I wrote previously that lemniscate meant "shaped like an infinity symbol."

http://wordsmith.org/board/ubbthreads.ph...=true#Post59953

Well, that's kind of indirectly true, but what it really means according to the online references is "ribboned" as in "decorated with ribbons." I think one site may have said something similar to "like a flowing ribbon."

The infinity symbol that looks like a numeral "8" on its side is a lemniscate. It has a different meaning than the alephs, which denote the size (what we call "cardinality" of sets). The lemniscate is meant to symbolize some unachievable limit.

http://en.wikipedia.org/wiki/Infinity

I guess the first mathematicians who used the symbol in this way liked the way the points just came back on each other.

Variants of it can be described by formulae in Cartesian coordinates, e.g.
(x^2 + y^2)^2 = a^2 (x^2 - y^2)

But I prefer using polar coordinates (because it's easier to program as a function):
r^2 = a^2 cos(2theta)

Some vague references online to lemiscate being applied to an order of transparent, ribbon-shaped fish, but not much detail.

Anyway, I thought it was interesting.