Segment trisection without compass

The name of the pictureThe name of the pictureThe name of the pictureClash Royale CLAN TAG#URR8PPP











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1
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I'm trying to figure out how to trisect a segment using only pen and ruler.
There is a parallel line provided.



No measurement is allowed.




geometry




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  • I think you need a compass too..!!
    – Vidyanshu Mishra
    Oct 9 '17 at 20:40










  • If we are given one fixed circle with its center included, we can do everything with just a straightedge. en.wikipedia.org/wiki/Poncelet%E2%80%93Steiner_theorem
    – Will Jagy
    Oct 9 '17 at 20:40











  • Do you have a given line parallel to the segment?
    – Oscar Lanzi
    Oct 9 '17 at 20:45










  • @OscarLanzi yes i do i forgot about it.
    – Kazz
    Oct 9 '17 at 20:49










  • What is a "metric oc."? Please describe the problem fully; there's no need to be terse here.
    – Chris Culter
    Oct 9 '17 at 21:02














up vote
1
down vote

favorite












I'm trying to figure out how to trisect a segment using only pen and ruler.
There is a parallel line provided.



No measurement is allowed.




geometry




share|cite|improve this question






















  • I think you need a compass too..!!
    – Vidyanshu Mishra
    Oct 9 '17 at 20:40










  • If we are given one fixed circle with its center included, we can do everything with just a straightedge. en.wikipedia.org/wiki/Poncelet%E2%80%93Steiner_theorem
    – Will Jagy
    Oct 9 '17 at 20:40











  • Do you have a given line parallel to the segment?
    – Oscar Lanzi
    Oct 9 '17 at 20:45










  • @OscarLanzi yes i do i forgot about it.
    – Kazz
    Oct 9 '17 at 20:49










  • What is a "metric oc."? Please describe the problem fully; there's no need to be terse here.
    – Chris Culter
    Oct 9 '17 at 21:02












up vote
1
down vote

favorite









up vote
1
down vote

favorite











I'm trying to figure out how to trisect a segment using only pen and ruler.
There is a parallel line provided.



No measurement is allowed.




geometry




share|cite|improve this question














I'm trying to figure out how to trisect a segment using only pen and ruler.
There is a parallel line provided.



No measurement is allowed.





geometry





share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Oct 9 '17 at 21:12

























asked Oct 9 '17 at 20:38









Kazz

339111




339111











  • I think you need a compass too..!!
    – Vidyanshu Mishra
    Oct 9 '17 at 20:40










  • If we are given one fixed circle with its center included, we can do everything with just a straightedge. en.wikipedia.org/wiki/Poncelet%E2%80%93Steiner_theorem
    – Will Jagy
    Oct 9 '17 at 20:40











  • Do you have a given line parallel to the segment?
    – Oscar Lanzi
    Oct 9 '17 at 20:45










  • @OscarLanzi yes i do i forgot about it.
    – Kazz
    Oct 9 '17 at 20:49










  • What is a "metric oc."? Please describe the problem fully; there's no need to be terse here.
    – Chris Culter
    Oct 9 '17 at 21:02
















  • I think you need a compass too..!!
    – Vidyanshu Mishra
    Oct 9 '17 at 20:40










  • If we are given one fixed circle with its center included, we can do everything with just a straightedge. en.wikipedia.org/wiki/Poncelet%E2%80%93Steiner_theorem
    – Will Jagy
    Oct 9 '17 at 20:40











  • Do you have a given line parallel to the segment?
    – Oscar Lanzi
    Oct 9 '17 at 20:45










  • @OscarLanzi yes i do i forgot about it.
    – Kazz
    Oct 9 '17 at 20:49










  • What is a "metric oc."? Please describe the problem fully; there's no need to be terse here.
    – Chris Culter
    Oct 9 '17 at 21:02















I think you need a compass too..!!
– Vidyanshu Mishra
Oct 9 '17 at 20:40




I think you need a compass too..!!
– Vidyanshu Mishra
Oct 9 '17 at 20:40












If we are given one fixed circle with its center included, we can do everything with just a straightedge. en.wikipedia.org/wiki/Poncelet%E2%80%93Steiner_theorem
– Will Jagy
Oct 9 '17 at 20:40





If we are given one fixed circle with its center included, we can do everything with just a straightedge. en.wikipedia.org/wiki/Poncelet%E2%80%93Steiner_theorem
– Will Jagy
Oct 9 '17 at 20:40













Do you have a given line parallel to the segment?
– Oscar Lanzi
Oct 9 '17 at 20:45




Do you have a given line parallel to the segment?
– Oscar Lanzi
Oct 9 '17 at 20:45












@OscarLanzi yes i do i forgot about it.
– Kazz
Oct 9 '17 at 20:49




@OscarLanzi yes i do i forgot about it.
– Kazz
Oct 9 '17 at 20:49












What is a "metric oc."? Please describe the problem fully; there's no need to be terse here.
– Chris Culter
Oct 9 '17 at 21:02




What is a "metric oc."? Please describe the problem fully; there's no need to be terse here.
– Chris Culter
Oct 9 '17 at 21:02










1 Answer
1






active

oldest

votes

















up vote
3
down vote



accepted










lets mark ends of the segment as A and B.



  • mark points C and D on the parallel line.

  • draw lines BD and AC, mark the cross point as E

  • draw lines BC and AD, mark the cross point as F

  • draw line EF, mark its cross point with line CD as G

  • draw line BG, mark its cross point with line AD as H

The line EH cuts segment AB in 2:1 ratio.






share|cite|improve this answer






















  • can this be done easier (faster) ?
    – Kazz
    Oct 9 '17 at 21:13










  • Beat me to it, +1.
    – Oscar Lanzi
    Oct 9 '17 at 21:24










  • I know of no faster method without compasses.
    – Oscar Lanzi
    Oct 9 '17 at 21:27










Your Answer




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1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes








up vote
3
down vote



accepted










lets mark ends of the segment as A and B.



  • mark points C and D on the parallel line.

  • draw lines BD and AC, mark the cross point as E

  • draw lines BC and AD, mark the cross point as F

  • draw line EF, mark its cross point with line CD as G

  • draw line BG, mark its cross point with line AD as H

The line EH cuts segment AB in 2:1 ratio.






share|cite|improve this answer






















  • can this be done easier (faster) ?
    – Kazz
    Oct 9 '17 at 21:13










  • Beat me to it, +1.
    – Oscar Lanzi
    Oct 9 '17 at 21:24










  • I know of no faster method without compasses.
    – Oscar Lanzi
    Oct 9 '17 at 21:27














up vote
3
down vote



accepted










lets mark ends of the segment as A and B.



  • mark points C and D on the parallel line.

  • draw lines BD and AC, mark the cross point as E

  • draw lines BC and AD, mark the cross point as F

  • draw line EF, mark its cross point with line CD as G

  • draw line BG, mark its cross point with line AD as H

The line EH cuts segment AB in 2:1 ratio.






share|cite|improve this answer






















  • can this be done easier (faster) ?
    – Kazz
    Oct 9 '17 at 21:13










  • Beat me to it, +1.
    – Oscar Lanzi
    Oct 9 '17 at 21:24










  • I know of no faster method without compasses.
    – Oscar Lanzi
    Oct 9 '17 at 21:27












up vote
3
down vote



accepted







up vote
3
down vote



accepted






lets mark ends of the segment as A and B.



  • mark points C and D on the parallel line.

  • draw lines BD and AC, mark the cross point as E

  • draw lines BC and AD, mark the cross point as F

  • draw line EF, mark its cross point with line CD as G

  • draw line BG, mark its cross point with line AD as H

The line EH cuts segment AB in 2:1 ratio.






share|cite|improve this answer














lets mark ends of the segment as A and B.



  • mark points C and D on the parallel line.

  • draw lines BD and AC, mark the cross point as E

  • draw lines BC and AD, mark the cross point as F

  • draw line EF, mark its cross point with line CD as G

  • draw line BG, mark its cross point with line AD as H

The line EH cuts segment AB in 2:1 ratio.







share|cite|improve this answer














share|cite|improve this answer



share|cite|improve this answer








edited Aug 11 at 18:50









Community♦

1




1










answered Oct 9 '17 at 21:11









Kazz

339111




339111











  • can this be done easier (faster) ?
    – Kazz
    Oct 9 '17 at 21:13










  • Beat me to it, +1.
    – Oscar Lanzi
    Oct 9 '17 at 21:24










  • I know of no faster method without compasses.
    – Oscar Lanzi
    Oct 9 '17 at 21:27
















  • can this be done easier (faster) ?
    – Kazz
    Oct 9 '17 at 21:13










  • Beat me to it, +1.
    – Oscar Lanzi
    Oct 9 '17 at 21:24










  • I know of no faster method without compasses.
    – Oscar Lanzi
    Oct 9 '17 at 21:27















can this be done easier (faster) ?
– Kazz
Oct 9 '17 at 21:13




can this be done easier (faster) ?
– Kazz
Oct 9 '17 at 21:13












Beat me to it, +1.
– Oscar Lanzi
Oct 9 '17 at 21:24




Beat me to it, +1.
– Oscar Lanzi
Oct 9 '17 at 21:24












I know of no faster method without compasses.
– Oscar Lanzi
Oct 9 '17 at 21:27




I know of no faster method without compasses.
– Oscar Lanzi
Oct 9 '17 at 21:27












 

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