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GXWeb Lemniscatoid
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About the Lemniscate (from Wolfram MathWorld)
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Curves0 0 2 \(a\) 0 0 10 \(\theta\) 0 0 5
The Lemniscatoid is a variation on the Lemniscate, 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.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 points (E (Curve 1) and G (Curve 2) where
\(a = Length(AB)\)
\(= Length(BE) = Length(EC)\)
\(= Length(CD) = Length(DF)\)
\(= Length(FG) = Length(GB)\)
and \(\theta= Angle(BAD)\).
Cartesian equation: \[X^4+2·X^2·Y^2+Y^4-X^2·a^2+3·Y^2·a^2\]
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