File:Poncelet point.svg
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Summary
| Description |
English: Example of Poncelet point |
| Date | |
| Source | Own work |
| Author | Claudio Rocchini |
Licensing
I, the copyright holder of this work, hereby publish it under the following license:
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International 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.
Source Code
Carmetal project:
<?xml version="1.0" encoding="utf-8"?>
<CaR>
<Construction>
<Window x="-2.1728144453469938" y="-0.19062402553764457" w="3.3635856610148616"/>
<Windowdim w="636" h="488"/>
<Preferences minfontsize="16" minpointsize="2" minlinesize="1" arrowsize="10" selectionsize="8" monkeyspeed="20" gridopacity="20" digits.lengths="2" digits.edit="4" digits.angles="2" colorbackground="255,255,255" colorbackgroundx="3" colorbackgroundy="2" colorbackgroundPal="4" fig3D="false" figDP="false"/>
<Objects>
<Point name="A" n="0" type="thick" showname="true" x="-4.721393652349716" y="1.4620468511947649" shape="circle">Punto</Point>
<Point name="B" n="1" type="thick" showname="true" x="-0.540488111088254" y="0.6237700509418409" shape="circle">Punto</Point>
<Point name="C" n="2" type="thick" showname="true" x="-0.22613431099340708" y="-0.8641712695071009" shape="circle">Punto</Point>
<Point name="D" n="3" type="thick" showname="true" x="-4.553738292299132" y="-2.3730695099623658" shape="circle">Punto</Point>
<Segment name="s1" n="6" color="1" from="A" to="B">Segmento da A a B</Segment>
<Segment name="s2" n="9" color="1" from="B" to="C">Segmento da B a C</Segment>
<Segment name="s3" n="12" color="1" from="C" to="D">Segmento da C a D</Segment>
<Segment name="s4" n="15" color="1" from="D" to="A">Segmento da D a A</Segment>
<Segment name="s5" n="18" color="1" from="A" to="C">Segmento da A a C</Segment>
<Segment name="s6" n="21" color="1" from="B" to="D">Segmento da B a D</Segment>
<Midpoint name="P1" n="24" color="2" first="A" second="B" shape="circle">Punto medio tra A e B</Midpoint>
<Midpoint name="P2" n="27" color="2" first="B" second="C" shape="circle">Punto medio tra B e C</Midpoint>
<Midpoint name="P3" n="30" color="2" first="C" second="D" shape="circle">Punto medio tra C e D</Midpoint>
<Midpoint name="P4" n="33" color="2" first="D" second="A" shape="circle">Punto medio tra D e A</Midpoint>
<Midpoint name="P5" n="36" color="2" first="A" second="C" shape="circle">Punto medio tra A e C</Midpoint>
<Midpoint name="P6" n="39" color="2" first="B" second="D" shape="circle">Punto medio tra B e D</Midpoint>
<Point name="P7" n="124" color="4" type="thin" hidden="true" x="(x(P1)^2*y(P5)-x(P1)^2*y(P2)+y(P5)^2*y(P2)-y(P5)^2*y(P1)-y(P5)*y(P2)^2+y(P5)*y(P1)^2-y(P5)*x(P2)^2+y(P2)^2*y(P1)-y(P2)*y(P1)^2+y(P2)*x(P5)^2+y(P1)*x(P2)^2-y(P1)*x(P5)^2)/(2*x(P1)*y(P5)+(-(2*x(P1)))*y(P2)+(-(2*y(P5)))*x(P2)+2*y(P2)*x(P5)+2*y(P1)*x(P2)+(-(2*y(P1)))*x(P5))" actx="-1.257067673623934" y="(-x(P1)^2*x(P5)+x(P1)^2*x(P2)+x(P1)*x(P5)^2-x(P1)*x(P2)^2+x(P1)*y(P5)^2-x(P1)*y(P2)^2-x(P5)^2*x(P2)+x(P5)*x(P2)^2+x(P5)*y(P2)^2-x(P5)*y(P1)^2-x(P2)*y(P5)^2+x(P2)*y(P1)^2)/(2*x(P1)*y(P5)+(-(2*x(P1)))*y(P2)+2*x(P5)*y(P2)+(-(2*x(P5)))*y(P1)+(-(2*x(P2)))*y(P5)+2*x(P2)*y(P1))" acty="0.9445748304077586" shape="circle" fixed="true">Point à "(x(A)^2*y(P4)-x(A)^2*y(P5)+y(P4)^2*y(P5)-y(P4)^2*y(A)-y(P4)*y(P5)^2+y(P4)*y(A)^2-y(P4)*x(P5)^2+y(P5)^2*y(A)-y(P5)*y(A)^2+y(P5)*x(P4)^2+y(A)*x(P5)^2-y(A)*x(P4)^2)/(2*x(A)*y(P4)+(-(2*x(A)))*y(P5)+(-(2*y(P4)))*x(P5)+2*y(P5)*x(P4)+2*y(A)*x(P5)+(-(2*y(A)))*x(P4))", "(-x(A)^2*x(P4)+x(A)^2*x(P5)+x(A)*x(P4)^2-x(A)*x(P5)^2+x(A)*y(P4)^2-x(A)*y(P5)^2-x(P4)^2*x(P5)+x(P4)*x(P5)^2+x(P4)*y(P5)^2-x(P4)*y(A)^2-x(P5)*y(P4)^2+x(P5)*y(A)^2)/(2*x(A)*y(P4)+(-(2*x(A)))*y(P5)+2*x(P4)*y(P5)+(-(2*x(P4)))*y(A)+(-(2*x(P5)))*y(P4)+2*x(P5)*y(A))" </Point>
<Circle name="c1" n="125" color="4" large="true" through="P1" midpoint="P7">Cercle de centre P10 passant par P7 </Circle>
<Point name="P8" n="207" color="4" type="thin" hidden="true" x="(x(P2)^2*y(P6)-x(P2)^2*y(P3)+y(P6)^2*y(P3)-y(P6)^2*y(P2)-y(P6)*y(P3)^2+y(P6)*y(P2)^2-y(P6)*x(P3)^2+y(P3)^2*y(P2)-y(P3)*y(P2)^2+y(P3)*x(P6)^2+y(P2)*x(P3)^2-y(P2)*x(P6)^2)/(2*x(P2)*y(P6)+(-(2*x(P2)))*y(P3)+(-(2*y(P6)))*x(P3)+2*y(P3)*x(P6)+2*y(P2)*x(P3)+(-(2*y(P2)))*x(P6))" actx="-1.2907444993565804" y="(-x(P2)^2*x(P6)+x(P2)^2*x(P3)+x(P2)*x(P6)^2-x(P2)*x(P3)^2+x(P2)*y(P6)^2-x(P2)*y(P3)^2-x(P6)^2*x(P3)+x(P6)*x(P3)^2+x(P6)*y(P3)^2-x(P6)*y(P2)^2-x(P3)*y(P6)^2+x(P3)*y(P2)^2)/(2*x(P2)*y(P6)+(-(2*x(P2)))*y(P3)+2*x(P6)*y(P3)+(-(2*x(P6)))*y(P2)+(-(2*x(P3)))*y(P6)+2*x(P3)*y(P2))" acty="-0.9978082457534702" shape="circle" fixed="true">Point à "(x(A)^2*y(P4)-x(A)^2*y(P5)+y(P4)^2*y(P5)-y(P4)^2*y(A)-y(P4)*y(P5)^2+y(P4)*y(A)^2-y(P4)*x(P5)^2+y(P5)^2*y(A)-y(P5)*y(A)^2+y(P5)*x(P4)^2+y(A)*x(P5)^2-y(A)*x(P4)^2)/(2*x(A)*y(P4)+(-(2*x(A)))*y(P5)+(-(2*y(P4)))*x(P5)+2*y(P5)*x(P4)+2*y(A)*x(P5)+(-(2*y(A)))*x(P4))", "(-x(A)^2*x(P4)+x(A)^2*x(P5)+x(A)*x(P4)^2-x(A)*x(P5)^2+x(A)*y(P4)^2-x(A)*y(P5)^2-x(P4)^2*x(P5)+x(P4)*x(P5)^2+x(P4)*y(P5)^2-x(P4)*y(A)^2-x(P5)*y(P4)^2+x(P5)*y(A)^2)/(2*x(A)*y(P4)+(-(2*x(A)))*y(P5)+2*x(P4)*y(P5)+(-(2*x(P4)))*y(A)+(-(2*x(P5)))*y(P4)+2*x(P5)*y(A))" </Point>
<Circle name="c2" n="208" color="4" large="true" through="P2" midpoint="P8">Cercle de centre P10 passant par P7 </Circle>
<Point name="P9" n="344" color="4" type="thin" hidden="true" x="(x(P4)^2*y(P5)-x(P4)^2*y(P3)+y(P5)^2*y(P3)-y(P5)^2*y(P4)-y(P5)*y(P3)^2+y(P5)*y(P4)^2-y(P5)*x(P3)^2+y(P3)^2*y(P4)-y(P3)*y(P4)^2+y(P3)*x(P5)^2+y(P4)*x(P3)^2-y(P4)*x(P5)^2)/(2*x(P4)*y(P5)+(-(2*x(P4)))*y(P3)+(-(2*y(P5)))*x(P3)+2*y(P3)*x(P5)+2*y(P4)*x(P3)+(-(2*y(P4)))*x(P5))" actx="-3.339067256787198" y="(-x(P4)^2*x(P5)+x(P4)^2*x(P3)+x(P4)*x(P5)^2-x(P4)*x(P3)^2+x(P4)*y(P5)^2-x(P4)*y(P3)^2-x(P5)^2*x(P3)+x(P5)*x(P3)^2+x(P5)*y(P3)^2-x(P5)*y(P4)^2-x(P3)*y(P5)^2+x(P3)*y(P4)^2)/(2*x(P4)*y(P5)+(-(2*x(P4)))*y(P3)+2*x(P5)*y(P3)+(-(2*x(P5)))*y(P4)+(-(2*x(P3)))*y(P5)+2*x(P3)*y(P4))" acty="-0.6995010640412224" shape="circle" fixed="true">Point à "(x(A)^2*y(P4)-x(A)^2*y(P5)+y(P4)^2*y(P5)-y(P4)^2*y(A)-y(P4)*y(P5)^2+y(P4)*y(A)^2-y(P4)*x(P5)^2+y(P5)^2*y(A)-y(P5)*y(A)^2+y(P5)*x(P4)^2+y(A)*x(P5)^2-y(A)*x(P4)^2)/(2*x(A)*y(P4)+(-(2*x(A)))*y(P5)+(-(2*y(P4)))*x(P5)+2*y(P5)*x(P4)+2*y(A)*x(P5)+(-(2*y(A)))*x(P4))", "(-x(A)^2*x(P4)+x(A)^2*x(P5)+x(A)*x(P4)^2-x(A)*x(P5)^2+x(A)*y(P4)^2-x(A)*y(P5)^2-x(P4)^2*x(P5)+x(P4)*x(P5)^2+x(P4)*y(P5)^2-x(P4)*y(A)^2-x(P5)*y(P4)^2+x(P5)*y(A)^2)/(2*x(A)*y(P4)+(-(2*x(A)))*y(P5)+2*x(P4)*y(P5)+(-(2*x(P4)))*y(A)+(-(2*x(P5)))*y(P4)+2*x(P5)*y(A))" </Point>
<Circle name="c3" n="345" color="4" large="true" through="P4" midpoint="P9">Cercle de centre P10 passant par P7 </Circle>
<Point name="P10" n="466" color="4" type="thin" hidden="true" x="(x(P4)^2*y(P1)-x(P4)^2*y(P6)+y(P1)^2*y(P6)-y(P1)^2*y(P4)-y(P1)*y(P6)^2+y(P1)*y(P4)^2-y(P1)*x(P6)^2+y(P6)^2*y(P4)-y(P6)*y(P4)^2+y(P6)*x(P1)^2+y(P4)*x(P6)^2-y(P4)*x(P1)^2)/(2*x(P4)*y(P1)+(-(2*x(P4)))*y(P6)+(-(2*y(P1)))*x(P6)+2*y(P6)*x(P1)+2*y(P4)*x(P6)+(-(2*y(P4)))*x(P1))" actx="-3.449665633074582" y="(-x(P4)^2*x(P1)+x(P4)^2*x(P6)+x(P4)*x(P1)^2-x(P4)*x(P6)^2+x(P4)*y(P1)^2-x(P4)*y(P6)^2-x(P1)^2*x(P6)+x(P1)*x(P6)^2+x(P1)*y(P6)^2-x(P1)*y(P4)^2-x(P6)*y(P1)^2+x(P6)*y(P4)^2)/(2*x(P4)*y(P1)+(-(2*x(P4)))*y(P6)+2*x(P1)*y(P6)+(-(2*x(P1)))*y(P4)+(-(2*x(P6)))*y(P1)+2*x(P6)*y(P4))" acty="0.046505815801173904" shape="circle" fixed="true">Point à "(x(A)^2*y(P4)-x(A)^2*y(P5)+y(P4)^2*y(P5)-y(P4)^2*y(A)-y(P4)*y(P5)^2+y(P4)*y(A)^2-y(P4)*x(P5)^2+y(P5)^2*y(A)-y(P5)*y(A)^2+y(P5)*x(P4)^2+y(A)*x(P5)^2-y(A)*x(P4)^2)/(2*x(A)*y(P4)+(-(2*x(A)))*y(P5)+(-(2*y(P4)))*x(P5)+2*y(P5)*x(P4)+2*y(A)*x(P5)+(-(2*y(A)))*x(P4))", "(-x(A)^2*x(P4)+x(A)^2*x(P5)+x(A)*x(P4)^2-x(A)*x(P5)^2+x(A)*y(P4)^2-x(A)*y(P5)^2-x(P4)^2*x(P5)+x(P4)*x(P5)^2+x(P4)*y(P5)^2-x(P4)*y(A)^2-x(P5)*y(P4)^2+x(P5)*y(A)^2)/(2*x(A)*y(P4)+(-(2*x(A)))*y(P5)+2*x(P4)*y(P5)+(-(2*x(P4)))*y(A)+(-(2*x(P5)))*y(P4)+2*x(P5)*y(A))" </Point>
<Circle name="c4" n="467" color="4" large="true" through="P4" midpoint="P10">Cercle de centre P10 passant par P7 </Circle>
<Intersection name="PP" n="469" color="2" type="thick" showname="true" first="c3" second="c1" shape="circle" which="first">Intersezione tra c3 e c1</Intersection>
</Objects>
</Construction>
</CaR>
File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 14:07, 5 August 2014 | | 478 × 393 (10 KB) | Rocchini | User created page with UploadWizard |
File usage
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