Pythagoräische Tripel: Gleichverteilung und geometrische Anwendungen (2. Teil)

Year, pages: 2005, 4 - 6

The first part of this article appeared in [Acta Math. Inform. Univ. Ostraviensis 11 (2003), 29–72]. In this earlier paper the author continued his investigations on Pythagoreian triples, uniform distribution and applications which he already started in [Bonner Math. Schriften 121, Univ. Bonn, Bonn, 1980] and in [Aequationes Math. 58 (1999)]. In the first part of this paper the author focuses on the construction of Pythagoreian triples by means of prime numbers in the Gaussian number field and various geometric applications. In the first three sections of part I applications to line geometry and to spherical trigonometry are discussed. Sections 4–6 are devoted to rotations in the three dimensional space. The present second part is not self-content, it makes use of the notation and results of the first part. It starts with Section 7, which is devoted to the ortho gonal group in higher dimensions. Section 8 gives applications to non Euclidean geometry and in Section 9 Clifford's surface is discussed. In Section 10 Gödel's cosmological model is considered. In Sections 11 and 12 applications to a probabilistic model and to infinite series are discussed. The paper ends with several remarks on solitons, Doppler's phenomenon and aberration and on extensions of the theory to quaternions and imaginary quadratic number fields.

Hlawka, E. 2005. Pythagoräische Tripel: Gleichverteilung und geometrische Anwendungen (2. Teil). In Mathematica Slovaca, vol. 55, no.1, pp. 4-6. 0139-9918.

Hlawka, E. (2005). Pythagoräische Tripel: Gleichverteilung und geometrische Anwendungen (2. Teil). Mathematica Slovaca, 55(1), 4-6. 0139-9918.