Image:Neusis-trisection.png

[edit] Summary

Neusis trisection of an angle θ>135° to find φ=θ/3, using only the length of the ruler. The radius of the arc is equal to the length of the ruler. Used in en:Neusis_construction.

[edit] Licensing

I, the copyright holder of this work, hereby publish it under the following licenses: Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation license, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled "GNU Free Documentation license". Aragonés | العربية | Asturianu | Български | বাংলা | ইমার ঠার/বিষ্ণুপ্রিয়া মণিপুরী | Brezhoneg | Bosanski | Català | Cebuano | Česky | Dansk | Deutsch | Ελληνικά | English | Esperanto | Español | Eesti | Euskara | فارسی | Suomi | Français | Gaeilge | Galego | עברית | Hrvatski | Magyar | Bahasa Indonesia | Ido | Íslenska | Italiano | 日本語 | ქართული | ភាសាខ្មែរ | 한국어 | Kurdî / كوردی | Latina | Lëtzebuergesch | Lietuvių | Bahasa Melayu | Nnapulitano | Nederlands | ‪Norsk (nynorsk)‬ | ‪Norsk (bokmål)‬ | Occitan | Polski | Português | Română | Русский | Slovenčina | Slovenščina | Shqip | Српски / Srpski | Svenska | తెలుగు | ไทย | Türkçe | Українська | اردو | Tiếng Việt | Volapük | Yorùbá | ‪中文(中国大陆)‬ | ‪中文(台灣)‬ | +/- This file is licensed under the Creative Commons Attribution ShareAlike license versions 2.5, 2.0, and 1.0 العربية | Български | Català | Česky | Dansk | Deutsch | English | Español | Euskara | فارسی | Français | עברית | Italiano | 日本語 | 한국어 | Lietuvių | Nederlands | Polski | Português | Русский | Svenska | தமிழ் | Türkçe | 中文 | 中文 | +/- You may select the license of your choice.

[edit] Metapost source

The Metapost source for this file. All done via command line on MacOSX:

• Metapost (mpost command from teTeX)
• \convertMPtoPDF TeX command from supp-pdf.tex, processed via pdfTeX
• ghostscript to a png at 1200x1200.

I hereby make this source available under the GPL version 2 or later.

u=2cm;
path unitcircle;   unitcircle=fullcircle scaled 2u;
path tick[];   tick0:=(-1mm,0)--(1mm,0);   tick1:=tick0 rotated 90;
thick=1mm;
thin=0.25mm;
path ruler[],anglemark[];
beginfig(3)
    pickup  pencircle scaled thin;
    theta=162;
    z0=(0,0);
    z1=(u,0)=-z3=-.5z3l;
%  z2=(0,u)=-z4;
    z5=u*dir(theta);
    z7=(-u,0) rotated (-theta/3);
    y6=y0;
    x6=2x7;
    ruler0:=unitsquare xscaled u yscaled .1u rotated angle(z7-z6) shifted z6;
    ruler1:=unitsquare yscaled 0.5 shifted 0.25up xscaled u yscaled .1u rotated angle(z7-z6) shifted z6;
    fill ruler0 withcolor (1,1,.5);
    fill ruler1 withcolor (.9,.9,.3);
    draw ruler0 withpen pencircle scaled 0.25;
    draw subpath(0,4) of unitcircle ;
    draw z1--.3[z3,z3l] ;
    draw z0--z5 ;
    label.bot("O",z0);
    label.bot("A",z6);
    label.ulft("P",z5);
    label.top("B",z7);
    anglemark0= unitcircle scaled 0.2 cutbefore (z0--z1) cutafter (z0--z5);
    draw anglemark0;
    label.urt(btex $\theta$ etex, point .4length(anglemark0) of anglemark0);
    draw z6--z7--z0 withcolor blue;
    anglemark1= unitcircle scaled 0.3 cutbefore (z0--z7) cutafter (z0--z3);
    label.ulft(btex $\varphi$ etex, point 0 of anglemark1 rotated (theta/6)) withcolor blue;
    draw anglemark1 withcolor blue;
    for i = 0,5,6,7:
        if known(x[i]):
            drawdot z[i] withpen pencircle scaled thick;
%          label(decimal i,z[i]) withcolor green;
        fi
    endfor
    clip currentpicture to bbox( (.4u,0)--(0,u)--(-1.25u,0)--(0,-0.25u));
endfig;
bye

• Neusis construction