
Encyclopedia of Triangle Centers - salgernon
http://faculty.evansville.edu/ck6/encyclopedia/ETC.html
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rwmj
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...](https://en.wikipedia.org/wiki/Triangle_center#/media/File:Trigonometric_centres.png)

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

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thanatropism
This GeoGebra project is incredible!

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praptak
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.

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onion2k
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
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.

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pkilgore
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.

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kortex
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.

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tomatotomato37
I think it's just a genuinely fucking massive page; there's 1.7 mb of pure
html composed of 11690-something paragraph nodes

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ninjis
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.

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gjm11
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.)

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twic
You mean these:

[http://faculty.evansville.edu/ck6/encyclopedia/Search_6_9_13...](http://faculty.evansville.edu/ck6/encyclopedia/Search_6_9_13.html)

[http://faculty.evansville.edu/ck6/encyclopedia/Search_9_13_6...](http://faculty.evansville.edu/ck6/encyclopedia/Search_9_13_6.html)

[http://faculty.evansville.edu/ck6/encyclopedia/Search_13_6_9...](http://faculty.evansville.edu/ck6/encyclopedia/Search_13_6_9.html)

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qubex
Something keeps causing Safari Mobile to crash and reload.

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orpheline
Firefox Focus as well.

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OskarS
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)

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Tempest1981
Reminds me of [https://oeis.org/](https://oeis.org/)

The On-Line Encyclopedia of Integer Sequences

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yuchi
Please please, tell me all this is autogenerated…

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6nf
I don't know about everything but the first few pages seem like they were not
autogenerated...

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na85
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.

