Search results
Results from the WOW.Com Content Network
The lemniscate has been a common decorative motif since ancient times; for instance, it is commonly seen on Viking Age combs. [4] The English mathematician John Wallis is credited with introducing the infinity symbol with its mathematical meaning in 1655, in his De sectionibus conicis. [5] [6] [7] Wallis did not explain his choice of this symbol.
Another lemniscate, the lemniscate of Gerono or lemniscate of Huygens, is the zero set of the quartic polynomial (). [ 12 ] [ 13 ] Viviani's curve , a three-dimensional curve formed by intersecting a sphere with a cylinder, also has a figure eight shape, and has the lemniscate of Gerono as its planar projection.
In algebraic geometry, the lemniscate of Gerono, or lemniscate of Huygens, or figure-eight curve, is a plane algebraic curve of degree four and genus zero and is a lemniscate curve shaped like an symbol, or figure eight. It has equation
A lemniscate is a mathematical curve shaped like a figure eight. Lemniscate may also refer to: Polynomial lemniscate, the set of complex numbers for which a given polynomial has a constant absolute value; The infinity symbol ∞, sometimes called a lemniscate because of its shape; Lemniscate, by Vinyl Williams
The lemniscate is symmetric to the line connecting its foci F 1 and F 2 and as well to the perpendicular bisector of the line segment F 1 F 2. The lemniscate is symmetric to the midpoint of the line segment F 1 F 2. The area enclosed by the lemniscate is a 2 = 2c 2. The lemniscate is the circle inversion of a hyperbola and vice versa.
Lemniscate of Bernoulli. In mathematics, the lemniscate constant ϖ is a transcendental mathematical constant that is the ratio of the perimeter of Bernoulli's lemniscate to its diameter, analogous to the definition of π for the circle. [1] Equivalently, the perimeter of the lemniscate (+) = is 2ϖ.
The lemniscate sine (red) and lemniscate cosine (purple) applied to a real argument, in comparison with the trigonometric sine y = sin(πx/ϖ) (pale dashed red).. In mathematics, the lemniscate elliptic functions are elliptic functions related to the arc length of the lemniscate of Bernoulli.
Main page; Contents; Current events; Random article; About Wikipedia; Contact us