منابع مشابه
Rational hypersurfaces with rational convolutions
The aim of this article is to focus on the investigation of such rationally parametrized hypersurfaces which admit rational convolution (RC) generally, or in some special cases. Examples of such hypersurfaces are presented and their properties are discussed. We also aim to examine links between well-known curves and surfaces (PH/PN or LN) and general objects defined and explored in this article...
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The ancient Greeks posed and solved the problem of finding all right triangles with rational sidelengths. There are 4 natural nonEuclidean generalizations of this problem. We solve them all. The result is that the only rational-sided nonEuclidean triangle with one right angle is the isoceles spherical triangle with legs of length 45 and hypotenuse 60. We next ask which simplices have rational d...
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The eigenvalues of the 3 off-diagonal matrices of rank n with elements 1 + i cot [(j − k)π/n], sin[(j − k)π/n] and sin[(j − k)π/n], (j = 1, 2, . . . , n, k = 1, 2, . . . , n, j 6= k) are computed. The sums over k from 1 to n− 1 of cot (kπ/n) sin (2skπ/n) and sin(kπ/n)cos(2skπ/n) are moreover computed for s integer and p=2 and 4. The results are given by simple formulae in terms of integers. In ...
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W e consider the rational linear relations between real numbers whose squared trigonometric functions have rational values, angles we call “geodetic.” We construct a convenient basis for the vector space over generated by these angles. Geodetic angles and rational linear combinations of geodetic angles appear naturally in Euclidean geometry; for illustration we apply our results to equidecompos...
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ژورنال
عنوان ژورنال: Mathematika
سال: 2011
ISSN: 0025-5793,2041-7942
DOI: 10.1112/s0025579311001847