File:Hypercycle (vector format).svg
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| Description |
Italiano: Hypercycle generated by all points P equidistance from a line L |
| Date | |
| Source | Own work |
| Author | Claudio Rocchini |
Licensing edit
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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 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.
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Carmetal project:
<?xml version="1.0" encoding="utf-8"?>
<CaR>
<Construction>
<Window x="-0.6246001852892138" y="-0.2943209022126289" w="5.65685424949241"/>
<Windowdim w="960" h="734"/>
<Preferences minfontsize="19" minpointsize="3" minlinesize="1" arrowsize="10" selectionsize="8" monkeyspeed="20" gridopacity="20" digits.lengths="2" digits.edit="4" digits.angles="2" colorbackground="255,255,255" colorbackgroundx="10" colorbackgroundy="7" colorbackgroundPal="4" fig3D="false" figDP="false"/>
<Objects>
<Point name="P1" n="0" color="4" type="thin" x="-0.31244323342416" y="-0.40690281562216146" shape="circle">Punto</Point>
<Point name="P2" n="3" color="2" x="2.979143520318564" y="1.6522357218209853" shape="circle">Punto</Point>
<Circle name="c4" n="4" color="4" type="thick" through="P2" midpoint="P1" acute="true">Circonferenza di centro P1 per P2</Circle>
<Ray name="r6" n="8" color="4" type="thin" from="P1" to="P2">Semiretta da P1 puntando a P2</Ray>
<PointOn name="P3" n="5" color="2" on="c4" alpha="-1.3008839324204509" x="0.7228408399411335" y="-4.148931912413665" shape="circle">Punto su c4</PointOn>
<Plumb name="p6" n="19" color="4" type="thin" point="P2" line="r6" valid="true">Retta perpendicolare per P2 a r6</Plumb>
<Line name="l1" n="164" color="2" type="thin" from="P2" to="P3">Retta per P2 e P3</Line>
<Ray name="r7" n="11" color="4" type="thin" from="P1" to="P3">Semiretta da P1 puntando a P3</Ray>
<PointOn name="P25" n="665" color="4" type="thin" on="p6" alpha="-9.490235681942561" x="8.01229196989879" y="-6.393383582079987" shape="circle">Punto su p6</PointOn>
<Angle name="a1" n="666" color="1" xcoffset="-0.037363657680490915" ycoffset="-0.30320934785334275" unit="°" first="P1" root="P2" second="P25" display="small" filled="true" acute="true">Angolo P1 - P2 - P25</Angle>
<Plumb name="p5" n="16" color="4" type="thin" point="P3" line="r7" valid="true">Retta perpendicolare per P3 a r7</Plumb>
<Intersection name="P4" n="20" color="4" type="thin" first="p5" second="p6" shape="circle">Intersezione tra p5 e p6</Intersection>
<Circle name="c5" n="23" color="4" type="thin" through="P2" midpoint="P4" acute="true">Circonferenza di centro P4 per P2</Circle>
<Angle name="a2" n="669" color="1" xcoffset="0.19874138967385074" ycoffset="0.2320211446644915" unit="°" first="P4" root="P3" second="P1" display="small" filled="true" acute="true">Angolo P4 - P3 - P1</Angle>
<Ray name="r8" n="26" color="4" type="thin" from="P1" to="P4">Semiretta da P1 puntando a P4</Ray>
<Intersection name="P5" n="27" color="4" type="thin" hidden="true" first="r8" second="c5" shape="circle" which="second">Intersezione tra r8 e c5</Intersection>
<Point name="P6" n="158" type="thick" hidden="super" showname="true" bold="true" large="true" x="if(a(P3,P2,P5)<180,x(P2),x(P3))" actx="0.7228408399411335" y="if(a(P3,P2,P5)<180,y(P2),y(P3))" acty="-4.148931912413665" shape="circle" fixed="true">Point à "if(a(C,A,B)<180,x(A),x(C))", "if(a(C,A,B)<180,y(A),y(C))" </Point>
<Point name="P7" n="159" type="thick" hidden="super" showname="true" bold="true" large="true" x="if(a(P3,P2,P5)<180,x(P3),x(P2))" actx="2.979143520318564" y="if(a(P3,P2,P5)<180,y(P3),y(P2))" acty="1.6522357218209853" shape="diamond" fixed="true">Point à "if(a(C,A,B)<180,x(C),x(A))", "if(a(C,A,B)<180,y(C),y(A))" </Point>
<Point name="P8" n="160" hidden="super" x="(x(P5)^2*y(P6)-x(P5)^2*y(P7)+y(P6)^2*y(P7)-y(P6)^2*y(P5)-y(P6)*y(P7)^2+y(P6)*y(P5)^2-y(P6)*x(P7)^2+y(P7)^2*y(P5)-y(P7)*y(P5)^2+y(P7)*x(P6)^2+y(P5)*x(P7)^2-y(P5)*x(P6)^2)/(2*x(P5)*y(P6)+(-(2*x(P5)))*y(P7)+(-(2*y(P6)))*x(P7)+2*y(P7)*x(P6)+2*y(P5)*x(P7)+(-(2*y(P5)))*x(P6))" actx="5.739893335862397" y="(-x(P5)^2*x(P6)+x(P5)^2*x(P7)+x(P5)*x(P6)^2-x(P5)*x(P7)^2+x(P5)*y(P6)^2-x(P5)*y(P7)^2-x(P6)^2*x(P7)+x(P6)*x(P7)^2+x(P6)*y(P7)^2-x(P6)*y(P5)^2-x(P7)*y(P6)^2+x(P7)*y(P5)^2)/(2*x(P5)*y(P6)+(-(2*x(P5)))*y(P7)+2*x(P6)*y(P7)+(-(2*x(P6)))*y(P5)+(-(2*x(P7)))*y(P6)+2*x(P7)*y(P5))" acty="-2.7608949918246735" fixed="true">Point à "(x(B)^2*y(P4)-x(B)^2*y(P5)+y(P4)^2*y(P5)-y(P4)^2*y(B)-y(P4)*y(P5)^2+y(P4)*y(B)^2-y(P4)*x(P5)^2+y(P5)^2*y(B)-y(P5)*y(B)^2+y(P5)*x(P4)^2+y(B)*x(P5)^2-y(B)*x(P4)^2)/(2*x(B)*y(P4)+(-(2*x(B)))*y(P5)+(-(2*y(P4)))*x(P5)+2*y(P5)*x(P4)+2*y(B)*x(P5)+(-(2*y(B)))*x(P4))", "(-x(B)^2*x(P4)+x(B)^2*x(P5)+x(B)*x(P4)^2-x(B)*x(P5)^2+x(B)*y(P4)^2-x(B)*y(P5)^2-x(P4)^2*x(P5)+x(P4)*x(P5)^2+x(P4)*y(P5)^2-x(P4)*y(B)^2-x(P5)*y(P4)^2+x(P5)*y(B)^2)/(2*x(B)*y(P4)+(-(2*x(B)))*y(P5)+2*x(P4)*y(P5)+(-(2*x(P4)))*y(B)+(-(2*x(P5)))*y(P4)+2*x(P5)*y(B))" </Point>
<Circle name="L" n="161" color="2" type="thick" showname="true" through="P6" midpoint="P8" start="P7" end="P6">Circonferenza di centro P8 per P6</Circle>
<PointOn name="Q" n="165" color="2" on="L" alpha="0.35965931700710363" x="1.3042609370095848" y="-0.036445054315230596" shape="circle">Punto su L</PointOn>
<Ray name="r1" n="168" color="2" type="thin" from="P4" to="Q">Semiretta da P4 puntando a P9</Ray>
<Intersection name="P10" n="171" color="2" first="r1" second="c5" shape="circle" which="first">Intersezione tra r1 e c5</Intersection>
<PointOn name="P26" n="672" color="2" type="thin" on="r1" alpha="15.170117334741487" x="-7.186583640898022" y="5.17879347304011" shape="circle">Punto su r1</PointOn>
<Plumb name="p1" n="172" color="2" type="thin" point="P10" line="r1" valid="true">Retta perpendicolare per P10 a r1</Plumb>
<Intersection name="P11" n="173" color="2" type="thin" first="p1" second="l1" shape="circle">Intersezione tra p1 e l1</Intersection>
<Circle name="c1" n="182" color="4" through="Q" midpoint="P11" acute="true">Circonferenza di centro P11 per P9</Circle>
<Angle name="a3" n="673" color="1" xcoffset="-0.15796157058386534" ycoffset="0.26149587713689254" unit="°" first="P11" root="Q" second="P26" display="small" filled="true" acute="true">Angolo P11 - P9 - P26</Angle>
<Intersection name="A" n="183" color="2" type="thin" first="c4" second="c1" shape="circle" which="second">Intersezione tra c4 e c1</Intersection>
<Intersection name="B" n="184" color="4" type="thin" first="c4" second="c1" shape="circle" which="first">Intersezione tra c4 e c1</Intersection>
<Ray name="r2" n="187" color="2" type="thin" from="P1" to="A">Semiretta da P1 puntando a P12</Ray>
<Point name="P14" n="316" type="thick" hidden="super" showname="true" bold="true" large="true" x="if(a(A,B,Q)<180,x(B),x(A))" actx="3.5507764158917716" y="if(a(A,B,Q)<180,y(B),y(A))" acty="-0.7943674139241965" shape="circle" fixed="true">Point à "if(a(C,A,B)<180,x(A),x(C))", "if(a(C,A,B)<180,y(A),y(C))" </Point>
<Point name="P15" n="317" type="thick" hidden="super" showname="true" bold="true" large="true" x="if(a(A,B,Q)<180,x(A),x(B))" actx="-1.110359265265748" y="if(a(A,B,Q)<180,y(A),y(B))" acty="3.3928241324529553" shape="diamond" fixed="true">Point à "if(a(C,A,B)<180,x(C),x(A))", "if(a(C,A,B)<180,y(C),y(A))" </Point>
<Angle name="a4" n="682" color="1" xcoffset="0.20661416276412772" ycoffset="-0.298834234011413" unit="°" first="P11" root="A" second="P1" display="small" filled="true" acute="true">Angolo P11 - P12 - P1</Angle>
<Angle name="a5" n="685" color="1" xcoffset="-0.30151471816025427" ycoffset="0.20268247680707835" unit="°" first="P1" root="B" second="P11" display="small" filled="true" acute="true">Angolo P1 - P13 - P11</Angle>
<Ray name="r9" n="679" color="2" type="thin" from="P11" to="A">Semiretta da P11 puntando a P12</Ray>
<Point name="P16" n="318" hidden="super" x="(x(Q)^2*y(P14)-x(Q)^2*y(P15)+y(P14)^2*y(P15)-y(P14)^2*y(Q)-y(P14)*y(P15)^2+y(P14)*y(Q)^2-y(P14)*x(P15)^2+y(P15)^2*y(Q)-y(P15)*y(Q)^2+y(P15)*x(P14)^2+y(Q)*x(P15)^2-y(Q)*x(P14)^2)/(2*x(Q)*y(P14)+(-(2*x(Q)))*y(P15)+(-(2*y(P14)))*x(P15)+2*y(P15)*x(P14)+2*y(Q)*x(P15)+(-(2*y(Q)))*x(P14))" actx="4.080051389268624" y="(-x(Q)^2*x(P14)+x(Q)^2*x(P15)+x(Q)*x(P14)^2-x(Q)*x(P15)^2+x(Q)*y(P14)^2-x(Q)*y(P15)^2-x(P14)^2*x(P15)+x(P14)*x(P15)^2+x(P14)*y(P15)^2-x(P14)*y(Q)^2-x(P15)*y(P14)^2+x(P15)*y(Q)^2)/(2*x(Q)*y(P14)+(-(2*x(Q)))*y(P15)+2*x(P14)*y(P15)+(-(2*x(P14)))*y(Q)+(-(2*x(P15)))*y(P14)+2*x(P15)*y(Q))" acty="4.482773997190576" fixed="true">Point à "(x(B)^2*y(P4)-x(B)^2*y(P5)+y(P4)^2*y(P5)-y(P4)^2*y(B)-y(P4)*y(P5)^2+y(P4)*y(B)^2-y(P4)*x(P5)^2+y(P5)^2*y(B)-y(P5)*y(B)^2+y(P5)*x(P4)^2+y(B)*x(P5)^2-y(B)*x(P4)^2)/(2*x(B)*y(P4)+(-(2*x(B)))*y(P5)+(-(2*y(P4)))*x(P5)+2*y(P5)*x(P4)+2*y(B)*x(P5)+(-(2*y(B)))*x(P4))", "(-x(B)^2*x(P4)+x(B)^2*x(P5)+x(B)*x(P4)^2-x(B)*x(P5)^2+x(B)*y(P4)^2-x(B)*y(P5)^2-x(P4)^2*x(P5)+x(P4)*x(P5)^2+x(P4)*y(P5)^2-x(P4)*y(B)^2-x(P5)*y(P4)^2+x(P5)*y(B)^2)/(2*x(B)*y(P4)+(-(2*x(B)))*y(P5)+2*x(P4)*y(P5)+(-(2*x(P4)))*y(B)+(-(2*x(P5)))*y(P4)+2*x(P5)*y(B))" </Point>
<Circle name="c2" n="319" color="2" type="thin" through="P14" midpoint="P16" start="P15" end="P14">Circonferenza di centro P16 per P14</Circle>
<PointOn name="P" n="320" type="thick" showname="true" on="c2" alpha="0.24117720898094178" x="-0.543990769442031" y="1.885354588467374" shape="circle">Punto su c2</PointOn>
<Midpoint name="P17" n="325" color="2" type="thin" hidden="true" first="P" second="Q" shape="circle">Punto medio tra P e P9</Midpoint>
<Point name="P22" n="659" type="thick" hidden="super" showname="true" bold="true" large="true" x="if(a(P3,P2,P)<180,x(P2),x(P3))" actx="0.7228408399411335" y="if(a(P3,P2,P)<180,y(P2),y(P3))" acty="-4.148931912413665" shape="circle" fixed="true">Point à "if(a(C,A,B)<180,x(A),x(C))", "if(a(C,A,B)<180,y(A),y(C))" </Point>
<Point name="P23" n="660" type="thick" hidden="super" showname="true" bold="true" large="true" x="if(a(P3,P2,P)<180,x(P3),x(P2))" actx="2.979143520318564" y="if(a(P3,P2,P)<180,y(P3),y(P2))" acty="1.6522357218209853" shape="diamond" fixed="true">Point à "if(a(C,A,B)<180,x(C),x(A))", "if(a(C,A,B)<180,y(C),y(A))" </Point>
<Ray name="r11" n="697" color="2" type="thin" from="P11" to="P">Semiretta da P11 puntando a P</Ray>
<Point name="P24" n="661" hidden="super" x="(x(P)^2*y(P22)-x(P)^2*y(P23)+y(P22)^2*y(P23)-y(P22)^2*y(P)-y(P22)*y(P23)^2+y(P22)*y(P)^2-y(P22)*x(P23)^2+y(P23)^2*y(P)-y(P23)*y(P)^2+y(P23)*x(P22)^2+y(P)*x(P23)^2-y(P)*x(P22)^2)/(2*x(P)*y(P22)+(-(2*x(P)))*y(P23)+(-(2*y(P22)))*x(P23)+2*y(P23)*x(P22)+2*y(P)*x(P23)+(-(2*y(P)))*x(P22))" actx="1.0388389916056415" y="(-x(P)^2*x(P22)+x(P)^2*x(P23)+x(P)*x(P22)^2-x(P)*x(P23)^2+x(P)*y(P22)^2-x(P)*y(P23)^2-x(P22)^2*x(P23)+x(P22)*x(P23)^2+x(P22)*y(P23)^2-x(P22)*y(P)^2-x(P23)*y(P22)^2+x(P23)*y(P)^2)/(2*x(P)*y(P22)+(-(2*x(P)))*y(P23)+2*x(P22)*y(P23)+(-(2*x(P22)))*y(P)+(-(2*x(P23)))*y(P22)+2*x(P23)*y(P))" acty="-0.9324697184450556" fixed="true">Point à "(x(B)^2*y(P4)-x(B)^2*y(P5)+y(P4)^2*y(P5)-y(P4)^2*y(B)-y(P4)*y(P5)^2+y(P4)*y(B)^2-y(P4)*x(P5)^2+y(P5)^2*y(B)-y(P5)*y(B)^2+y(P5)*x(P4)^2+y(B)*x(P5)^2-y(B)*x(P4)^2)/(2*x(B)*y(P4)+(-(2*x(B)))*y(P5)+(-(2*y(P4)))*x(P5)+2*y(P5)*x(P4)+2*y(B)*x(P5)+(-(2*y(B)))*x(P4))", "(-x(B)^2*x(P4)+x(B)^2*x(P5)+x(B)*x(P4)^2-x(B)*x(P5)^2+x(B)*y(P4)^2-x(B)*y(P5)^2-x(P4)^2*x(P5)+x(P4)*x(P5)^2+x(P4)*y(P5)^2-x(P4)*y(B)^2-x(P5)*y(P4)^2+x(P5)*y(B)^2)/(2*x(B)*y(P4)+(-(2*x(B)))*y(P5)+2*x(P4)*y(P5)+(-(2*x(P4)))*y(B)+(-(2*x(P5)))*y(P4)+2*x(P5)*y(B))" </Point>
<Plumb name="p3" n="700" color="2" type="thin" point="P" line="r11" valid="true">Retta perpendicolare per P a r11</Plumb>
<Circle name="HC" n="662" color="5" type="thick" showname="true" through="P22" midpoint="P24" start="P23" end="P22">Circonferenza di centro P24 per P22</Circle>
<PointOn name="P27" n="703" color="2" type="thin" on="p3" alpha="10.064889748723015" x="4.385237697241658" y="-6.889878307426889" shape="circle">Punto su p3</PointOn>
<Angle name="a7" n="704" color="1" xcoffset="0.23025188108477865" ycoffset="-0.2810255912347315" unit="°" first="P11" root="P" second="P27" display="small" filled="true" acute="true">Angolo P11 - P - P27</Angle>
<Ray name="r4" n="328" color="2" type="thin" from="P1" to="P17">Semiretta da P1 puntando a P17</Ray>
<Intersection name="P18" n="329" color="4" type="thin" hidden="true" first="r4" second="c1" shape="circle" which="second">Intersezione tra r4 e c1</Intersection>
<Point name="P19" n="410" type="thick" hidden="super" showname="true" bold="true" large="true" x="if(a(P,Q,P18)<180,x(Q),x(P))" actx="1.3042609370095848" y="if(a(P,Q,P18)<180,y(Q),y(P))" acty="-0.036445054315230596" shape="circle" fixed="true">Point à "if(a(C,A,B)<180,x(A),x(C))", "if(a(C,A,B)<180,y(A),y(C))" </Point>
<Point name="P20" n="411" type="thick" hidden="super" showname="true" bold="true" large="true" x="if(a(P,Q,P18)<180,x(P),x(Q))" actx="-0.543990769442031" y="if(a(P,Q,P18)<180,y(P),y(Q))" acty="1.885354588467374" shape="diamond" fixed="true">Point à "if(a(C,A,B)<180,x(C),x(A))", "if(a(C,A,B)<180,y(C),y(A))" </Point>
<Point name="P21" n="412" hidden="super" x="(x(P18)^2*y(P19)-x(P18)^2*y(P20)+y(P19)^2*y(P20)-y(P19)^2*y(P18)-y(P19)*y(P20)^2+y(P19)*y(P18)^2-y(P19)*x(P20)^2+y(P20)^2*y(P18)-y(P20)*y(P18)^2+y(P20)*x(P19)^2+y(P18)*x(P20)^2-y(P18)*x(P19)^2)/(2*x(P18)*y(P19)+(-(2*x(P18)))*y(P20)+(-(2*y(P19)))*x(P20)+2*y(P20)*x(P19)+2*y(P18)*x(P20)+(-(2*y(P18)))*x(P19))" actx="4.080051389268609" y="(-x(P18)^2*x(P19)+x(P18)^2*x(P20)+x(P18)*x(P19)^2-x(P18)*x(P20)^2+x(P18)*y(P19)^2-x(P18)*y(P20)^2-x(P19)^2*x(P20)+x(P19)*x(P20)^2+x(P19)*y(P20)^2-x(P19)*y(P18)^2-x(P20)*y(P19)^2+x(P20)*y(P18)^2)/(2*x(P18)*y(P19)+(-(2*x(P18)))*y(P20)+2*x(P19)*y(P20)+(-(2*x(P19)))*y(P18)+(-(2*x(P20)))*y(P19)+2*x(P20)*y(P18))" acty="4.482773997190561" fixed="true">Point à "(x(B)^2*y(P4)-x(B)^2*y(P5)+y(P4)^2*y(P5)-y(P4)^2*y(B)-y(P4)*y(P5)^2+y(P4)*y(B)^2-y(P4)*x(P5)^2+y(P5)^2*y(B)-y(P5)*y(B)^2+y(P5)*x(P4)^2+y(B)*x(P5)^2-y(B)*x(P4)^2)/(2*x(B)*y(P4)+(-(2*x(B)))*y(P5)+(-(2*y(P4)))*x(P5)+2*y(P5)*x(P4)+2*y(B)*x(P5)+(-(2*y(B)))*x(P4))", "(-x(B)^2*x(P4)+x(B)^2*x(P5)+x(B)*x(P4)^2-x(B)*x(P5)^2+x(B)*y(P4)^2-x(B)*y(P5)^2-x(P4)^2*x(P5)+x(P4)*x(P5)^2+x(P4)*y(P5)^2-x(P4)*y(B)^2-x(P5)*y(P4)^2+x(P5)*y(B)^2)/(2*x(B)*y(P4)+(-(2*x(B)))*y(P5)+2*x(P4)*y(P5)+(-(2*x(P4)))*y(B)+(-(2*x(P5)))*y(P4)+2*x(P5)*y(B))" </Point>
<Circle name="radii" n="413" color="1" type="thick" showname="true" through="P19" midpoint="P21" start="P20" end="P19">Circonferenza di centro P21 per P19</Circle>
</Objects>
</Construction>
</CaR>
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 08:05, 11 September 2021 | | 400 × 319 (24 KB) | Rocchini (talk | contribs) | Reverted to version as of 08:01, 11 September 2021 (UTC) |
| 08:02, 11 September 2021 |  | 400 × 298 (18 KB) | Rocchini (talk | contribs) | Reverted to version as of 15:21, 29 May 2013 (UTC) | |
| 08:01, 11 September 2021 |  | 400 × 319 (24 KB) | Rocchini (talk | contribs) | Correction of an error | |
| 15:21, 29 May 2013 |  | 400 × 298 (18 KB) | Rocchini (talk | contribs) | User created page with UploadWizard |
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