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I have been teaching trigonometry for many years and, surprisingly, did not know of this issue. I read the responses and the references therein, and I am putting my thoughts on this issue here. The question is how to approach trigonometry, right triangles first and then unit circle; or circle first and then triangle. I think the answer depends on the ...


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Books about middle school algebra and trigonometry written by someone like Gelfand are rare (I don't know other examples; for example V.I. Arnold's books nomially for children are aimed at very special children, their author's claims to the contrary), but there are many undergraduate textbooks written by superb mathematicians. I list below some that occur to ...


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This may not qualify, as it is a stretch to classify this as a "textbook." It arose from a series of lecture Klein gave to high-school teachers. Klein, Felix. Elementary Mathematics from an Advanced Standpoint: Geometry. Transl. from the Third German Ed. by ER Hedrick and CA Noble. Dover, 1939.           I love this (...


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