ellauri078.html on line 44: The infinity symbol ( ∞ {\displaystyle \infty } \infty , ∞, or in unicode ∞) is a mathematical symbol representing the concept of infinity. In algebraic geometry, the figure is called a lemniscate.
ellauri078.html on line 48: 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.
ellauri078.html on line 50: The consideration of curves with a figure-eight shape can be traced back to Proclus, a Greek Neoplatonist philosopher and mathematician who lived in the 5th century AD. Proclus considered the cross-sections of a torus by a plane parallel to the axis of the torus. As he observed, for most such sections the cross section consists of either one or two ovals; however, when the plane is tangent to the inner surface of the torus, the cross-section takes on a figure-eight shape, which Proclus called a horse fetter (a device for holding two feet of a horse together), or "hippopede" in Greek. The name "lemniscate of Booth" dates to its study by the 19th-century mathematician James Booth.
ellauri078.html on line 64: Lorenz attractor, a three-dimensional dynamic system exhibiting a lemniscate shape
ellauri078.html on line 65: Polynomial lemniscate, a level set of the absolute value of a complex polynomial
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