Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Areas of Cyclic and Semicyclic Polygons   We investigate the ``generalized Heron polynomial'' that relates the squared
area of an n-gon inscribed in a circle to the squares of its side lengths. For
a (2m+1)-gon or (2m+2)-gon, we express it as the defining polynomial of a
certain variety derived from the variety of binary (2m-1)-forms having m-1
double roots. Thus we obtain explicit formulas for the areas of cyclic
heptagons and octagons, and illuminate some mysterious features of Robbins'
formulas for the areas of cyclic pentagons and hexagons. We also introduce a
companion family of polynomials that relate the squared area of an n-gon
inscribed in a circle, one of whose sides is a diameter, to the squared lengths
of the other sides. By similar algebraic techniques we obtain explicit formulas
for these polynomials for all n <= 7.

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The categories of this paper are: eess
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The categories of this paper are: nlin
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The categories of this paper are: dg-ga
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The categories of this paper are: plasm-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: q-bio
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The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
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The categories of this paper are: stat
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The categories of this paper are: q-fin
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The categories of this paper are: supr-con