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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.

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.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue

	This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
	You are free: to share – to copy, distribute and transmit the work to remix – to adapt the work Under the following conditions: attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
	This licensing tag was added to this file as part of the GFDL licensing update.http://creativecommons.org/licenses/by-sa/3.0/CC BY-SA 3.0Creative Commons Attribution-Share Alike 3.0truetrue

This file is licensed under the Creative Commons Attribution-Share Alike 2.5 Generic, 2.0 Generic and 1.0 Generic license.

You are free:

• to share – to copy, distribute and transmit the work
• to remix – to adapt the work

Under the following conditions:

• attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
• share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.

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You may select the license of your choice.

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