We investigate the affine circle geometry arising from a quaternion skew field and one of its maximal commutative subfields.

A circle C holds a convex body K ⊂ R3 if K can’t be moved far away from its position without intersecting C . One of our results says that there is a convex body K ⊂ R3 such that the set of radii of all circles holding K has infinitely many components. Another result says that the circle is unique in the sense that every frame different from the circle holds a convex body K (actually a tetrahed...

In this note, we follow the strategy of Haller, Rybicki and Teichmann to give a short, self contained, and elementary proof that Diff0(M) is a perfect group, given a theorem of Herman on diffeomorphisms of the circle.

Time-frequency representations are often very useful tools for the analysis of signals in which local frequencies can be extracted. They are usually deened for signals deened on at spaces (of the form IR or IR n .) It is shown here how the same kind of methods can be developed to construct phase-space representation theorems for functions deened on more general spaces, in particular the circle ...

We give a counterexample of Bowers-Stephenson's conjecture in the spherical case: spherical inversive distance circle packings are not determined by their inversive distances.

Background & Aims: The relationship between variations of Willis circle and some cerebrovascular diseases has been shown in previous studies. A few studies have been conducted in Iran on these variations. Methods: This study was performed on 100 recently deceased Iranians due to car accidents who had been referred to Kerman Forensic Medicine Center for autopsy. The length and diameter of cerebr...

In theological sources, many symbols are used to explain the transcendent truths of existence. Among shapes, circle has most use a symbol which is important for Religious, philosophers, and mystics. However, what refer mostly shape rotation circular line that begins at point on surface ends same point; then, superficial intermediate facts explained with it. Contrary, present article proposes no...

We review the construction of integral Apollonian circle packings. There are a number of Diophantine problems that arise in the context of such packings. We discuss some of them and describe some recent advances. 1. AN INTEGRAL PACKING. The quarter, nickel, and dime in Figure 1 are placed so that they are mutually tangent. This configuration is unique up to rigid motions. As far as I can tell t...