mathematics, the lemniscate constant ϖ is a transcendental mathematical constant that is the ratio of the perimeter of Bernoulli's lemniscate to its diameter...

the lemniscate of Bernoulli, and the lemniscate constants arise in evaluating the arc length of this lemniscate. Another lemniscate, the lemniscate of...

In geometry, the lemniscate of Bernoulli is a plane curve defined from two given points F1 and F2, known as foci, at distance 2c from each other as the...

)}{}^{2}=x^{2}-y^{2}.} The lemniscate functions have periods related to a number ϖ = {\displaystyle \varpi =} 2.622057... called the lemniscate constant, the ratio of...

"Wallis's Constant". MathWorld. Weisstein, Eric W. "e". MathWorld. Weisstein, Eric W. "Natural Logarithm of 2". MathWorld. Weisstein, Eric W. "Lemniscate Constant"...

lemniscate or use different alphabets such as Hebrew, Cyrillic or Gothic. Erdős–Borwein constant E B {\displaystyle E_{B}} Embree–Trefethen constant β...

is the lemniscate constant and γ {\displaystyle \gamma } is the Euler-Mascheroni constant. Another way to define/understand Sierpiński's constant is, Let...

figure eight. Lemniscate may also refer to: Polynomial lemniscate, the set of complex numbers for which a given polynomial has a constant absolute value...

group, than the usual notation ω {\displaystyle \omega } ). The lemniscate constant. Lower-case pi was fairly common in 8-bit character encodings, for...

interesting series that relates to the natural logarithm of the lemniscate constant is the following ∑ n = 2 ∞ [ 2 ( − 1 ) n ζ ( n ) 4 n n − ( − 1 )...

Ascending factorial Cahen–Mellin integral Elliptic gamma function Lemniscate constant Pseudogamma function Hadamard's gamma function Inverse gamma function...

{2}})={\frac {\pi }{\varpi }}} where ϖ {\displaystyle \varpi } is the lemniscate constant. In 1941, M ( 1 , 2 ) {\displaystyle M(1,{\sqrt {2}})} (and hence...

the radius of the squircle, and ϖ {\displaystyle \varpi } is the lemniscate constant. In terms of the p-norm ‖ · ‖p on R2, the squircle can be expressed...

\,}}}}}}}}}\quad } (Ramanujan, ϖ {\displaystyle \varpi } is the lemniscate constant) π = 3 + 1 2 6 + 3 2 6 + 5 2 6 + 7 2 6 + ⋱ {\displaystyle \pi ={3+{\cfrac...

\Gamma } is the gamma function and ϖ {\displaystyle \varpi } is the lemniscate constant. The inverse function of sine is arcsine or inverse sine, denoted...

Catalan's constant and ϖ = Γ ( 1 / 4 ) 2 2 2 π {\displaystyle \varpi ={\frac {\Gamma (1/4)^{2}}{2{\sqrt {2\pi }}}}} being the lemniscate constant. Similar...

{\displaystyle \Gamma \left({\tfrac {1}{4}}\right)} is related to the lemniscate constant ϖ {\displaystyle \varpi } by Γ ( 1 4 ) = 2 ϖ 2 π {\displaystyle \Gamma...

{\displaystyle \pi } and Γ ( 1 / 4 ) {\displaystyle \Gamma (1/4)} such as the lemniscate constant ϖ {\displaystyle \varpi } (following from their respective algebraic...

compute. Bloch's constant (also 2nd Landau's constant): 0.4332 < B < 0.4719 1st Landau's constant: 0.5 < L < 0.5433 3rd Landau's constant: 0.5 < A ≤ 0.7853...

y-cruncher is a computer program for the calculation of some mathematical constant with theoretical accuracy limited only by computing time and available...

includes, alongside the algebraic numbers, many well known mathematical constants such as the number π. Sums and products of periods remain periods, such...

(2006). "A geometric interpretation of an infinite product for the lemniscate constant". The American Mathematical Monthly. 113 (6): 510–520. doi:10.2307/27641976...

\varpi {\bigr )}} With the letter ϖ {\displaystyle \varpi } the Lemniscate constant is represented. Note that the following modular identities hold:...

radius; A ≈ 1.3110287771 and B ≈ 0.5990701173 are the first and second lemniscate constants. The volume of the balloon is given by: V = 2 3 π a r 2 , {\displaystyle...

{\displaystyle \operatorname {sl} } is the lemniscate sine and ϖ {\displaystyle \varpi } is the lemniscate constant. The function λ ∗ ( x ) {\displaystyle...

others' tails; and Möbius Band II (1963), depicting ants crawling around a lemniscate-shaped Möbius strip. It is also a popular subject of mathematical sculpture...

{\displaystyle \operatorname {cl} } is lemniscate cosine and ϖ {\displaystyle \varpi } is Lemniscate constant.[citation needed] The cm and sm functions...

flowers are often presented on this card. According to Eden Gray, the lemniscate above her represents enlightenment and spiritual powers, whereas the lion...

rather than the product. Cassini ovals are the special case of polynomial lemniscates when the polynomial used has degree 2. Cassini ovals are named after...

the parabola, the logarithmic spiral and epicycloids around 1692. The lemniscate of Bernoulli was first conceived by Jacob Bernoulli in 1694. In 1695,...