6 ms·

Encyclopedia of Triangle Centers

66 points by salgernon 7y ago

murkle 7y ago
GeoGebra has a lot of these built in, eg https://www.geogebra.org/graphing?command=A=(0,0);B=(1,2);C=(3,2);Polygon(A,B,C);D=TriangleCenter(A,B,C,100) https://www.geogebra.org/graphing?command=A=(0,0);B=(1,2);C=... https://wiki.geogebra.org/en/TriangleCenter_Command https://wiki.geogebra.org/en/TriangleCenter_Command
- thanatropism 7y ago
  This GeoGebra project is incredible!
qubex 7y ago
Something keeps causing Safari Mobile to crash and reload.
- orpheline 7y ago
  Firefox Focus as well.
praptak 7y ago
I had to refresh parts of that knowledge recently in connection with a very simple problem that has a complex algorithmic solution: given a finite set of points on a 2D plane find the minimum radius disc that covers all points. Even for the 3 points case the solution is not 100% trivial.
- onion2k 7y ago
  Why isn't that a disc with a diameter equal to the distance between the two points that are farthest apart? Edit: Ah. I get it now. If the points made an equilateral triangle you'd want to put the disc on the triangle center. That sounds like a fun problem..
  - praptak 7y ago
    Yes, that's what I meant by the solution not being trivial even for 3 points. It's either the circumscribed circle (for acute triangles) or the longest edge being the diameter (for obtuse triangles). For a larger number of points it's generally the same, only you don't know which of the multiple possible triangles will work.
rwmj 7y ago
A case of a picture is worth a thousand words. Wikipedia has a nice illustration of the first few Triangle Centers: https://en.wikipedia.org/wiki/Triangle_center#/media/File:Trigonometric_centres.png https://en.wikipedia.org/wiki/Triangle_center#/media/File:Tr...
Tempest1981 7y ago
Reminds me of https://oeis.org/ https://oeis.org/ The On-Line Encyclopedia of Integer Sequences
SoWhat2019 7y ago
So many pictures.
yuchi 7y ago
Please please, tell me all this is autogenerated…
- 6nf 7y ago
  I don't know about everything but the first few pages seem like they were not autogenerated...
- StrangeDoctor 7y ago
  I don’t exactly know what you mean by autogenerated but I believe I remember Dr. Kimberling talking in class about having tooling to keep track of the findings, very much a labor of love and part of his research.
na85 7y ago
I can't be the only one that read the phrase about "well-known triangle centers" and expected to see something related to the center of the Bermuda triangle, the Texas Triangle, or perhaps TriBeCa.
gjm11 7y ago
The Online Encyclopedia of Integer Sequences has a search facility, so that if you have a mysterious sequence of integers you can put it in any see whether it's one of the sequences in the OEIS (or do fancier things -- see whether it's a subsequence of one of those sequences, enter just one large number from the sequence to see whether other seqs containing that number are enlightening, etc.). The obvious counterpart for this (I think) would be to have a set of "standard" triangles, including a couple with random vertex positions that hopefully satisfy no "interesting" mathematical relationships, and report (say) 12 decimal places of the coordinates of each centre for each of those triangles. Then, if you run across some mysterious point in a triangle, you can look for its coordinates and see whether they match any of the centres. (This would also give a way of verifying that no two of the thousands of triangle centres catalogued here are coincidentally equivalent to one another.)
- twic 7y ago
  You mean these: http://faculty.evansville.edu/ck6/encyclopedia/Search_6_9_13.html http://faculty.evansville.edu/ck6/encyclopedia/Search_6_9_13... http://faculty.evansville.edu/ck6/encyclopedia/Search_9_13_6.html http://faculty.evansville.edu/ck6/encyclopedia/Search_9_13_6... http://faculty.evansville.edu/ck6/encyclopedia/Search_13_6_9.html http://faculty.evansville.edu/ck6/encyclopedia/Search_13_6_9...
pkilgore 7y ago
Cool site, but proof that it doesn't take JavaScript to build a rough browsing experience in 2019. I think I heard my Pixel 3s fan kick on when I started to scroll.
- Aardwolf 7y ago
  Strange, scrolls super smooth in both firefox and chrome on a desktop PC for me, much smoother than JS heavy sites. I can just grab the scrollbar and go anywhere and see the text fly by and respond immediately. It's about 20k lines worth of fixed position text, pretty easy for a modern computer. I wonder what the pixel 3 browser is doing differently, isn't it also Chrome? Pixel 3 surely has a better CPU than computers in the year 2000, and even then you could scroll through 20k text lines easily.
- kortex 7y ago
  Yeah I was really curious to check these out but I couldn't even make it past the first paragraph with each scroll tic taking several seconds. Need to check it out on desktop as now I'm curious why it's so un-performant.
  - tomatotomato37 7y ago
    I think it's just a genuinely fucking massive page; there's 1.7 mb of pure html composed of 11690-something paragraph nodes
OskarS 7y ago
There's a fun numberphile video about triangle centers, for anyone curious about these things: https://www.youtube.com/watch?v=wVH4MS6v23U https://www.youtube.com/watch?v=wVH4MS6v23U
ninjis 7y ago
Wow. This is the last thing I expected to see on HN. I worked for the IT department at the University of Evansville for many years, leaving just three years ago. I've had more than one run-in with this particular site. This site is maintained by hand (no auto-gen) by Dr. Kimberling. He's an extremely smart individual (I've had many classes with him), and he prefers to keep things simple. Until about 2 year prior to me leaving he kept a secondary computer in his office that was only for running QBasic (an old AMD-K6 running Windows 2K, off the network). He finally gave that up and transitioned to using Mathematica.

66 points by salgernon 7y ago

GeoGebra has a lot of these built in, eg https://www.geogebra.org/graphing?command=A=(0,0);B=(1,2);C=(3,2);Polygon(A,B,C);D=TriangleCenter(A,B,C,100) https://www.geogebra.org/graphing?command=A=(0,0);B=(1,2);C=... https://wiki.geogebra.org/en/TriangleCenter_Command https://wiki.geogebra.org/en/TriangleCenter_Command

thanatropism 7y ago
This GeoGebra project is incredible!

qubex 7y ago

Something keeps causing Safari Mobile to crash and reload.

orpheline 7y ago
Firefox Focus as well.

praptak 7y ago

I had to refresh parts of that knowledge recently in connection with a very simple problem that has a complex algorithmic solution: given a finite set of points on a 2D plane find the minimum radius disc that covers all points. Even for the 3 points case the solution is not 100% trivial.

onion2k 7y ago
Why isn't that a disc with a diameter equal to the distance between the two points that are farthest apart? Edit: Ah. I get it now. If the points made an equilateral triangle you'd want to put the disc on the triangle center. That sounds like a fun problem..
- praptak 7y ago
  Yes, that's what I meant by the solution not being trivial even for 3 points. It's either the circumscribed circle (for acute triangles) or the longest edge being the diameter (for obtuse triangles). For a larger number of points it's generally the same, only you don't know which of the multiple possible triangles will work.

rwmj 7y ago

A case of a picture is worth a thousand words. Wikipedia has a nice illustration of the first few Triangle Centers: https://en.wikipedia.org/wiki/Triangle_center#/media/File:Trigonometric_centres.png https://en.wikipedia.org/wiki/Triangle_center#/media/File:Tr...

Tempest1981 7y ago

Reminds me of https://oeis.org/ https://oeis.org/ The On-Line Encyclopedia of Integer Sequences

SoWhat2019 7y ago

So many pictures.

yuchi 7y ago

Please please, tell me all this is autogenerated…

6nf 7y ago
I don't know about everything but the first few pages seem like they were not autogenerated...
StrangeDoctor 7y ago
I don’t exactly know what you mean by autogenerated but I believe I remember Dr. Kimberling talking in class about having tooling to keep track of the findings, very much a labor of love and part of his research.

na85 7y ago

I can't be the only one that read the phrase about "well-known triangle centers" and expected to see something related to the center of the Bermuda triangle, the Texas Triangle, or perhaps TriBeCa.

gjm11 7y ago

The Online Encyclopedia of Integer Sequences has a search facility, so that if you have a mysterious sequence of integers you can put it in any see whether it's one of the sequences in the OEIS (or do fancier things -- see whether it's a subsequence of one of those sequences, enter just one large number from the sequence to see whether other seqs containing that number are enlightening, etc.). The obvious counterpart for this (I think) would be to have a set of "standard" triangles, including a couple with random vertex positions that hopefully satisfy no "interesting" mathematical relationships, and report (say) 12 decimal places of the coordinates of each centre for each of those triangles. Then, if you run across some mysterious point in a triangle, you can look for its coordinates and see whether they match any of the centres. (This would also give a way of verifying that no two of the thousands of triangle centres catalogued here are coincidentally equivalent to one another.)

twic 7y ago
You mean these: http://faculty.evansville.edu/ck6/encyclopedia/Search_6_9_13.html http://faculty.evansville.edu/ck6/encyclopedia/Search_6_9_13... http://faculty.evansville.edu/ck6/encyclopedia/Search_9_13_6.html http://faculty.evansville.edu/ck6/encyclopedia/Search_9_13_6... http://faculty.evansville.edu/ck6/encyclopedia/Search_13_6_9.html http://faculty.evansville.edu/ck6/encyclopedia/Search_13_6_9...

pkilgore 7y ago

Cool site, but proof that it doesn't take JavaScript to build a rough browsing experience in 2019. I think I heard my Pixel 3s fan kick on when I started to scroll.

Aardwolf 7y ago
Strange, scrolls super smooth in both firefox and chrome on a desktop PC for me, much smoother than JS heavy sites. I can just grab the scrollbar and go anywhere and see the text fly by and respond immediately. It's about 20k lines worth of fixed position text, pretty easy for a modern computer. I wonder what the pixel 3 browser is doing differently, isn't it also Chrome? Pixel 3 surely has a better CPU than computers in the year 2000, and even then you could scroll through 20k text lines easily.
kortex 7y ago
Yeah I was really curious to check these out but I couldn't even make it past the first paragraph with each scroll tic taking several seconds. Need to check it out on desktop as now I'm curious why it's so un-performant.
- tomatotomato37 7y ago
  I think it's just a genuinely fucking massive page; there's 1.7 mb of pure html composed of 11690-something paragraph nodes

OskarS 7y ago

There's a fun numberphile video about triangle centers, for anyone curious about these things: https://www.youtube.com/watch?v=wVH4MS6v23U https://www.youtube.com/watch?v=wVH4MS6v23U

ninjis 7y ago

Wow. This is the last thing I expected to see on HN. I worked for the IT department at the University of Evansville for many years, leaving just three years ago. I've had more than one run-in with this particular site. This site is maintained by hand (no auto-gen) by Dr. Kimberling. He's an extremely smart individual (I've had many classes with him), and he prefers to keep things simple. Until about 2 year prior to me leaving he kept a secondary computer in his office that was only for running QBasic (an old AMD-K6 running Windows 2K, off the network). He finally gave that up and transitioned to using Mathematica.