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The Brocard Angle and a Geometrical Gem from Dmitriev and Dynkin
The American Mathematical Monthly
Vol. 122, No. 5 (May 2015), pp. 495-499
Published by: Mathematical Association of America
Stable URL: http://www.jstor.org/stable/10.4169/amer.math.monthly.122.5.495
Page Count: 5
You can always find the topics here!Topics: Geometric angles, Mathematical problems, Triangles, Mathematical inequalities, Matrices, Eigenvalues, Sine function, Geometric planes, Principal components analysis
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In a celebrated paper on the eigenvalues of special matrices, N. Dmitriev and E. Dynkin formulated and proved a nice geometrical lemma. This lesser-known gem provides a simple proof of the maximal value of the Brocard angle and yields also the solution to some challenging problems from the past few decades.
Copyright the Mathematical Association of America 2015