25 Sep
Classification of Triangles
Here is a curious diagram I cam across in H. Jacobs' Geometry. (Jacobs, in turn, credits a 1901 publication.) The diagram that presents all possible kinds of triangles could serve as a great poster.
As you can see, all possible triangle classes do appear there. The diagram is curious in that its dimensions (up to a coefficient of proportionality, of course) are uniquely determined from the manner in which it combines various triangles. Finding ratios of the segments in the diagram is a good exercise that needs not more than the Pythagorean theorem.
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