On the areas of cyclic and semicyclic polygons

  title={On the areas of cyclic and semicyclic polygons},
  author={F. Miller Maley and David P. Robbins and Julie Roskies},
  journal={Adv. Appl. Math.},

On Circumradius Equations of Cyclic Polygons

In a masterfully written (in german language) thirty pages long paper (and published in 1828 in Crelle’s Journal ) A. F. Möbius studied some properties of the polynomial equations for the

A "right" path to cyclic polygons

It is well known that Heron's theorem provides an explicit formula for the area of a triangle, as a symmetric function of the lengths of its sides. It has been extended by Brahmagupta to

The geometry of cyclic hyperbolic polygons

A hyperbolic polygon is defined to be cyclic, horocyclic, or equidistant if its vertices lie on a metric circle, horocycle, or a component of the equidistant locus to a hyperbolic geodesic,

Intrinsic Geometry of Cyclic Polygons via ”New” Brahmagupta Formula

Finding explicit equations for the area or circumradius of polygons inscribed in a circle in terms of side lengths is a classical subject (cf.[1]). For triangle / cyclic quadrilaterals we have famous

Computation and Analysis of Explicit Formulae for the Circumradius of Cyclic Polygons (Extended Abstract)

A more efficient method for computing the circumradius of cyclic heptagons than before is found and 25 out of 39 coefficients in the ci_{1} .cumradius formula for cyclic octagons are succeeded in.

Computation and Analysis of Explicit Formulae for the Circumradius of Cyclic Polygons ∗

The present work has succeeded in explicitly computing the circumradius of cyclic heptagons, which is converted into an expression in the form of elementary symmetric polynomials for the first time.

Integrated Circumradius and Area Formulae for Cyclic Pentagons and Hexagons

Computations of the relations between the circumradius R and area S of cyclic polygons given by the lengths of the sides are described, and a polynomial equation in 4SR itself with degree 7 for cyclic pentagons is derived, showing that this type of formula exists only for n-gons, where n is an odd number.

Computation with Pentagons

The paper deals with properties of pentagons in a plane which are related to the area of a pentagon. First the formulas of Gauss and Monge holding for any pentagon in a plane are studied. Both



Rigidity and polynomial invariants of convex polytopes

We present an algebraic approach to the classical problem of constructing a simplicial convex polytope given its planar triangulation and lengths of its edges. We introduce polynomial invariants of a

Discriminants, Resultants, and Multidimensional Determinants

Preface.- Introduction.- General Discriminants and Resultants.- Projective Dual Varieties and General Discriminants.- The Cayley Method of Studying Discriminants.- Associated Varieties and General

Areas of polygons inscribed in a circle

AbstractHeron of Alexandria showed that the areaK of a triangle with sidesa,b, andc is given by % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn%

Classical Invariant Theory

Introduction Notes to the reader A brief history Acknowledgements 1. Prelude - quadratic polynomials and quadratic forms 2. Basic invariant theory for binary forms 3. Groups and transformations 4.