“Cyclic Hexagon”的概念、定义、习题解题方法及翻译-数学辞典

单词

Cyclic Hexagon

释义

Cyclic Hexagon

A hexagon (not necessarily regular) on whose Vertices a Circle may be Circumscribed. Let

(1)

where the sum runs over all distinct permutations of the Squares of the six side lengths, so

Then define

The Area of the hexagon then satisfies

(13)

or this equation with

replaced by

, a seventh order Polynomial in

. This is

times the Discriminant of the Cubic Equation

(14)

See also Concyclic, Cyclic Pentagon, Cyclic Polygon, Fuhrmann's Theorem

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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