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I think this is the same family as the Lemniscate of Booth. Richard Pinch (talk) 20:52, 21 August 2008 (UTC)[reply]

Yes, I think so, too. It might seem as though the hippopede is a two-parameter family of curves (a and b) whereas this lemniscate is only a one-parameter family (c). However, if the equations on the hippopede page are right, then b is only a scaling parameter

${\displaystyle {\frac {r^{2}}{4b^{2}}}=\alpha -\sin ^{2}\theta }$

where α=a/b. Thus, the shape of the curve depends only on one parameter, α, and not on b. If we take b=1, then the Cartesian equation for the hippopede becomes

${\displaystyle \left(x^{2}+y^{2}\right)^{2}+4y^{2}=4a\left(x^{2}+y^{2}\right)}$

which is the same as the equation for this lemniscate if we take a=c. Perhaps this lemniscate could be a subsection of hippopede or something? I think "hippopede" is a prettier and shorter name than "lemniscate of Booth", and is more historically correct, methinks. Hoping that you agree, Willow (talk) 21:57, 21 August 2008 (UTC)[reply]

There are no perfect options with this merge. Strictly speaking, hippopede applies when the curve is defined as a spiric section and the Booth name is applied in other contexts. On the other hand, the lemniscate of Booth only applies when when the curve crosses itself, the remaining cases being called ovals of Booth. One or two of the sources I've found combine them and call the entire family curves of Booth, this doesn't seem to have gathered much momentum though. So it appears to me that the best compromise is to merge everything into the Hippopede article, try to explain everything into a Terminology section and create a couple redirects. I'd like to do some preliminary work on the Hippopede article and do the merge after that.--RDBury (talk) 11:49, 16 September 2009 (UTC)[reply]

The merge is complete; the other page is redirected here.--RDBury (talk) 13:32, 20 September 2009 (UTC)[reply]

So the coordinate origin is always part of the curve? --RokerHRO (talk) 17:39, 22 November 2020 (UTC)[reply]