+x,0.+y); #define L(x,y) fprintf(o,"%6.4f %6.4f L\n",0.+x,0.+y); #define S(x,y) fprintf(o,"S\n",); main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; //DB y1= 1.1996786402577337; //DB zL= 2.798386045783887; //DB fL= -0.33650841691839534; DB Ho=1.199678640257734; DB Jo=1.50887956153832; FILE *o;o=fopen("cihplot1.eps","w");ado(o,320,271); fprintf(o,"10 -90 translate\n 100 100 scale\n"); for(m=0;m<4;m++){M(m,1)L(m,3.5)} for(n=1;n<4;n++){M(0,n)L(3,n)} fprintf(o,"2 setlinecap .008 W 0 0 0 RGB S\n"); for(m=0;m<3;m++){M(.5+m,1)L(.5+m,3.5)} for(n=1;n<4;n++){M(0,n+.5)L(3,n+.5)} fprintf(o,"2 setlinecap .003 W 0 0 0 RGB S\n"); //M(fL,zL) DO(m,274){ x=.298+.01*m; //z=x; y=Re(ACip5(z)); y=cosh(x)/x; if(m==0)M(x,y) else L(x,y) } fprintf(o,"1 setlinejoin 1 setlinecap .012 W 0 .4 0 RGB S\n"); p=1.8;q=.7; // M(fL,1)L(fL,zL) L(0,zL) fprintf(o,"2 setlinecap .003 W 0 0 0 RGB S\n"); M(Ho,1)L(Ho,Jo) L(0,Jo) fprintf(o,"2 setlinecap .003 W 0 0 0 RGB S\n"); fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o); system("epstopdf cihplot1.eps"); system( "open cihplot1.pdf"); getchar(); system("killall Preview");//for mac }
Latex generator of labels
FIle cihplot1.pdf should be generated with the code above in order to compile the latex document below. % Copyleft 2012 by Dmitrii Kouznetsov %<br> \documentclass[12pt]{article} %<br> \usepackage{geometry} %<br> \usepackage{graphicx} %<br> \usepackage{rotating} %<br> \paperwidth 610pt %<br> \paperheight 510pt %<br> \topmargin -92pt %<br> \oddsidemargin -106pt %<br> \textwidth 900pt %<br> \textheight 900pt %<br> \pagestyle {empty} %<br> \newcommand \sx {\scalebox} %<br> \newcommand \rot {\begin{rotate}} %<br> \newcommand \ero {\end{rotate}} %<br> \newcommand \ing {\includegraphics} %<br> \begin{document} %<br> \parindent 0pt \sx{2}{ \begin{picture}(340,260) %<br> %\put(4,6){\ing{acosplot}} %<br> % \put(4,6){\ing{aciplot}} %<br> \put(4,6){\ing{cihplot1}} %<br> \put(16,250){\sx{1.8}{$y$}} %v \put(16,210){\sx{1.8}{\bf 3}} %<br> \put(16,160){\sx{1.8}{\bf 2.5}} %<br> \put(16,110){\sx{1.8}{\bf 2}} %<br> \put(13, 68){\sx{1.8}{$J$}} %<br> \put(12, 52){\sx{1.8}{\bf 1.5}} %<br> %\put(58, 19){\sx{2}{\bf 0}} %<br> \put(108, 19){\sx{2}{\bf 1}} %<br> \put(124, 19){\sx{2}{$H$}} %<br> \put(208, 19){\sx{2}{\bf 2}} %<br> \put(300, 21){\sx{2.1}{$x$}} %<br> \put(230,124){\sx{1.6}{\rot{54}$y\!=\!\mathrm{Cih}(x)$\ero}} \end{picture} %<br> } %<br> \end{document}
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current | 17:50, 20 June 2013 | 1,267 × 1,059 (87 KB) | Maintenance script (talk | contribs) | Importing image file |
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