Add to ORKGAbstract. It is well known that the area U of the triangle formed by three tangents to a parabola X is half of the area T of the triangle formed by joining their points of contact. In this article, we study some properties of U and T for strictly convex plane curves. As a result, we establish a characterization for parabolas. 1
We show that the number of unit-area triangles determined by a set S of n points in the plane is O(n...
In this paper we provide an estimate from above for the value of the relaxed area function...
AreaThe black central triangle with one angle equal to 60° is called a eutrigon. The areas of equila...
Abstract. Archimedes knew that the area between a parabola and any chord AB on the parabola is four ...
A brief summary of Archimedes\u27 Quadrature of the Parabola is given showing the use of recursive...
We study functions defined in the plane E 2 in which level curves are strictly convex, and i...
Consider the family of generalized parabolas {y=−axr+c|a,r,c,x>0,risafixedconstant} that pass throug...
The works elucidates the extremum areas of the polygons circumscribing parabolic figures. It is show...
International audienceWe start by recalling the classical theorem of Girard on the area of a spheric...
IT is well-known that of all plane convex sets of constant width d, the Reuleaux triangle, bounded b...
In this paper we provide an estimate from above for the value of the relaxed area functional A¯(u, Ω...
International audienceWe investigate the vertex curve, that is the set of points in the hyperbolic r...
A curvature-area inequality for planar curves with cusps is derived. Using this inequality, the tota...
We study some characterizations of hyperbolic geometry in the Poincaré disk. We first obtain the hyp...
This is a review of various methods used by many mathematicians to determine the area of the segment...
We show that the number of unit-area triangles determined by a set S of n points in the plane is O(n...
In this paper we provide an estimate from above for the value of the relaxed area function...
AreaThe black central triangle with one angle equal to 60° is called a eutrigon. The areas of equila...
Abstract. Archimedes knew that the area between a parabola and any chord AB on the parabola is four ...
A brief summary of Archimedes\u27 Quadrature of the Parabola is given showing the use of recursive...
We study functions defined in the plane E 2 in which level curves are strictly convex, and i...
Consider the family of generalized parabolas {y=−axr+c|a,r,c,x>0,risafixedconstant} that pass throug...
The works elucidates the extremum areas of the polygons circumscribing parabolic figures. It is show...
International audienceWe start by recalling the classical theorem of Girard on the area of a spheric...
IT is well-known that of all plane convex sets of constant width d, the Reuleaux triangle, bounded b...
In this paper we provide an estimate from above for the value of the relaxed area functional A¯(u, Ω...
International audienceWe investigate the vertex curve, that is the set of points in the hyperbolic r...
A curvature-area inequality for planar curves with cusps is derived. Using this inequality, the tota...
We study some characterizations of hyperbolic geometry in the Poincaré disk. We first obtain the hyp...
This is a review of various methods used by many mathematicians to determine the area of the segment...
We show that the number of unit-area triangles determined by a set S of n points in the plane is O(n...
In this paper we provide an estimate from above for the value of the relaxed area function...
AreaThe black central triangle with one angle equal to 60° is called a eutrigon. The areas of equila...