the hermeneutic circle articulated by different hermeneuticans in various versions is one of the basic problems in modern hermeneutics. romanic hermeneutics introduced the circle as a methodological principle, but in philosophical hermeneutics the circle has ontological dimensions and regards as a process of understanding. heidegger believes that hermeneutic circle reflects dasein’s existential...

The drawbacks of the standard Hough transform (SHT) are the computational time spending and the large storage requirement. Moreover, the voting method of SHT affects accuracy of detection. In this paper, a new voting method is proposed to reduce the computation and storage requirements of SHT for circle detection. This method improves the efficiency of circle detection by letting each pixel onl...

The derivation of the Hardy-Ramanujan-Rademacher formula for the number of partitions of n is reviewed. Next, the steps for finding analogous formulas for certain restricted classes of partitions or overpartitions is examined, bearing in mind how these calculations can be automated in a CAS. Finally, a number of new formulas of this type which were conjectured with the aid of Mathematica are pr...

A two-step circle detection method using pairs of chords is proposed. It is shown how the center of the circle is computed from two intersecting chords. First, a 2D HT method based on the idea finds the centers of the circles in the image. Then, a 1D radius histogram is used to compute the radii. The experimental results show that the proposed method detects the circles effectively.

1 Waring’s Problem Problem 1. (Waring’s) For every natural number k ≥ 2 there exists a positive integer s such that every natural number is the sum of at most s k powers of natural number (for example, every natural number is the sum of at most 4 squares, or 9 cubes, or 19 fourth powers, etc.). The affirmative answer, known as the Hilbert-Waring theorem, was provided by Hilbert in 1909. Let A =...

There are other problems that can be attacked with the circle method but that don’t quite fit into our framework here; for example, determining asymptotics of the partition function p(n) or proving theorems about small gaps in primes. For this talk, we’ll concentrate on Waring’s problem, as it is of moderate difficulty and illustrates some basic ideas nicely. There will be no effort at complete...

The Andreev-Koebe-Thurston circle packing theorem is generalized and improved in two ways. First, we get simultaneous circle packings of the map and its dual map so that, in the corresponding straight-line representations of the map and the dual, any two edges dual to each other are perpendicular. Necessary and sufficient condition for a map to have such a primal-dual circle packing representat...

In an earlier work, the author extended the AndreevKoebe-Thurston circle packing theorem. Additionally, a polynomial time algorithm for constructing primal-dual circle packings of arbitrary (essentially) 3-connected maps was found. In this note, additional details concerning surfaces of constant curvature 0 (with special emphasis on planar graphs where a slightly different treatment is necessar...

A circle graph is the intersection graph of a set of chords on a circle. A graph is Helly circle if there is a model of chords satisfying the Helly property. In 2003 it was conjectured that Helly circle graphs are exactly diamond-free circle graphs. In this work, we propose a method to compress any Helly circle representation of a graph and give some ideas to advance in an inductive proof of th...