: Mathématiques: strophoid

geometry > Euclidean geometry > plane curve > strophoid

strophoid

In geometry, a strophoid is a curve generated from a given curve $C$ and points $A$ (the fixed point) and $O$ (the pole) as follows: Let $L$ be a variable line passing through $O$ and intersecting $C$ at $K$ . Now let $P 1$ and $P 2$ be the two points on $L$ whose distance from $K$ is the same as the distance from $A$ to $K$ (i.e. $KP 1 = KP 2 = AK$ ). The locus of such points $P 1$ and $P 2$ is then the strophoid of $C$ with respect to the pole $O$ and fixed point $A$ . Note that $AP 1$ and $AP 2$ are at right angles in this construction.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Strophoid)

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