## 26 Citations

### Comments on generalized Heron polynomials and Robbins' conjectures

- MathematicsDiscret. Math.
- 2009

### On Circumradius Equations of Cyclic Polygons

- Mathematics
- 2009

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

- Mathematics
- 2019

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

- Mathematics
- 2011

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

- Mathematics
- 2012

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)

- Computer Science
- 2021

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 ∗

- Computer Science
- 2018

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

- MathematicsADG
- 2014

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

- Mathematics
- 2008

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…

## References

SHOWING 1-7 OF 7 REFERENCES

### Rigidity and polynomial invariants of convex polytopes

- Mathematics
- 2005

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

- Mathematics
- 1994

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

- MathematicsDiscret. Comput. Geom.
- 1994

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

- Mathematics
- 1999

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.…