Wyniki wyszukiwania - BazTech

Ograniczanie wyników

Znaleziono wyników: 2

Liczba wyników na stronie

Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: punkty przecięcia

Sortuj według:

Ogranicz wyniki do:

On the geometric nature of the twin paradox in curved spacetimes

Sokołowski L. M.

Demonstratio Mathematica

2017

Vol. 50, nr 1

56--65

The famous „twin paradox” of special relativity is of purely geometric nature and formulated in curved spacetimes of general relativity motivates investigations of the timelike geodesic structure of these manifolds. Except for the maximally symmetric spacetimes the search for the longest timelike curves is hard, complicated and requires both advanced methods of global Lorentzian geometry and solving the intricate geodesic deviation equation. This article is a theoretical introduction to the problem. First we describe the procedure of determining the locally longest curves; it is algorithmic in the sense of consisting of a small number of definite steps and is effective if the geodesic deviation equation may be solved. Then we discuss the problem of globally maximal timelike curves; due to its nonlocal nature there is no prescription of how to solve it in finite number of steps. In the case of sufficiently high symmetry of the manifold also the globally longest curves may be found. Finally we briefly present some results recently found.

A generalization of the radical axis

Fazekas S.

Zeszyty Naukowe. Geometria i Grafika Inżynierska / Politechnika Śląska

2004

z. 6

9-16

We can generalise the radical axis as the support of the real or imaginary intersection points of two real non-degenerative second order curves. The new definition is based on projective-properties, which gives a radical axis also in non-constructable cases.

Autor prezentuje uogólnienie osi potęgowej opartej o rzeczywiste lub urojone punkty przecięcia z dwoma nie zdegenerowanymi krzywymi stopnia drugiego. Nowa definicja bazuje na własnościach rzutowych, które także umożliwiają wyznaczenie osi potęgowej w nie konstruktywnych przypadkach.