Topic
Concyclic points
About: Concyclic points is a research topic. Over the lifetime, 144 publications have been published within this topic receiving 1357 citations.
Papers published on a yearly basis
Papers
TL;DR: In this paper, it was shown that two critical circle maps with the same rotation number in a special set are Cワン1+α conjugate for some α>0 provided their successive renormalizations converge together at an exponential rate in the Cワン0 sense.
Abstract: We prove that two C
3 critical circle maps with the same rotation number in a special set ? are C
1+α conjugate for some α>0 provided their successive renormalizations converge together at an exponential rate in the C
0 sense. The set ? has full Lebesgue measure and contains all rotation numbers of bounded type. By contrast, we also give examples of C
∞ critical circle maps with the same rotation number that are not C
1+β conjugate for any β>0. The class of rotation numbers for which such examples exist contains Diophantine numbers.
142 citations
1 Feb 1884
TL;DR: In this article, the authors considered the problem of circumscribing any triangle ABC and diminishing its radius still causing it to pass through A and B: if ACB is an acute angle, C passes without the circle, but if ACBs is an obtuse angle, it remains within the circle.
Abstract: If we consider the circle circumscribing any triangle ABC (see figures 11, 12), and diminish its radius still causing it to pass through A and B: then if ACB be an acute angle, C passes without the circle, but if ACB be an obtuse angle, C remains within the circle. If C be a right angle, the radius of the circle, being ½AB, cannot be farther diminished.
79 citations
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69 citations
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58 citations
TL;DR: A complete characterization of the centers of annuli which are locally minimal in arbitrary dimension is given and it is shown that, for d=2, a locally minimal annulus has two points on the inner circle and twopoints on the outer circle that interlace anglewise as seen from the center of the annulus.
Abstract: Given a set of points S={p
1
,. . ., p
n
} in Euclidean d -dimensional space, we address the problem of computing the d -dimensional annulus of smallest width containing the set. We give a complete characterization of the centers of annuli which are locally minimal in arbitrary dimension and we show that, for d=2 , a locally minimal annulus has two points on the inner circle and two points on the outer circle that interlace anglewise as seen from the center of the annulus. Using this characterization, we show that, given a circular order of the points, there is at most one locally minimal annulus consistent with that order and it can be computed in time O(n log n) using a simple algorithm. Furthermore, when points are in convex position, the problem can be solved in optimal Θ(n) time.
54 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 1 |
| 2020 | 1 |
| 2018 | 1 |
| 2017 | 5 |
| 2016 | 8 |
| 2015 | 2 |