Encyclopedia of Triangle Centers(faculty.evansville.edu)
faculty.evansville.edu
Encyclopedia of Triangle Centers
http://faculty.evansville.edu/ck6/encyclopedia/ETC.html
12 comments
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:Tr...
GeoGebra has a lot of these built in, eg
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
This GeoGebra project is incredible!
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.
Even for the 3 points case the solution is not 100% trivial.
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..
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..
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.
For a larger number of points it's generally the same, only you don't know which of the multiple possible triangles will work.
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.
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.
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.
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.
I think it's just a genuinely fucking massive page; there's 1.7 mb of pure html composed of 11690-something paragraph nodes
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.
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.
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.)
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.)
There's a fun numberphile video about triangle centers, for anyone curious about these things: https://www.youtube.com/watch?v=wVH4MS6v23U
Reminds me of https://oeis.org/
The On-Line Encyclopedia of Integer Sequences
The On-Line Encyclopedia of Integer Sequences
Please please, tell me all this is autogenerated…
I don't know about everything but the first few pages seem like they were not autogenerated...
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.
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.