## lemniscate of Bernoullilemniskus for a pendant ribbon (the type fastened
to a victor's garland). It has the Cartesian equationx^{2} + y^{2})^{2} = a^{2}(x^{2}
- y^{2})
At the time he wrote his article, Bernoulli wasn't aware that the curve he was describing was a special case of a Cassinian oval, which had been described by Cassini in 1680. The general properties of the lemniscate were discovered by Giovanni Fagnano (1715–1797) in 1750; Leonhard Euler's investigations of the length of arc of the curve (1751) led to later work on elliptic functions. There is a relationship between the lemniscate and the rectangular hyperbola. If a tangent is drawn to the hyperbola and the perpendicular to the tangent is drawn through the origin, the point where the perpendicular meets the tangent is on the lemniscate. ## Related category• PLANE CURVES | ||||||

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