منابع مشابه
Perspective Isoconjugate Triangle Pairs, Hofstadter Pairs, and Crosssums on the Nine-Point Circle
The r-Hofstadter triangle and the (1 − r)-Hofstadter triangle are proved perspective, and homogeneous trilinear coordinates are found for the perspector. More generally, given a triangle DEF inscribed in a reference triangle ABC, triangles A′B′C′ and A′′B′′C′′ derived in a certain manner from DEF are perspective to each other and to ABC. Trilinears for the three perspectors, denoted by P ∗, P1,...
متن کاملGenerating the Nine-Point Graphs
A program has been written which recently generated all the (unlabelled) nine-point graphs. Written in MACRO-10 assembly language and run on a 165K PDP10, it generates the complete set of 274,668 graphs in less than six hours. The algorithm on which this program is based is discussed with an emphasis on coding of graphs and various programming techniques designed to save space and time during e...
متن کاملThe Arbelos and Nine-Point Circles
We construct some new Archimedean circles in an arbelos in connection with the nine-point circles of some appropriate triangles. We also construct two new pairs of Archimedes circles analogous to those of Frank Power, and one pair of Archimedean circles related to the tangents of the arbelos.
متن کاملPoint perturbations of circle billiards
The spectral statistics of the circular billiard with a point-scatterer is investigated. In the semiclassical limit, the spectrum is demonstrated to be composed of two uncorrelated level sequences. The first corresponds to states for which the scatterer is located in the classically forbidden region and its energy levels are not affected by the scatterer in the semiclassical limit while the sec...
متن کاملComputing the Closest Point to a Circle
In this paper we consider the problem of computing the closest point to the boundary of a circle among a set S of n points. We present two algorithms to solve this problem. One algorithm runs in O(n) preprocessing time and space and O(log n) query time. The other algorithm runs in O(n ) preprocessing time and O(n log n) space and O(n ) query time. Thus we exhibit a trade-off between preprocessi...
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ژورنال
عنوان ژورنال: Časopis pro pěstování matematiky a fysiky
سال: 1886
ISSN: 1802-114X
DOI: 10.21136/cpmf.1886.109133