Interesting Esoterica

Clark Kimberling's Encyclopedia of Triangle Centers

Article by Clark Kimberling
  • Published in 1999
  • Added on
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Long ago, someone drew a triangle and three segments across it. Each segment started at a vertex and stopped at the midpoint of the opposite side. The segments met in a point. The person was impressed and repeated the experiment on a different shape of triangle. Again the segments met in a point. The person drew yet a third triangle, very carefully, with the same result. He told his friends. To their surprise and delight, the coincidence worked for them, too. Word spread, and the magic of the three segments was regarded as the work of a higher power. Centuries passed, and someone proved that the three medians do indeed concur in a point, now called the centroid. The ancients found other points, too, now called the incenter, circumcenter, and orthocenter. More centuries passed, more special points were discovered, and a definition of triangle center emerged. Like the definition of continuous function, this definition is satisfied by infinitely many objects, of which only finitely many will ever be published. The Encyclopedia of Triangle Centers (ETC) extends a list of 400 triangle centers published in the 1998 book Triangle Centers and Central Triangles.

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Other information

key
EncyclopediaOfTriangleCenters
type
article
date_added
2022-02-16
date_published
1999-09-14

BibTeX entry

@article{EncyclopediaOfTriangleCenters,
	key = {EncyclopediaOfTriangleCenters},
	type = {article},
	title = {Clark Kimberling's Encyclopedia of Triangle Centers},
	author = {Clark Kimberling},
	abstract = {Long ago, someone drew a triangle and three segments across it. Each segment started at a vertex and stopped at the midpoint of the opposite side. The segments met in a point. The person was impressed and repeated the experiment on a different shape of triangle. Again the segments met in a point. The person drew yet a third triangle, very carefully, with the same result. He told his friends. To their surprise and delight, the coincidence worked for them, too. Word spread, and the magic of the three segments was regarded as the work of a higher power.

Centuries passed, and someone proved that the three medians do indeed concur in a point, now called the centroid. The ancients found other points, too, now called the incenter, circumcenter, and orthocenter. More centuries passed, more special points were discovered, and a definition of triangle center emerged. Like the definition of continuous function, this definition is satisfied by infinitely many objects, of which only finitely many will ever be published. The Encyclopedia of Triangle Centers (ETC) extends a list of 400 triangle centers published in the 1998 book Triangle Centers and Central Triangles.},
	comment = {},
	date_added = {2022-02-16},
	date_published = {1999-09-14},
	urls = {https://faculty.evansville.edu/ck6/encyclopedia/ETC.html},
	collections = {geometry,lists-and-catalogues},
	url = {https://faculty.evansville.edu/ck6/encyclopedia/ETC.html},
	year = 1999,
	urldate = {2022-02-16}
}