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GXWeb Lemniscate of Bernoulli
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About the Lemniscate (from Wolfram MathWorld)
\(a\) 0 0 5 \(b\) 0 0 5 \(t\) 0 0 5
The Lemniscate of Bernoulli is any of several figure-eight or ∞-shaped curves. The word comes from the Latin meaning "decorated with ribbons", from the Greek meaning "ribbons", or which alternatively may refer to the wool from which the ribbons were made.
Curves that have been called a lemniscate include three quartic plane curves: the hippopede or lemniscate of Booth, the lemniscate of Bernoulli, and the lemniscate of Gerono. The study of lemniscates (and in particular the hippopede) dates to ancient Greek mathematics, but the term "lemniscate" for curves of this type comes from the work of Jacob Bernoulli in the late 17th century.
The Leminiscate constructed here is the locus of point D where
\(a = Length(AE) = Length(BC)\)
\(b = Length(AB) = Length(BD) = Length(CE)\)
and \(t = Length(AC)\).
Cartesian equation: \[X^4+2·X^2·Y^2+Y^4+4·Y^2·a^2+b^2·(-4·X^2-4·Y^2)\]
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