Lemniscate of Booth

In Geometry algebraic, the lemniscate of Booth , so called curve of Booth , oval of Booth or hippopède of Proclus , is a Lemniscate Euclidean plane . It is generalized in the Espace by the surfaces of elasticity of Fresnel.

It is defined like the whole of the points solutions of the equation:

$\backslash \; left\; (x^2+y^2\; \backslash \; right)\; ^2\; +\; 4\; y^2\; =\; 4\; C\; \backslash \; left\; (x^2+y^2\; \backslash \; right)$

with ( X, there ) the Cartesian Coordinated of the point and C a real parameter .

When C > 1, one observes a closed figure, called Ovale of Booth. When C < 1, it forms the Lemniscate of Booth. When C = 1, it is reduced to two tangent circles. Lastly, for C < 0, the figure is reduced to a single point coinciding with the origin.

External bond

• Lemniscate of Booth.

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