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单词 Cissoid of Diocles
释义

Cissoid of Diocles

中文百科

蔓叶线

Cisoide de Diocles (línea roja). El segmento OA es igual a OC menos OB.
Cissoid of Diocles construction

蔓叶线,有时又叫双蔓叶线是 Diocle 在公元前180年发现的曲线。

蔓叶线的标准曲线方程为:

y^2  = \frac{{x^3 }}{{2a - x}}

其中a是常数。

英语百科

Cissoid of Diocles 蔓叶线

Cissoid of Diocles construction
Mechanism to generate the cissoid
Newton's construction

In geometry, the cissoid of Diocles is a cubic plane curve notable for the property that it can be used to construct two mean proportionals to a given ratio. In particular, it can be used to double a cube. It can be defined as the cissoid of a circle and a line tangent to it with respect to the point on the circle opposite to the point of tangency. In fact, the family of cissoids is named for this example and some authors refer to it simply as the cissoid. It has a single cusp at the pole, and is symmetric about the diameter of the circle which is the line of tangency of the cusp. The line is an asymptote. It is a member of the conchoid of de Sluze family of curves and in form it resembles a tractrix.

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