Related papers: Two circles and only a straightedge
We construct an infinite family of smoothly slice knots that we prove are topologically doubly slice. Using the correction terms coming from Heegaard Floer homology, we show that none of these knots is smoothly doubly slice. We use these…
Any four mutually tangent spheres in R^3 determine three coincident lines through opposite pairs of tangencies. As a consequence, we define two new triangle centers.
Generalized circumcenters have been recently introduced and employed to speed up classical projection-type methods for solving feasibility problems. In this note, circumcenters are enforced in a new setting; they are proven to provide…
We characterize when two conic curved creases are compatible with each other, when the rule lines must converge to conic foci and reflect at the crease. Namely, two conics are compatible (can be connected by rule segments in a foldable…
Given a smooth, closed, oriented 4-manifold X and alpha in H_2(X,Z) such that alpha.alpha > 0, a closed 2-form w is constructed, Poincare dual to alpha, which is symplectic on the complement of a finite set of unknotted circles. The number…
We generalise the well-known ``embroidery'' envelopes of chords joining points at angles $t$ and $mt$ of a single circle in several ways. Firstly we allow $m$ to be rational (possibly negative) instead of integral, finding formulas for the…
In this paper techniques of twist map theory are applied to the annulus maps arising from dual billiards on a strictly convex closed curve G in the plane. It is shown that there do not exist invariant circles near G when there is a point on…
Consider a triangle $ABC$ with given lengths $l_a,l_b,l_c$ of its internal angle bisectors. We prove that in general, it is impossible to construct a square of the same area as $ABC$ using a ruler and compass. Moreover, it is impossible to…
We show how to construct a cubic partial cube from any simplicial arrangement of lines or pseudolines in the projective plane. As a consequence, we find nine new infinite families of cubic partial cubes as well as many sporadic examples.
We prove that any $n$ points in $\mathbb{R}^2$, not all on a line or circle, determine at least $\frac{1}{4}n^2-O(n)$ ordinary circles (circles containing exactly three of the $n$ points). The main term of this bound is best possible for…
In this note, we completely describe the shape of the bisector of two given points in a two-dimensional normed vector space. More precisely, we show that, depending on the position of two given points with respect to the shape of the unit…
We discuss a string-net construction on 2-framed surfaces, taking as algebraic input a finite, rigid tensor category, which is neither assumed to be pivotal nor semi-simple. It is shown that circle categories of our framed string-net…
An oriented link projection is the image of a generic immersion of oriented circles into the 2-sphere. The circle arrangement of a link projection is a disjoint union of unoriented circles on the 2-sphere obtained by orientation-incoherent…
In this paper we give a classification of tilings of the sphere by congruent quadrilaterals with exactly two equal edges. The tilings are the earth map tilings, $(p,q)$-earth map tilings and their flip modifications, and quadrilateral…
On the perimeter length determination of the eight-centered oval. Several studies have shown that an eight-centered oval coincides almost perfectly with the ellipse constructed on the same axes and can be considered as a representation of…
In this paper, we consider a problem of covering a straight line segment by equal circles that are initially arbitrarily placed on a plane by moving their centers on a segment or on a straight line containing a segment so that the segment…
Let G be a finite group, and let B be a non-nilpotent block of G with respect to an algebraically closed field of characteristic 2. Suppose that B has an elementary abelian defect group of order 16 and only one simple module. The main…
We first introduce a configuration of arbitrary isogonal conjugates related to a known property concerning the spiral center of two pairs of isogonal conjugates. We then consider a special case where two conics are tangent at exactly two…
We give sufficient conditions for the descent construction to be the universal central extension of a twisted form of a split simple Lie algebra over a ring. In particular, the universal central extensions of twisted multiloop Lie tori are…
It is known that the complex projective space $\mathbb{CP}^n$ admits a spin structure if and only if $n$ is odd. In this paper, we provide another proof that $\mathbb{CP}^{2m}$ does not admit a spin structure, by using a circle action.