“Cyclic Pentagon”的概念、定义、习题解题方法及翻译-数学辞典

单词

Cyclic Pentagon

释义

Cyclic Pentagon

A cyclic pentagon is a not necessarily regular Pentagon on whose Vertices a Circle may be Circumscribed. Let

(1)

where the Sum runs over all distinct Permutations of the Squares of the 5 side lengths, so

Then define

The Area of the pentagon then satisfies

(12)

a seventh order Polynomial in

. This is

times the Discriminant of the Cubic Equation

(13)

See also Concyclic, Cyclic Hexagon, Cyclic Polygon

References

Robbins, D. P. ``Areas of Polygons Inscribed in a Circle.'' Discr. Comput. Geom. 12, 223-236, 1994.

Robbins, D. P. ``Areas of Polygons Inscribed in a Circle.'' Amer. Math. Monthly 102, 523-530, 1995.

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