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\iteman{ZMATH 2015e.00652}
\itemau{Akopyan, Arseniy V.}
\itemti{The lemniscate of Bernoulli, without formulas.}
\itemso{Math. Intell. 36, No. 4, 47-50 (2014).}
\itemab
``A polynomial lemniscate with foci $F_1,F_2,\dots,F_n$ is a locus of points $X$ such that the product of distances from $X$ to the foci is constant ($\prod_{i=1,\dots,n}|F_iX|=\mathrm{const}$). The $n$-th root of this value is called the {\it radius} of the lemniscate. It is clear that a lemniscate is an algebraic curve of degree (at most) $2n$" (from the text). Using purely synthetic arguments, the author presents three constructions of the Bernoulli lemniscate ($n=2$, $\mathrm{const}=(1/4)|F_1F_2|^2$), one is based on a three-bar linkage invented by James Watt. In the same way it is proved that the Bernoulli lemniscate is an inversion image of an equilateral hyperbola. Finally, a very simple construction of the normal of the Bernoulli lemniscate is described.
\itemrv{Rolf Riesinger (Wien)}
\itemcc{G70}
\itemut{polynomial lemniscate; radius of a lemniscate; Cassini oval; lemniscate of Bernoulli; equilateral hyperbola}
\itemli{doi:10.1007/s00283-014-9445-5}
\end