Difference between revisions of "File:2014arc.png"

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(Importing image file)
 
 
Line 1: Line 1:
  +
Price $y$ of Russian rouble, measured in the USA cents, versus time $x$:
−
Importing image file
  
  +
  +
Data by https://www.mataf.net/en/currency/converter-USD-RUB
  +
available for 29 November 2014‎ (thick green line),
  +
  +
the lineal approximation of the data available 2014.10.27 (thin black straight line), and
  +
  +
the approximation Arc, made 2014.11.29 (thick ping arc):
  +
  +
$\mathrm{Arc}(x) = .01 \sqrt{(a+x)(b-x)}$
  +
  +
with $a=471$ и $b=123$.
  +
  +
At the specific choice of ratio of the scale of ordinate axis to that of the abscise axis, approximation Arc appears as arc of the perfect circle. In order to stress this, this arc is a little bit extended below the abscissa axis (to values that would correspond to negative branch of the square root). This approximation suggests imaginary values of rouble for time $x>132$.
  +
  +
Basically, graphic is the same, as the image from 2014.11.29, loaded as
  +
http://mizugadro.mydns.jp/t/index.php/File:RubleArc.png
  +
  +
The difference is, that a little bit more space at the left to provide the same range with the later figure http://mizugadro.mydns.jp/t/index.php/File:2015Arc.png , that figure shows that the good agreement of this approximation takes place also for the extended experimental data, since the beginning of year 2014, and more space is necessary.
  +
  +
This image is used as figure 1 in the article
  +
<ref name="r">
  +
http://mizugadro.mydns.jp/PAPERS/2015ARC/r02.pdf
  +
Дмитрий Кузнецов (Dmitrii Kouznetsov).
  +
Простая модель коллапсирующей экономики. 2015, in Russian.
  +
(The English version is expected to be loaded soon.)
  +
</ref>
  +
and, perhaps, the ubldated versions of that file.
  +
  +
This image is loaded for use in the articles
  +
  +
[[Model of collapsing economics]],
  +
  +
[[Модель коллапсирующей экономики]],
  +
  +
that is supposed to be basically the same as
  +
<ref name="r">
  +
http://mizugadro.mydns.jp/PAPERS/2015ARC/r02.pdf
  +
Дмитрий Кузнецов (Dmitrii Kouznetsov).
  +
Простая модель коллапсирующей экономики. 2015, in Russian.
  +
(The English version is expected to be loaded soon.)
  +
</ref>,
  +
  +
but needs some [[TORI]]fication at the uploading.
  +
  +
==References==
  +
<references/>
  +
  +
== Similar figures==
  +
  +
http://mizugadro.mydns.jp/t/index.php/File:RubleArc.png
  +
  +
http://mizugadro.mydns.jp/t/index.php/File:Ruble85210.png
  +
  +
http://mizugadro.mydns.jp/t/index.php/File:Ruble85210a.png
  +
  +
http://mizugadro.mydns.jp/t/index.php/File:2015arc.png
  +
  +
==Input files==
  +
  +
===original file===
  +
<poem><nomathjax><nowiki>
  +
2015-01-14 65 878.91
  +
2015-01-13 64 695.20
  +
2015-01-12 62 871.70
  +
2015-01-11 61 860.0
  +
2015-01-10 61 860.00
  +
2015-01-09 61 624.00
  +
2015-01-08 61 134.80
  +
2015-01-07 63 539.30
  +
2015-01-06 62 602.90
  +
2015-01-05 58 229.90
  +
2015-01-04 58 729.40
  +
2015-01-03 58 729.40
  +
2015-01-02 61 006.10
  +
2015-01-01 60 545.80
  +
2014-12-31 57 612.50
  +
2014-12-30 57 623.40
  +
2014-12-29 51 048.00
  +
2014-12-28 51 048.80
  +
2014-12-27 51 048.80
  +
2014-12-26 51 047.00
  +
2014-12-25 52 467.30
  +
2014-12-24 54 606.00
  +
2014-12-23 54 716.00
  +
2014-12-22 56 646.90
  +
2014-12-21 58 879.90
  +
2014-12-20 58 879.90
  +
2014-12-19 60 284.50
  +
2014-12-18 60 457.00
  +
2014-12-17 68 311.40
  +
2014-12-16 65 610.50
  +
2014-12-15 58 453.63
  +
2014-12-14 58 175.80
  +
2014-12-13 58 175.80
  +
2014-12-12 57 303.60
  +
2014-12-11 54 958.80
  +
2014-12-10 54 316.50
  +
2014-12-09 54 207.30
  +
2014-12-08 53 422.50
  +
2014-12-07 52 677.50
  +
2014-12-06 52 677.50
  +
2014-12-05 53 722.00
  +
2014-12-04 52 657.30
  +
2014-12-03 54 729.00
  +
2014-12-02 51 196.50
  +
2014-12-01 52 329.90
  +
2014-11-30 50 213.30
  +
2014-11-29 50 213.30
  +
2014-11-28 49 370.10
  +
2014-11-27 47 730.20
  +
2014-11-26 46 663.40
  +
2014-11-25 45 292.30
  +
2014-11-24 44 380.80
  +
2014-11-23 45 772.90
  +
2014-11-22 45 772.90
  +
2014-11-21 45 481.20
  +
2014-11-20 46 670.90
  +
2014-11-19 46 965.50
  +
2014-11-18 46 630.00
  +
2014-11-17 47 392.50
  +
2014-11-16 47 241.60
  +
2014-11-15 47 346.00
  +
2014-11-14 47 428.50
  +
2014-11-13 46 284.50
  +
2014-11-12 46 408.00
  +
2014-11-11 46 143.70
  +
2014-11-10 45 713.80
  +
2014-11-09 46 610.90
  +
2014-11-08 46 699.90
  +
2014-11-07 47 937.00
  +
2014-11-06 45 367.20
  +
2014-11-05 44 531.60
  +
2014-11-04 43 605.60
  +
2014-11-03 43 359.80
  +
2014-11-02 43 028.30
  +
2014-11-01 43 028.30
  +
2014-10-31 42 271.10
  +
2014-10-30 43 388.00
  +
2014-10-29 42 750.50
  +
2014-10-28 42 539.90
  +
2014-10-27 41 984.50
  +
2014-10-26 41 895.20
  +
2014-10-25 41 895.20
  +
2014-10-24 41 926.50
  +
2014-10-23 41 539.70
  +
2014-10-22 41 000.30
  +
2014-10-21 40 970.30
  +
2014-10-20 40 934.30
  +
2014-10-19 40 717.90
  +
2014-10-18 40 717.90
  +
2014-10-17 39 889.10
  +
2014-10-16 39 889.10
  +
2014-10-15 39 889.10
  +
2014-10-14 39 889.10
  +
2014-10-13 39 889.10
  +
2014-10-12 39 889.10
  +
2014-10-11 39 889.10
  +
2014-10-10 39 889.10
  +
2014-10-09 39 889.10
  +
2014-10-08 39 889.10
  +
2014-10-07 39 889.10
  +
2014-10-06 39 975.10
  +
2014-10-05 39 980.70
  +
2014-10-04 39 571.00
  +
2014-10-03 39 571.00
  +
2014-10-02 39 571.00
  +
2014-10-01 39 685.50
  +
2014-09-30 39 431.50
  +
2014-09-29 39 143.50
  +
2014-09-28 39 152.70
  +
2014-09-27 39 152.70
  +
2014-09-26 38 494.80
  +
2014-09-25 38 206.50
  +
2014-09-24 38 581.00
  +
2014-09-23 38 731.10
  +
2014-09-22 38 432.20
  +
2014-09-21 38 435.60
  +
2014-09-20 38 435.60
  +
2014-09-19 38 477.30
  +
2014-09-18 38 432.90
  +
2014-09-17 38 336.40
  +
2014-09-16 38 302.80
  +
2014-09-15 37 793.80
  +
2014-09-14 37 785.30
  +
2014-09-13 37 785.30
  +
2014-09-12 37 532.40
  +
2014-09-11 37 310.80
  +
2014-09-10 37 093.10
  +
2014-09-09 37 046.50
  +
2014-09-08 36 975.80
  +
2014-09-07 36 945.60
  +
2014-09-06 36 945.60
  +
2014-09-05 36 958.60
  +
2014-09-04 36 806.70
  +
2014-09-03 37 453.60
  +
2014-09-02 37 328.10
  +
2014-09-01 37 057.80
  +
2014-08-31 37 068.00
  +
2014-08-30 37 068.00
  +
2014-08-29 36 754.00
  +
2014-08-28 35 937.50
  +
2014-08-27 36 164.90
  +
2014-08-26 36 146.10
  +
2014-08-25 36 141.30
  +
2014-08-24 36 112.70
  +
2014-08-23 36 112.70
  +
2014-08-22 36 047.10
  +
2014-08-21 36 367.10
  +
2014-08-20 36 182.00
  +
2014-08-19 36 082.10
  +
2014-08-18 36 113.90
  +
2014-08-17 36 127.70
  +
2014-08-16 36 127.70
  +
2014-08-15 36 029.60
  +
2014-08-14 36 043.80
  +
2014-08-13 36 213.10
  +
2014-08-12 35 947.10
  +
2014-08-11 36 148.90
  +
2014-08-10 36 149.10
  +
2014-08-09 36 149.10
  +
2014-08-08 36 361.00
  +
2014-08-07 36 174.10
  +
2014-08-06 36 100.30
  +
2014-08-05 35 831.90
  +
2014-08-04 35 761.40
  +
2014-08-03 35 753.90
  +
2014-08-02 35 753.90
  +
2014-08-01 35 728.90
  +
2014-07-31 35 558.70
  +
2014-07-30 35 813.00
  +
2014-07-29 35 559.30
  +
2014-07-28 35 115.30
  +
2014-07-27 35 128.60
  +
2014-07-26 35 128.60
  +
2014-07-25 35 083.80
  +
2014-07-24 34 879.80
  +
2014-07-23 34 984.80
  +
2014-07-22 35 170.30
  +
2014-07-21 35 317.80
  +
2014-07-20 35 317.80
  +
2014-07-19 35 158.60
  +
2014-07-18 35 266.00
  +
2014-07-17 34 486.00
  +
2014-07-16 34 399.30
  +
2014-07-15 34 344.90
  +
2014-07-14 34 199.50
  +
2014-07-13 34 116.30
  +
2014-07-12 34 116.30
  +
2014-07-11 34 012.70
  +
2014-07-10 33 918.00
  +
2014-07-09 34 231.20
  +
2014-07-08 34 432.30
  +
2014-07-07 34 387.40
  +
2014-07-06 34 404.20
  +
2014-07-05 34 404.20
  +
2014-07-04 34 305.50
  +
2014-07-03 34 304.00
  +
2014-07-02 34 355.00
  +
2014-07-01 33 985.80
  +
2014-06-30 33 722.00
  +
2014-06-29 33 744.70
  +
2014-06-28 33 744.70
  +
2014-06-27 33 742.80
  +
2014-06-26 33 634.60
  +
2014-06-25 33 737.20
  +
2014-06-24 33 791.70
  +
2014-06-23 34 091.20
  +
2014-06-22 34 462.20
  +
2014-06-21 34 462.20
  +
2014-06-20 34 475.00
  +
2014-06-19 34 416.90
  +
2014-06-18 34 455.40
  +
2014-06-17 34 811.00
  +
2014-06-16 34 602.60
  +
2014-06-15 34 394.80
  +
2014-06-14 34 394.80
  +
2014-06-13 34 390.20
  +
2014-06-12 34 344.60
  +
2014-06-11 34 354.90
  +
2014-06-10 34 289.80
  +
2014-06-09 34 336.40
  +
2014-06-08 34 409.70
  +
2014-06-07 34 409.70
  +
2014-06-06 34 407.30
  +
2014-06-05 34 694.70
  +
2014-06-04 34 970.60
  +
2014-06-03 35 075.60
  +
2014-06-02 35 043.00
  +
2014-06-01 34 891.40
  +
2014-05-31 34 891.40
  +
  +
2014-05-30 34 893.2
  +
2014-05-29 34 688.3
  +
2014-05-28 34 512.9
  +
2014-05-27 34 405.9
  +
2014-05-26 34 170.1
  +
2014-05-25 34 118.6
  +
2014-05-24 34 118.6
  +
2014-05-23 34 115.4
  +
2014-05-22 34 303.1
  +
2014-05-21 34 325.4
  +
2014-05-20 34 508.1
  +
2014-05-19 34 546.4
  +
2014-05-18 34 762.2
  +
2014-05-17 34 762.2
  +
2014-05-16 34 779.8
  +
2014-05-15 34 757.2
  +
2014-05-14 34 634.4
  +
2014-05-13 34 849.7
  +
2014-05-12 35 001.1
  +
2014-05-11 35 214.7
  +
2014-05-10 35 214.7
  +
2014-05-09 35 203.3
  +
2014-05-08 35 034.7
  +
2014-05-07 35 918
  +
2014-05-06 35 439
  +
2014-05-05 35 667.7
  +
2014-05-04 35 851.7
  +
2014-05-03 35 851.2
  +
2014-05-02 35 822.3
  +
2014-05-01 35 589
  +
  +
2014-04-30 35 597.1
  +
2014-04-29 35 624.1
  +
2014-04-28 35 875.7
  +
2014-04-27 36 020.5
  +
2014-04-26 36 035.3
  +
2014-04-25 36 017.2
  +
2014-04-24 35 726.7
  +
2014-04-23 35 695.2
  +
2014-04-22 35 673.9
  +
2014-04-21 35 661.7
  +
2014-04-20 35 600.7
  +
2014-04-19 35 625
  +
2014-04-18 35 577.1
  +
2014-04-17 35 451.5
  +
2014-04-16 36 033
  +
2014-04-15 36 249
  +
2014-04-14 35 940.8
  +
2014-04-13 35 750.8
  +
2014-04-12 35 750.8
  +
2014-04-11 35 747.1
  +
2014-04-10 35 566.8
  +
2014-04-09 35 568.6
  +
2014-04-08 35 675.8
  +
2014-04-07 35 564.7
  +
2014-04-06 35 324.9
  +
2014-04-05 35 313.9
  +
2014-04-04 35 312
  +
2014-04-03 35 564.8
  +
2014-04-02 35 452.6
  +
2014-04-01 35 030.4
  +
  +
2014-03-31 35 157.2
  +
2014-03-30 35 786.3
  +
2014-03-29 35 786.3
  +
2014-03-28 35 752.4
  +
2014-03-27 35 615.7
  +
2014-03-26 35 515.4
  +
2014-03-25 35 517.4
  +
2014-03-24 36 095
  +
2014-03-23 36 249
  +
2014-03-22 36 249.5
  +
2014-03-21 36 245.4
  +
2014-03-20 36 300.6
  +
2014-03-19 36 189
  +
2014-03-18 36 238.5
  +
2014-03-17 36 208
  +
2014-03-16 36 616.8
  +
2014-03-15 36 616.8
  +
2014-03-14 36 563.2
  +
2014-03-13 36 568.1
  +
2014-03-12 36 468.9
  +
2014-03-11 36 441.3
  +
2014-03-10 36 369
  +
2014-03-09 36 403.1
  +
2014-03-08 36 403.1
  +
2014-03-07 36 385
  +
2014-03-06 36 178.3
  +
2014-03-05 36 056.4
  +
2014-03-04 36 028.4
  +
2014-03-03 36 513.3
  +
2014-03-02 35 982
  +
2014-03-01 35 982
  +
  +
2014-02-28 36 045.9
  +
2014-02-27 36 000.3
  +
2014-02-26 36 036.5
  +
2014-02-25 35 705.7
  +
2014-02-24 35 515.9
  +
2014-02-23 35 505.9
  +
2014-02-22 35 505.9
  +
2014-02-21 35 506
  +
2014-02-20 35 751.8
  +
  +
At the itme of the begiiinig of this table,
  +
The maximum was reached on 27 Oct 2014
  +
1 000.00 US Dollar = 41 984.50 Russian Ruble
  +
The minimum on 22 Feb 2009
  +
1 000.00 US Dollar = 27.60 Russian Ruble
  +
https://www.mataf.net/en/currency/converter-USD-RUB
  +
</nowiki></nomathjax></poem>
  +
  +
===Transformer of the input file===
  +
  +
<poem><nomathjax><nowiki>
  +
  +
#include<math.h>
  +
#include<stdio.h>
  +
#include<stdlib.h>
  +
#define DB double
  +
#define DO(x,y) for(x=0;x<y;x++)
  +
#include"daju24.cin"
  +
  +
int main(){
  +
int M=1024;
  +
int t[M];
  +
DB g[M];
  +
DB z;
  +
int j,jd,n,m,N; FILE *i,*o; int di; DB dr, x,y;
  +
  +
int zero=daju24(2014,10,27); //Date of beginning of the project
  +
  +
i=fopen("dollardat.txt","r");
  +
DO(n,M) { int Y,M,D; char c1,c2,c3;
  +
j=fscanf(i,"%4d%c%2d%c%2d%2d%lf",&Y,&c1,&M,&c2,&D, &di,&dr); if(j<3) break;
  +
t[n]=daju24(Y,M,D)-zero;
  +
z=di+dr/1000.;
  +
g[n]=10000./z; //printf("%4d %2d %2d %9.0f %9.3f\n",Y, M, D, t[n],f[n]);
  +
}
  +
fclose(i); N=n; printf("N=%4d\n",N);
  +
  +
o=fopen("ddat.txt","w");
  +
//DO(n,N) fprintf(o,"%4d %4.2lf\n",t[n],g[n]);
  +
for(n=N-1;n>=0;n--) fprintf(o,"%4d %4.2lf\n",t[n],g[n]);
  +
fclose(o);
  +
  +
}
  +
</nowiki></nomathjax></poem>
  +
  +
==[[C++]] generator of curves==
  +
<poem><nomathjax><nowiki>
  +
#include<math.h>
  +
#include<stdio.h>
  +
#include<stdlib.h>
  +
#define DB double
  +
#define DO(x,y) for(x=0;x<y;x++)
  +
  +
void ado(FILE *O, int X, int Y)
  +
{ fprintf(O,"%c!PS-Adobe-2.0 EPSF-2.0\n",'%');
  +
fprintf(O,"%c%cBoundingBox: 0 0 %d %d\n",'%','%',X,Y);
  +
fprintf(O,"/M {moveto} bind def\n");
  +
fprintf(O,"/L {lineto} bind def\n");
  +
fprintf(O,"/S {stroke} bind def\n");
  +
fprintf(O,"/s {show newpath} bind def\n");
  +
fprintf(O,"/C {closepath} bind def\n");
  +
fprintf(O,"/F {fill} bind def\n");
  +
fprintf(O,"/o {2 0 360 arc C F} bind def\n");
  +
// fprintf(O,"/times-Roman-Bold findfont 20 scalefont setfont\n");
  +
fprintf(O,"/Helvetica-Bold findfont 16 scalefont setfont\n");
  +
fprintf(O,"/W {setlinewidth} bind def\n");
  +
fprintf(O,"/RGB {setrgbcolor} bind def\n");}
  +
//#include"ado.cin"
  +
  +
DB arc(DB x){ return sqrt((123.-x)*(471.+x)); }
  +
  +
// http://stackoverflow.com/questions/12864741/converting-gregorian-date-to-julian-date-and-then-back-again-with-time
  +
void ju24da(int Mjd, int *Year, int *Month, int *Day) { int J, C, Y, M;
  +
J = Mjd + 2400000 + 68569;
  +
C = 4 * J / 146097;
  +
J = J - (146097 * C + 3) / 4;
  +
Y = 4000 * (J + 1) / 1461001;
  +
J = J - 1461 * Y / 4 + 31;
  +
M = 80 * J / 2447;
  +
*Day = J - 2447 * M / 80;
  +
J = M / 11;
  +
*Month = M + 2 - (12 * J);
  +
*Year = 100 * (C - 49) + Y + J;
  +
// http://www.leapsecond.com/tools/gpsdate.c
  +
}
  +
  +
int daju24(int Y,int M, int D) { int a, y,m;
  +
a=(14-M)/12; y=Y+4800-a; m=M+12*a-3;
  +
return D + (153*m+2)/5 +365*y + y/4 - y/100 + y/400 -32045 - 2400000; }
  +
  +
FILE *i,*o;
  +
int main(){ int j,n,m,N=200;
  +
  +
o=fopen("fig1.eps","w");
  +
ado(o,820,324);
  +
#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 o(x,y) fprintf(o,"%6.2f %6.2f o\n",0.+x,0.+y);
  +
fprintf(o,"310 10 translate \n");
  +
for(n=0;n<301;n+=50) {M(-300,n)L(500,n)}
  +
for(n=-300;n<501;n+=50) {M(n,0)L(n,300)}
  +
fprintf(o,"0 0 0 RGB 2 setlinecap .5 W S\n");
  +
//M(-20,0) L(50,0) M(0,-0.2) L(0,30) fprintf(o,"0 0 0 RGB .16 W S\n");
  +
DB x,y;
  +
  +
int no=daju24(2014,10,27);
  +
for(n=-300;n<100;n+=50) { int y,m,d; ju24da(no+n, &y, &m, &d);
  +
fprintf(o, "gsave %4d 8 translate 90 rotate 0 -6 M (%4d.%02d.%02d) show grestore\n",n,y,m,d); }
  +
  +
for(n=100;n<501;n+=50) { int y,m,d; ju24da(no+n, &y, &m, &d);
  +
fprintf(o, "gsave %4d 210 translate 90 rotate 0 -5 M (%4d.%02d.%02d) show grestore\n",n,y,m,d); }
  +
  +
M(-120,300) L(500,0)
  +
fprintf(o,"0 0 0 RGB .2 W S\n");
  +
  +
for(n=0;n<500;n++) { x=n-300.; y=arc(x); if(y>=0){if(n==0)M(x,y) else L(x,y) } }
  +
fprintf(o,"1 0 1 RGB 6 W S\n");
  +
  +
int T[1024], X[1024];
  +
DB F[1024], Y[1024];
  +
  +
int k,Ndd;
  +
i=fopen("ddat.txt","r");
  +
DO(n,1024){j=fscanf(i,"%lf%lf",&x,&y); if(j<2) break; //if(x>10) break;
  +
T[n]=x; F[n]=y;} // if(x>-321.) o(x,y);}
  +
fclose(i); Ndd=n;
  +
  +
DO(k,Ndd){if(T[k]>-150) break;}
  +
  +
for(n=k;n<Ndd;n++){ x=T[n]; y=F[n]; if(n==k) M(x,y) else L(x,y) if(x>32)break; }
  +
fprintf(o,"0 1 0 RGB 1 setlinejoin 1 setlinecap 10 W S\n");
  +
  +
nomore:
  +
fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
  +
system("epstopdf fig1.eps");
  +
system( "open fig1.pdf");
  +
}
  +
</nowiki></nomathjax></poem>
  +
  +
==[[Latex]] generator of labels==
  +
  +
<poem><nomathjax><nowiki>
  +
\documentclass[12pt]{article}
  +
\usepackage{geometry}
  +
\usepackage{graphicx}
  +
\usepackage{rotating}
  +
\usepackage{color}
  +
\definecolor{pink}{RGB}{255,127,255}
  +
\paperwidth 832pt
  +
\paperheight 342pt
  +
\textwidth 800pt
  +
\textheight 400pt
  +
\topmargin -92pt
  +
%\oddsidemargin -84pt
  +
\oddsidemargin 12pt
  +
\newcommand \sx {\scalebox}
  +
\newcommand \rot {\begin{rotate}}
  +
\newcommand \ero {\end{rotate}}
  +
\begin{document}
  +
\begin{picture}(730,318)
  +
%\put(-6,-8){\sx{.64}{\includegraphics{85210_original.png}}}
  +
%\put(-6.4,-8.4){\sx{.64}{\includegraphics{85210_original.png}}} %%%%%%%%
  +
\put(46,20){\sx{14.9}{\color{pink} \circle{50}}}
  +
%\put(10,10){\includegraphics{dollarplo}}
  +
%\put(-90,10){\includegraphics{08}}
  +
\put(-90,10){\includegraphics{fig1}}
  +
\put(-100,310){\sx{2.3}{$y$}}
  +
%\put(-104,308){\sx{1.3}{Ruble}}
  +
%\put(-104,296){\sx{1.3}{in cents}}
  +
%\put(-104,282){\sx{1.3}{of USA}}
  +
\put(-98,212){\sx{2.2}{2}}
  +
\put(-98,112){\sx{2.2}{1}}
  +
\put(-98, 12){\sx{2.2}{0}}
  +
\put(-18,-3){\sx{2.2}{$-200$}}
  +
\put(82,-3){\sx{2.2}{$-100$}}
  +
\put(215,-3){\sx{2.2}{$0$}}
  +
\put(302,-3){\sx{2.2}{$100$}}
  +
\put(402,-3){\sx{2.2}{$200$}}
  +
\put(502,-3){\sx{2.2}{$300$}}
  +
\put(602,-3){\sx{2.2}{$400$}}
  +
%\put(600,-2){\sx{2.5}{$400$}}
  +
\put(660,-1){\sx{1.9}{$x$, days}}
  +
%\put(86,30){\sx{2.4}{\rot{90}{\bf 2014.05.31}\ero}}
  +
%\put(130,30){\sx{2.4}{\rot{90}{\bf 2014.07.19}\ero}}
  +
%\put(180,30){\sx{2.}{\rot{90}{\bf 2014.09.07}\ero}}
  +
%\put(230,30){\sx{2.4}{\rot{90}{\bf 2014.10.27}\ero}}
  +
%\put(280,30){\sx{2.}{\rot{90}{\bf 2014.09.16}\ero}}
  +
%\put(330,30){\sx{2.4}{\rot{90}{\bf 2015.02.04}\ero}}
  +
%\put(380,192){\sx{2.}{\rot{90}{\bf 2014.03.26}\ero}}
  +
%\put(430,172){\sx{2.4}{\rot{90}{\bf 2015.05.15}\ero}}
  +
%\put(480,192){\sx{2.}{\rot{90}{\bf 2015.07.04}\ero}}
  +
%\put(530,172){\sx{2.4}{\rot{90}{\bf 2015.08.23}\ero}}
  +
%\put(630,172){\sx{2.4}{\rot{90}{\bf 2015.12.01}\ero}}
  +
%\put(730,172){\sx{2.4}{\rot{90}{\bf 2016.03.10}\ero}}
  +
%\put(-33,317){\sx{1.8}{\rot{2}$y\!=\!\mathrm{Arc}(x)$\ero}}
  +
\put(-42,290){\sx{1.8}{\rot{5}$y\!=\!\mathrm{Arc}(x)$\ero}}
  +
\put(380,192){\sx{2}{\rot{-26}$y=\mathrm{Linear}(x)=2.4-0.0048 x$\ero}}
  +
\put(302,144){\sx{2}{\rot{-79}$y\!=\!\mathrm{Arc}(x)$\ero}}
  +
\end{picture}
  +
\end{document}
  +
</nowiki></nomathjax></poem>
  +
  +
[[Category:Arc]]
  +
[[Category:Explicit plot]]
  +
[[Category:C++]]
  +
[[Category:Latex]]
  +
[[Category:Ruble]]
  +
[[Category:Rouble]]
  +
[[Category:Inflation]]

Latest revision as of 08:26, 1 December 2018

Price $y$ of Russian rouble, measured in the USA cents, versus time $x$:

Data by https://www.mataf.net/en/currency/converter-USD-RUB available for 29 November 2014‎ (thick green line),

the lineal approximation of the data available 2014.10.27 (thin black straight line), and

the approximation Arc, made 2014.11.29 (thick ping arc):

$\mathrm{Arc}(x) = .01 \sqrt{(a+x)(b-x)}$

with $a=471$ и $b=123$.

At the specific choice of ratio of the scale of ordinate axis to that of the abscise axis, approximation Arc appears as arc of the perfect circle. In order to stress this, this arc is a little bit extended below the abscissa axis (to values that would correspond to negative branch of the square root). This approximation suggests imaginary values of rouble for time $x>132$.

Basically, graphic is the same, as the image from 2014.11.29, loaded as http://mizugadro.mydns.jp/t/index.php/File:RubleArc.png

The difference is, that a little bit more space at the left to provide the same range with the later figure http://mizugadro.mydns.jp/t/index.php/File:2015Arc.png , that figure shows that the good agreement of this approximation takes place also for the extended experimental data, since the beginning of year 2014, and more space is necessary.

This image is used as figure 1 in the article [1] and, perhaps, the ubldated versions of that file.

This image is loaded for use in the articles

Model of collapsing economics,

Модель коллапсирующей экономики,

that is supposed to be basically the same as [1],

but needs some TORIfication at the uploading.

References

  1. ↑ 1.0 1.1 http://mizugadro.mydns.jp/PAPERS/2015ARC/r02.pdf Дмитрий Кузнецов (Dmitrii Kouznetsov). Простая модель коллапсирующей экономики. 2015, in Russian. (The English version is expected to be loaded soon.)

Similar figures

http://mizugadro.mydns.jp/t/index.php/File:RubleArc.png

http://mizugadro.mydns.jp/t/index.php/File:Ruble85210.png

http://mizugadro.mydns.jp/t/index.php/File:Ruble85210a.png

http://mizugadro.mydns.jp/t/index.php/File:2015arc.png

Input files

original file


2015-01-14 65 878.91
2015-01-13 64 695.20
2015-01-12 62 871.70
2015-01-11 61 860.0
2015-01-10 61 860.00
2015-01-09 61 624.00
2015-01-08 61 134.80
2015-01-07 63 539.30
2015-01-06 62 602.90
2015-01-05 58 229.90
2015-01-04 58 729.40
2015-01-03 58 729.40
2015-01-02 61 006.10
2015-01-01 60 545.80
2014-12-31 57 612.50
2014-12-30 57 623.40
2014-12-29 51 048.00
2014-12-28 51 048.80
2014-12-27 51 048.80
2014-12-26 51 047.00
2014-12-25 52 467.30
2014-12-24 54 606.00
2014-12-23 54 716.00
2014-12-22 56 646.90
2014-12-21 58 879.90
2014-12-20 58 879.90
2014-12-19 60 284.50
2014-12-18 60 457.00
2014-12-17 68 311.40
2014-12-16 65 610.50
2014-12-15 58 453.63
2014-12-14 58 175.80
2014-12-13 58 175.80
2014-12-12 57 303.60
2014-12-11 54 958.80
2014-12-10 54 316.50
2014-12-09 54 207.30
2014-12-08 53 422.50
2014-12-07 52 677.50
2014-12-06 52 677.50
2014-12-05 53 722.00
2014-12-04 52 657.30
2014-12-03 54 729.00
2014-12-02 51 196.50
2014-12-01 52 329.90
2014-11-30 50 213.30
2014-11-29 50 213.30
2014-11-28 49 370.10
2014-11-27 47 730.20
2014-11-26 46 663.40
2014-11-25 45 292.30
2014-11-24 44 380.80
2014-11-23 45 772.90
2014-11-22 45 772.90
2014-11-21 45 481.20
2014-11-20 46 670.90
2014-11-19 46 965.50
2014-11-18 46 630.00
2014-11-17 47 392.50
2014-11-16 47 241.60
2014-11-15 47 346.00
2014-11-14 47 428.50
2014-11-13 46 284.50
2014-11-12 46 408.00
2014-11-11 46 143.70
2014-11-10 45 713.80
2014-11-09 46 610.90
2014-11-08 46 699.90
2014-11-07 47 937.00
2014-11-06 45 367.20
2014-11-05 44 531.60
2014-11-04 43 605.60
2014-11-03 43 359.80
2014-11-02 43 028.30
2014-11-01 43 028.30
2014-10-31 42 271.10
2014-10-30 43 388.00
2014-10-29 42 750.50
2014-10-28 42 539.90
2014-10-27 41 984.50
2014-10-26 41 895.20
2014-10-25 41 895.20
2014-10-24 41 926.50
2014-10-23 41 539.70
2014-10-22 41 000.30
2014-10-21 40 970.30
2014-10-20 40 934.30
2014-10-19 40 717.90
2014-10-18 40 717.90
2014-10-17 39 889.10
2014-10-16 39 889.10
2014-10-15 39 889.10
2014-10-14 39 889.10
2014-10-13 39 889.10
2014-10-12 39 889.10
2014-10-11 39 889.10
2014-10-10 39 889.10
2014-10-09 39 889.10
2014-10-08 39 889.10
2014-10-07 39 889.10
2014-10-06 39 975.10
2014-10-05 39 980.70
2014-10-04 39 571.00
2014-10-03 39 571.00
2014-10-02 39 571.00
2014-10-01 39 685.50
2014-09-30 39 431.50
2014-09-29 39 143.50
2014-09-28 39 152.70
2014-09-27 39 152.70
2014-09-26 38 494.80
2014-09-25 38 206.50
2014-09-24 38 581.00
2014-09-23 38 731.10
2014-09-22 38 432.20
2014-09-21 38 435.60
2014-09-20 38 435.60
2014-09-19 38 477.30
2014-09-18 38 432.90
2014-09-17 38 336.40
2014-09-16 38 302.80
2014-09-15 37 793.80
2014-09-14 37 785.30
2014-09-13 37 785.30
2014-09-12 37 532.40
2014-09-11 37 310.80
2014-09-10 37 093.10
2014-09-09 37 046.50
2014-09-08 36 975.80
2014-09-07 36 945.60
2014-09-06 36 945.60
2014-09-05 36 958.60
2014-09-04 36 806.70
2014-09-03 37 453.60
2014-09-02 37 328.10
2014-09-01 37 057.80
2014-08-31 37 068.00
2014-08-30 37 068.00
2014-08-29 36 754.00
2014-08-28 35 937.50
2014-08-27 36 164.90
2014-08-26 36 146.10
2014-08-25 36 141.30
2014-08-24 36 112.70
2014-08-23 36 112.70
2014-08-22 36 047.10
2014-08-21 36 367.10
2014-08-20 36 182.00
2014-08-19 36 082.10
2014-08-18 36 113.90
2014-08-17 36 127.70
2014-08-16 36 127.70
2014-08-15 36 029.60
2014-08-14 36 043.80
2014-08-13 36 213.10
2014-08-12 35 947.10
2014-08-11 36 148.90
2014-08-10 36 149.10
2014-08-09 36 149.10
2014-08-08 36 361.00
2014-08-07 36 174.10
2014-08-06 36 100.30
2014-08-05 35 831.90
2014-08-04 35 761.40
2014-08-03 35 753.90
2014-08-02 35 753.90
2014-08-01 35 728.90
2014-07-31 35 558.70
2014-07-30 35 813.00
2014-07-29 35 559.30
2014-07-28 35 115.30
2014-07-27 35 128.60
2014-07-26 35 128.60
2014-07-25 35 083.80
2014-07-24 34 879.80
2014-07-23 34 984.80
2014-07-22 35 170.30
2014-07-21 35 317.80
2014-07-20 35 317.80
2014-07-19 35 158.60
2014-07-18 35 266.00
2014-07-17 34 486.00
2014-07-16 34 399.30
2014-07-15 34 344.90
2014-07-14 34 199.50
2014-07-13 34 116.30
2014-07-12 34 116.30
2014-07-11 34 012.70
2014-07-10 33 918.00
2014-07-09 34 231.20
2014-07-08 34 432.30
2014-07-07 34 387.40
2014-07-06 34 404.20
2014-07-05 34 404.20
2014-07-04 34 305.50
2014-07-03 34 304.00
2014-07-02 34 355.00
2014-07-01 33 985.80
2014-06-30 33 722.00
2014-06-29 33 744.70
2014-06-28 33 744.70
2014-06-27 33 742.80
2014-06-26 33 634.60
2014-06-25 33 737.20
2014-06-24 33 791.70
2014-06-23 34 091.20
2014-06-22 34 462.20
2014-06-21 34 462.20
2014-06-20 34 475.00
2014-06-19 34 416.90
2014-06-18 34 455.40
2014-06-17 34 811.00
2014-06-16 34 602.60
2014-06-15 34 394.80
2014-06-14 34 394.80
2014-06-13 34 390.20
2014-06-12 34 344.60
2014-06-11 34 354.90
2014-06-10 34 289.80
2014-06-09 34 336.40
2014-06-08 34 409.70
2014-06-07 34 409.70
2014-06-06 34 407.30
2014-06-05 34 694.70
2014-06-04 34 970.60
2014-06-03 35 075.60
2014-06-02 35 043.00
2014-06-01 34 891.40
2014-05-31 34 891.40

2014-05-30 34 893.2
2014-05-29 34 688.3
2014-05-28 34 512.9
2014-05-27 34 405.9
2014-05-26 34 170.1
2014-05-25 34 118.6
2014-05-24 34 118.6
2014-05-23 34 115.4
2014-05-22 34 303.1
2014-05-21 34 325.4
2014-05-20 34 508.1
2014-05-19 34 546.4
2014-05-18 34 762.2
2014-05-17 34 762.2
2014-05-16 34 779.8
2014-05-15 34 757.2
2014-05-14 34 634.4
2014-05-13 34 849.7
2014-05-12 35 001.1
2014-05-11 35 214.7
2014-05-10 35 214.7
2014-05-09 35 203.3
2014-05-08 35 034.7
2014-05-07 35 918
2014-05-06 35 439
2014-05-05 35 667.7
2014-05-04 35 851.7
2014-05-03 35 851.2
2014-05-02 35 822.3
2014-05-01 35 589

2014-04-30 35 597.1
2014-04-29 35 624.1
2014-04-28 35 875.7
2014-04-27 36 020.5
2014-04-26 36 035.3
2014-04-25 36 017.2
2014-04-24 35 726.7
2014-04-23 35 695.2
2014-04-22 35 673.9
2014-04-21 35 661.7
2014-04-20 35 600.7
2014-04-19 35 625
2014-04-18 35 577.1
2014-04-17 35 451.5
2014-04-16 36 033
2014-04-15 36 249
2014-04-14 35 940.8
2014-04-13 35 750.8
2014-04-12 35 750.8
2014-04-11 35 747.1
2014-04-10 35 566.8
2014-04-09 35 568.6
2014-04-08 35 675.8
2014-04-07 35 564.7
2014-04-06 35 324.9
2014-04-05 35 313.9
2014-04-04 35 312
2014-04-03 35 564.8
2014-04-02 35 452.6
2014-04-01 35 030.4

2014-03-31 35 157.2
2014-03-30 35 786.3
2014-03-29 35 786.3
2014-03-28 35 752.4
2014-03-27 35 615.7
2014-03-26 35 515.4
2014-03-25 35 517.4
2014-03-24 36 095
2014-03-23 36 249
2014-03-22 36 249.5
2014-03-21 36 245.4
2014-03-20 36 300.6
2014-03-19 36 189
2014-03-18 36 238.5
2014-03-17 36 208
2014-03-16 36 616.8
2014-03-15 36 616.8
2014-03-14 36 563.2
2014-03-13 36 568.1
2014-03-12 36 468.9
2014-03-11 36 441.3
2014-03-10 36 369
2014-03-09 36 403.1
2014-03-08 36 403.1
2014-03-07 36 385
2014-03-06 36 178.3
2014-03-05 36 056.4
2014-03-04 36 028.4
2014-03-03 36 513.3
2014-03-02 35 982
2014-03-01 35 982

2014-02-28 36 045.9
2014-02-27 36 000.3
2014-02-26 36 036.5
2014-02-25 35 705.7
2014-02-24 35 515.9
2014-02-23 35 505.9
2014-02-22 35 505.9
2014-02-21 35 506
2014-02-20 35 751.8

At the itme of the begiiinig of this table,
The maximum was reached on 27 Oct 2014
1 000.00 US Dollar = 41 984.50 Russian Ruble
The minimum on 22 Feb 2009
1 000.00 US Dollar = 27.60 Russian Ruble
https://www.mataf.net/en/currency/converter-USD-RUB

Transformer of the input file



#include<math.h>
#include<stdio.h>
#include<stdlib.h>
#define DB double
#define DO(x,y) for(x=0;x<y;x++)
#include"daju24.cin"

int main(){
int M=1024;
int t[M];
DB g[M];
DB z;
int j,jd,n,m,N; FILE *i,*o; int di; DB dr, x,y;

int zero=daju24(2014,10,27); //Date of beginning of the project

i=fopen("dollardat.txt","r");
DO(n,M) { int Y,M,D; char c1,c2,c3;
j=fscanf(i,"%4d%c%2d%c%2d%2d%lf",&Y,&c1,&M,&c2,&D, &di,&dr); if(j<3) break;
t[n]=daju24(Y,M,D)-zero;
z=di+dr/1000.;
g[n]=10000./z; //printf("%4d %2d %2d %9.0f %9.3f\n",Y, M, D, t[n],f[n]);
}
fclose(i); N=n; printf("N=%4d\n",N);

o=fopen("ddat.txt","w");
//DO(n,N) fprintf(o,"%4d %4.2lf\n",t[n],g[n]);
for(n=N-1;n>=0;n--) fprintf(o,"%4d %4.2lf\n",t[n],g[n]);
fclose(o);

}

C++ generator of curves


#include<math.h>
#include<stdio.h>
#include<stdlib.h>
#define DB double
#define DO(x,y) for(x=0;x<y;x++)

void ado(FILE *O, int X, int Y)
{ fprintf(O,"%c!PS-Adobe-2.0 EPSF-2.0\n",'%');
        fprintf(O,"%c%cBoundingBox: 0 0 %d %d\n",'%','%',X,Y);
        fprintf(O,"/M {moveto} bind def\n");
        fprintf(O,"/L {lineto} bind def\n");
        fprintf(O,"/S {stroke} bind def\n");
        fprintf(O,"/s {show newpath} bind def\n");
        fprintf(O,"/C {closepath} bind def\n");
        fprintf(O,"/F {fill} bind def\n");
        fprintf(O,"/o {2 0 360 arc C F} bind def\n");
// fprintf(O,"/times-Roman-Bold findfont 20 scalefont setfont\n");
        fprintf(O,"/Helvetica-Bold findfont 16 scalefont setfont\n");
        fprintf(O,"/W {setlinewidth} bind def\n");
        fprintf(O,"/RGB {setrgbcolor} bind def\n");}
//#include"ado.cin"

DB arc(DB x){ return sqrt((123.-x)*(471.+x)); }

// http://stackoverflow.com/questions/12864741/converting-gregorian-date-to-julian-date-and-then-back-again-with-time
void ju24da(int Mjd, int *Year, int *Month, int *Day) { int J, C, Y, M;
    J = Mjd + 2400000 + 68569;
    C = 4 * J / 146097;
    J = J - (146097 * C + 3) / 4;
    Y = 4000 * (J + 1) / 1461001;
    J = J - 1461 * Y / 4 + 31;
    M = 80 * J / 2447;
    *Day = J - 2447 * M / 80;
    J = M / 11;
    *Month = M + 2 - (12 * J);
    *Year = 100 * (C - 49) + Y + J;
// http://www.leapsecond.com/tools/gpsdate.c
}

int daju24(int Y,int M, int D) { int a, y,m;
  a=(14-M)/12; y=Y+4800-a; m=M+12*a-3;
  return D + (153*m+2)/5 +365*y + y/4 - y/100 + y/400 -32045 - 2400000; }

FILE *i,*o;
int main(){ int j,n,m,N=200;

o=fopen("fig1.eps","w");
ado(o,820,324);
#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 o(x,y) fprintf(o,"%6.2f %6.2f o\n",0.+x,0.+y);
fprintf(o,"310 10 translate \n");
for(n=0;n<301;n+=50) {M(-300,n)L(500,n)}
for(n=-300;n<501;n+=50) {M(n,0)L(n,300)}
fprintf(o,"0 0 0 RGB 2 setlinecap .5 W S\n");
//M(-20,0) L(50,0) M(0,-0.2) L(0,30) fprintf(o,"0 0 0 RGB .16 W S\n");
DB x,y;

int no=daju24(2014,10,27);
for(n=-300;n<100;n+=50) { int y,m,d; ju24da(no+n, &y, &m, &d);
fprintf(o, "gsave %4d 8 translate 90 rotate 0 -6 M (%4d.%02d.%02d) show grestore\n",n,y,m,d); }

for(n=100;n<501;n+=50) { int y,m,d; ju24da(no+n, &y, &m, &d);
fprintf(o, "gsave %4d 210 translate 90 rotate 0 -5 M (%4d.%02d.%02d) show grestore\n",n,y,m,d); }

M(-120,300) L(500,0)
fprintf(o,"0 0 0 RGB .2 W S\n");

for(n=0;n<500;n++) { x=n-300.; y=arc(x); if(y>=0){if(n==0)M(x,y) else L(x,y) } }
fprintf(o,"1 0 1 RGB 6 W S\n");
  
int T[1024], X[1024];
DB F[1024], Y[1024];

int k,Ndd;
i=fopen("ddat.txt","r");
DO(n,1024){j=fscanf(i,"%lf%lf",&x,&y); if(j<2) break; //if(x>10) break;
        T[n]=x; F[n]=y;} // if(x>-321.) o(x,y);}
fclose(i); Ndd=n;

DO(k,Ndd){if(T[k]>-150) break;}

for(n=k;n<Ndd;n++){ x=T[n]; y=F[n]; if(n==k) M(x,y) else L(x,y) if(x>32)break; }
fprintf(o,"0 1 0 RGB 1 setlinejoin 1 setlinecap 10 W S\n");

nomore:
fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
      system("epstopdf fig1.eps");
      system( "open fig1.pdf");
}

Latex generator of labels


\documentclass[12pt]{article}
\usepackage{geometry}
\usepackage{graphicx}
\usepackage{rotating}
\usepackage{color}
\definecolor{pink}{RGB}{255,127,255}
\paperwidth 832pt
\paperheight 342pt
\textwidth 800pt
\textheight 400pt
\topmargin -92pt
%\oddsidemargin -84pt
\oddsidemargin 12pt
\newcommand \sx {\scalebox}
\newcommand \rot {\begin{rotate}}
\newcommand \ero {\end{rotate}}
\begin{document}
\begin{picture}(730,318)
%\put(-6,-8){\sx{.64}{\includegraphics{85210_original.png}}}
%\put(-6.4,-8.4){\sx{.64}{\includegraphics{85210_original.png}}} %%%%%%%%
\put(46,20){\sx{14.9}{\color{pink} \circle{50}}}
%\put(10,10){\includegraphics{dollarplo}}
%\put(-90,10){\includegraphics{08}}
\put(-90,10){\includegraphics{fig1}}
\put(-100,310){\sx{2.3}{$y$}}
%\put(-104,308){\sx{1.3}{Ruble}}
%\put(-104,296){\sx{1.3}{in cents}}
%\put(-104,282){\sx{1.3}{of USA}}
\put(-98,212){\sx{2.2}{2}}
\put(-98,112){\sx{2.2}{1}}
\put(-98, 12){\sx{2.2}{0}}
\put(-18,-3){\sx{2.2}{$-200$}}
\put(82,-3){\sx{2.2}{$-100$}}
\put(215,-3){\sx{2.2}{$0$}}
\put(302,-3){\sx{2.2}{$100$}}
\put(402,-3){\sx{2.2}{$200$}}
\put(502,-3){\sx{2.2}{$300$}}
\put(602,-3){\sx{2.2}{$400$}}
%\put(600,-2){\sx{2.5}{$400$}}
\put(660,-1){\sx{1.9}{$x$, days}}
%\put(86,30){\sx{2.4}{\rot{90}{\bf 2014.05.31}\ero}}
%\put(130,30){\sx{2.4}{\rot{90}{\bf 2014.07.19}\ero}}
%\put(180,30){\sx{2.}{\rot{90}{\bf 2014.09.07}\ero}}
%\put(230,30){\sx{2.4}{\rot{90}{\bf 2014.10.27}\ero}}
%\put(280,30){\sx{2.}{\rot{90}{\bf 2014.09.16}\ero}}
%\put(330,30){\sx{2.4}{\rot{90}{\bf 2015.02.04}\ero}}
%\put(380,192){\sx{2.}{\rot{90}{\bf 2014.03.26}\ero}}
%\put(430,172){\sx{2.4}{\rot{90}{\bf 2015.05.15}\ero}}
%\put(480,192){\sx{2.}{\rot{90}{\bf 2015.07.04}\ero}}
%\put(530,172){\sx{2.4}{\rot{90}{\bf 2015.08.23}\ero}}
%\put(630,172){\sx{2.4}{\rot{90}{\bf 2015.12.01}\ero}}
%\put(730,172){\sx{2.4}{\rot{90}{\bf 2016.03.10}\ero}}
%\put(-33,317){\sx{1.8}{\rot{2}$y\!=\!\mathrm{Arc}(x)$\ero}}
\put(-42,290){\sx{1.8}{\rot{5}$y\!=\!\mathrm{Arc}(x)$\ero}}
\put(380,192){\sx{2}{\rot{-26}$y=\mathrm{Linear}(x)=2.4-0.0048 x$\ero}}
\put(302,144){\sx{2}{\rot{-79}$y\!=\!\mathrm{Arc}(x)$\ero}}
\end{picture}
\end{document}

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