Encyclopedia of Triangle Centers
March 30, 2011 9:07 PM   Subscribe

High School geometry taught us about the Centroid, Incenter and Circumcenter of a triangle. But there are actually an infinite number of ways of finding the center.

The Encyclopedia of Triangle Centers catalogs 3612 different ways of finding a triangles center. They also have sketches of many of them as well as biographies of famous geometers.
posted by Confess, Fletch (14 comments total) 16 users marked this as a favorite
Guy knocked on the door trying to sell us a complete leatherbound set of The Encyclopedia of Triangle Centers, I told him he could have a glass of water but we were Catholic and weren't interested. Dodged that bullet!
posted by tumid dahlia at 9:20 PM on March 30, 2011 [6 favorites]

Bah, you need The Geometer's Sketchpad to see these. Pics or it didn't happen!
posted by twoleftfeet at 9:37 PM on March 30, 2011

The bullet in the center of a love triangle is a dead giveaway.
posted by weapons-grade pandemonium at 9:38 PM on March 30, 2011 [2 favorites]

Dude, I did this. Today. Forreal.

Distributed load, bitches! Woo! Statics! Reprazent!

Yeah, that's me, the "old" dude in your college classes geeking out on every concept.
posted by spikeleemajortomdickandharryconnickjrmints at 9:50 PM on March 30, 2011 [3 favorites]

If you only have time to see one non-traditional triangle center, I'd recommend the first Morley center, which is remarkable for a number of reasons. First, although it is a fundamental result in plane geometry, Morleys' theorem wasn't discovered until about 1900 (the trisectors of an angle having been too difficult to work with in traditional Euclidean geometry). Second, Morley himself, who trained in England but came to the U.S. to train graduate students, played a pivotal role in shaping mathematics in America. And third, it's a wicked beautiful result.
posted by twoleftfeet at 9:55 PM on March 30, 2011 [4 favorites]

Oh man, I am such a geometry nerd.

posted by Bonzai at 10:38 PM on March 30, 2011


But seriously. The Centroid is the centre of mass of a uniform triangle. It is the centre. The rest of these are just interesting points on a triangle.

(cool post!)
posted by auto-correct at 11:10 PM on March 30, 2011

Finding the center of a circle.
posted by chavenet at 1:04 AM on March 31, 2011

You promised infinity and you gave me 3,612.
posted by Wolfdog at 5:45 AM on March 31, 2011 [1 favorite]

What is this "incenter" of which you speak? You mean orthocentre, right? And big ups to the Euler line, my personal fave of circular geometry.
posted by Go Banana at 7:21 AM on March 31, 2011

Dude, if it's infinite, it's NaN.
posted by overyield at 8:16 AM on March 31, 2011

Like we're ever going to actually use this in real life anyway, right you guys?
posted by Casimir at 8:36 AM on March 31, 2011

Does the Euler line divide a triangle in half by area? (math noob who loved high school math but never heard of the Euler line)
posted by mefireader at 10:52 AM on March 31, 2011

What is this "incenter" of which you speak? You mean orthocentre, right?

The incenter is the intersection of the three angle bisectors. The orthocenter is the intersection of the three altitudes, which pass through a vertex and are perpendicular to the opposite side
posted by leahwrenn at 9:13 PM on March 31, 2011

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