Loterre: Mathématiques: cissoid

geometry > Euclidean geometry > plane curve > cissoid

geometry > algebraic geometry > algebraic variety > algebraic curve > cissoid

cissoid

In geometry, a cissoid ((from Ancient Greek κισσοειδής (kissoeidēs) 'ivy-shaped') is a plane curve generated from two given curves $C 1$ , $C 2$ and a point $O$ (the pole). Let $L$ be a variable line passing through $O$ and intersecting $C 1$ at $P 1$ and $C 2$ at $P 2$ . Let $P$ be the point on $L$ so that ${\\displaystyle {\\overline {OP}}={\\overline {P_{1}P_{2}}}.}$ (There are actually two such points but $P$ is chosen so that $P$ is in the same direction from $O$ as $P 2$ is from $P 1$ .) Then the locus of such points $P$ is defined to be the cissoid of the curves $C 1$ , $C 2$ relative to $O$ .
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Cissoid)

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