Communities

Writing
Writing
Codidact Meta
Codidact Meta
The Great Outdoors
The Great Outdoors
Photography & Video
Photography & Video
Scientific Speculation
Scientific Speculation
Cooking
Cooking
Electrical Engineering
Electrical Engineering
Judaism
Judaism
Languages & Linguistics
Languages & Linguistics
Software Development
Software Development
Mathematics
Mathematics
Christianity
Christianity
Code Golf
Code Golf
Music
Music
Physics
Physics
Linux Systems
Linux Systems
Power Users
Power Users
Tabletop RPGs
Tabletop RPGs

Dashboard
Notifications
Mark all as read
Q&A

Do these major triangle lines have names?

+2
−0

Kimberling's Encyclopedia of Triangle Centers lists, among other things, lines on which each centre is found, but usually listing only two points on the line. As a little project I've assembled these triples to find lines which have many centres, which would seem to be a rough measure of how important the line is. I processed the first 10000 centres in the ETC, and found 12 lines with 99+ centres; of those twelve, I found names for eight in MathWorld. Eight of the twelve lines pass through (at least) two of five of the most important centres, and four of those eight are not listed under triangle lines in MathWorld.

Do the four lines marked ??? have common names?

  • X(1) Incentre -- X(2) Centroid: Nagel line (213+ centres)
  • X(1) Incentre -- X(3) Circumcentre: ??? (231+ centres)
  • X(1) Incentre -- X(4) Orthocentre: ??? (99+ centres)
  • X(1) Incentre -- X(6) Symmedian point: ??? (145+ centres)
  • X(2) Centroid -- X(3) Circumcentre -- X(4) Orthocentre: Euler line (960+ centres)
  • X(2) Centroid -- X(6) Symmedian point: ??? (197+ centres)
  • X(3) Circumcentre -- X(6) Symmedian point: Brocard axis (493+ centres)
  • X(4) Orthocentre -- X(6) Symmedian point: van Aubel line (100+ centres)
Why does this post require moderator attention?
You might want to add some details to your flag.
Why should this post be closed?

0 comment threads

0 answers

Sign up to answer this question »

This community is part of the Codidact network. We have other communities too — take a look!

You can also join us in chat!

Want to advertise this community? Use our templates!