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Lemniscate of Bernoulli: Quiz


Question 1: Once the first two derivatives are known, ________ is easily calculated:
Principal curvatureFrenet–Serret formulasGaussian curvatureCurvature

Question 2: For this reason the case of elliptic functions with complex multiplication by the ________ is called the lemniscatic case in some sources.
Imaginary unitComplex conjugateComplex numberEuler's formula

Question 3: The period lattices are of a very special form, being proportional to the ________.
Gaussian integerUnique factorization domainAlgebraic number theoryComplex number

Question 4: This lemniscate can be obtained as the inverse transform of a hyperbola, with the inversion ________ centered at the center of the hyperbola (bisector of its two foci).
PiConic sectionCirclePolar coordinate system

Question 5: The determination of the ________ of arcs of the lemniscate leads to elliptic integrals, as was discovered in the eighteenth century.
PiCalculusArc lengthCurve

Question 6: The lemniscate was first described in 1694 by Jakob Bernoulli as a modification of an ellipse, which is the locus of points for which the sum of the ________ to each of two fixed focal points is a constant.
Metric spaceEuclidean spaceEuclidean vectorDistance

Question 7: Around 1800, the elliptic functions inverting those integrals were studied by ________ (largely unpublished at the time, but allusions in the notes to his Disquisitiones Arithmeticae).
Benjamin FranklinCarl Friedrich GaussIsaac NewtonJean le Rond d'Alembert

Question 8: It is a special case of the Cassini oval and is a rational ________ of degree 4.
ManifoldAlgebraic geometryRiemann surfaceAlgebraic curve

Question 9: Its name is from lemniscus, which is ________ for "pendant ribbon".
Old LatinRoman EmpireVulgar LatinLatin


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