Book Review: The Elements of Non-Euclidean Plane Geometry and Trigonometry
نویسندگان
چکیده
منابع مشابه
Some Facts about Trigonometry and Euclidean Geometry
We calculate the values of the trigonometric functions for angles: π3 and π 6 , by [16]. After defining some trigonometric identities, we demonstrate conventional trigonometric formulas in the triangle, and the geometric property, by [14], of the triangle inscribed in a semicircle, by the proposition 3.31 in [15]. Then we define the diameter of the circumscribed circle of a triangle using the d...
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The paper presents the information processing that can be performed by a general hermitian matrix when two of its distinct eigenvalues are coupled, such as λ < λ′. Setting a = λ+λ ′ 2 and e = λ′−λ 2 > 0, the new spectral information that is provided by coupling is expressed in terms of the ratios e |a| (if λλ ′ > 0) or |a| e (if λλ ′ < 0) and of the product |a|e. The information is delivered in...
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This is a collection of some standard formulae from Euclidean, spherical and hyperbolic trigonometry, including some standard models of the hyperbolic plane. Proofs are not given.
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In [3], in my argument for the primacy of Euclidean geometry on the basis of rigid motions and the existence of similar but non-congruent triangles, I wrote the following: A: “The mobility of rigid objects is now recognized as one of the things every normal human child learns in infancy, and this learning appears to be part of our biological progaramming.” B. “. . . we are all used to thinking ...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1917
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1917-02997-7