Paper Info
Title
Arnol'd, the Jacobi Identity, and Orthocenters
Abstract
The three altitudes of a plane triangle pass through a single point, called the orthocenter of the triangle. This property holds literally in Euclidean geometry, and, properly interpreted, also in hyperbolic and spherical geometries. Recently, V. I. Arnol'd offered a fresh look at this circle of ideas and connected it with the well-known Jacobi identity. The main goal of this article is to present an elementary version of Amol'd's approach. In addition, several related ideas, including ones of M. Chasles, W. Fenchel and T. Jorgensen, and A. A. Kirillov, are discussed.
Year
DOI
Venue
2011
10.4169/amer.math.monthly.118.01.041
AMERICAN MATHEMATICAL MONTHLY
Field
DocType
Volume
Jacobi identity,Hyperbolic triangle,Algebra,Altitude (triangle),Mathematical analysis,Pure mathematics,Euclidean geometry,Mathematics
Journal
118
Issue
ISSN
Citations 
1
0002-9890
0
PageRank 
References 
Authors
0.34
0
1
Name
Order
Citations
PageRank
Nikolai V. Ivanov182.75