File:Neusis-heptagon.png
Neusis-heptagon.png (542 × 563 pixels, file size: 15 KB, MIME type: image/png)
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Geometric details: OPQR is a unit square. The arc centred on O through Q is drawn, as is the perpendicular bisector of OP. The en:Neusis construction involves finding unit interval AB through P with A on the perpendicular bisector and B on the arc. Angle PAO is the interior angle of a heptagon. The remainder of the construction can be carried out with ruler and compass. (Two of the vertices lie on the lines OR and PQ.)
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Summary[edit]
DescriptionNeusis-heptagon.png | Neusis construction of a regular heptagon |
Date | |
Source | Own work |
Author | User:AndrewKepert |
Permission (Reusing this file) |
GFDL and CC. GPL source included |
The en:MetaPost source below is a bit of a cheat.
Licensing[edit]
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. | ||
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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 |
- 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.
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Metapost source[edit]
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; thick=1mm; thin=0.25mm; transform heptT; def drawruler(expr p,q) = path ruler[]; ruler0:=unitsquare xscaled abs(p-q) yscaled .1u rotated angle(q-p) shifted p; ruler1:=unitsquare yscaled 0.5 shifted 0.25up xscaled abs(p-q) yscaled .1u rotated angle(q-p) shifted p; fill ruler0 withcolor (1,1,.5); fill ruler1 withcolor (.9,.9,.3); draw ruler0 withpen pencircle scaled 0.25; enddef; beginfig(77) pickup pencircle scaled thin; z0=(0,0); z0d=(0,.4u); z1=(-0.5u,0); z1l=(.5u-u*sqrt(2),0); z2=(0.5u,0); z3=(.5u,-u); z3u=(.5u,-u*sqrt(2)); z4=(-.5u,-u); z5=(0,-u); z6=(0,whatever)=z1+whatever*dir(180/7); z7=z6-u*dir(180/7); drawruler(z6,z7); drawruler(z3,z4); for i = 0 upto 7: z[i]vtx=dir(360i/7); endfor; xxpart heptT= yypart heptT; xypart heptT=-yxpart heptT; for i = 6,7: z[i] = z[i]vtx transformed heptT; endfor draw (for i = 0 upto 6: z[i]vtx -- endfor cycle) transformed heptT dashed evenly withcolor blue; draw z1--z2--z3--z4--cycle; draw z1l--z1; draw z0d--z5; draw z2--z4 dashed evenly; draw z6--z7; label.urt("O",z2); label.ulft("A",z6); label.ulft("P",z1); label.llft("Q",z4); label.rt("R",z3); label.lft("B",z7); draw subpath (4,5) of unitcircle scaled (sqrt(2)) shifted z2; for i = 1,2,6,7,3,4: if known(x[i]): drawdot z[i] withpen pencircle scaled thick; fi endfor endfig; bye
See also[edit]
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 08:22, 19 May 2006 | 542 × 563 (15 KB) | AndrewKepert~commonswiki (talk | contribs) | {{Information| |Description=Neusis construction of a regular heptagon |Source=own work |Date=19 May 2006 |Author=User:AndrewKepert |Permission=GFDL and CC. GPL source included }} |
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