منابع مشابه
Ellipses, near Ellipses, and Harmonic Möbius Transformations
It is shown that an analytic function taking circles to ellipses must be a Möbius transformation. It then follows that a harmonic mapping taking circles to ellipses is a harmonic Möbius transformation. Analytic Möbius transformations take circles to circles. This is their most basic, most celebrated geometric property. We add the adjective ‘analytic’ because in a previous paper [1] we introduce...
متن کاملIntersection of Ellipses
3 Find-Intersection Query 4 3.1 Constructing Intersection Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3.1.1 Case d4 6= 0 and e(x̄) 6= 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.1.2 Case d4 6= 0 and e(x̄) = 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.1.3 Case d4 = 0, d2 6= 0, and e2 6= 0 . . . . . . . . ....
متن کاملEllipses and Lambda Definability
Ellipses are a meta-linguistic notation for denoting terms the size of which are specified by a meta-variable that ranges over the natural numbers. In this work, we present a systematic approach for encoding such meta-expressions in the λ-calculus, without ellipses: Terms that are parameterized by meta-variables are replaced with corresponding λ-abstractions over actual variables. We call such ...
متن کاملCombining Error Ellipses
The purpose of this document is to present a formalism for statistically averaging source positions and their uncertainties for use in the level-3 pipeline. More specifically, the problem addressed here is to find an improved estimate for the position of a source from previous independent estimates of its position. The uncertainties of the estimates are expressed in the form of error ellipses c...
متن کاملComputing bitangents for ellipses
We show how to compute the bitangents of two ellipses, and how to evaluate the predicates required to compute objects like convex hulls or visibility complexes for ellipses. Also, we show how to compute the tangency points of the bitangents.
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ژورنال
عنوان ژورنال: The College Mathematics Journal
سال: 1993
ISSN: 0746-8342
DOI: 10.2307/2687018