nobodyL is for #Lemniscate
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Kenneth A. Mendoza@Danpiker This animation stopped me mid-scroll. Thanks for this. The lemniscate contours of Log(Z-1)-Log(2Z)+Log(Z+1) passing through three fixed points — that’s exactly the geometry at the heart of Erdős #114 (the EHP conjecture on maximal lemniscate arclength).
I just finished computationally verifying EHP (Erdos 114) for all degrees n=3 through 12, bridging the gap between the classical n=2 case and Tao’s asymptotic proof for large n.
Preprint: https://zenodo.org/records/19229245
Interactive bound-sweep visualizer: https://mendozalab.io/workbench/interactive-morphism-engine
Kera Damo® - Visual artistSomething about the fact that true love is endless 💗
#art #heart #keradamo #pixelfedart #mastoart #lemniscate
#art #heart #keradamo #pixelfedart #mastoart #lemniscate
claude
Pustam | पुस्तम | পুস্তম🇳🇵Let \(\varpi=\dfrac{\Gamma^2\left(\frac14\right)}{2\sqrt{2\pi}}=2.62205755\ldots\) be the lemniscate constant. Then,
\[\Large\displaystyle\sum_{n=1}^\infty\dfrac{1}{\sinh^4(\pi n)}=\dfrac{\varpi^4}{30\pi^4}+\dfrac{1}{3\pi}-\dfrac{11}{90}\]
#Series #Sum #InfiniteSum #LemniscateConstant #GammaFunction #Lemniscate #LemniscateOfBernoulli #Bernoulli #Math #Maths #InfiniteSeries #HyperbolicSines
Thomas Maria Helzle"Lemniscating"
Another math-meditation, this time over lemniscate spirals, bells and an ambient sound...
Inspired by @fractalkitty 🙂
In my series of Tooll3 point generators, today I created first a lemniscate, but then extended it to be able to create lemnispirals by varying the radius over time.
#Tooll3 #realtime #particles #livingpainting #creativecoding #hlsl #gpu #shader #generative #procedural #mastoart #audioreactive #sounddesign #math #lemniscate #opensource
An interesting infinite product!
\[\displaystyle\prod_{n=1}^\infty\coth^{(-1)^n}\left(\dfrac{\pi n}{2}\right)=\dfrac{\sqrt\pi}{\sqrt[4]2\sqrt{\varpi}}\]
where \(\varpi=2.62205755\ldots\) is the lemniscate constant (the ratio of the perimeter of Bernoulli's lemniscate to its diameter, analogous to the definition of \(\pi\) for the circle). Both \(\varpi\) and \(\pi\) are proven to be transcendental.
#lemniscate #lemniscateconstant #product #infiniteproduct #HyperbolicFunction #HyperbolicCotangent #Function #pi #maths #math
Fractal KittyMathober Day 31 - Unity (Last day!!! - posted early)
from gas to solid
and back again to the stars
you are – lemniscate
#mathober2022 #mathart #haiku
#math #lemniscate #unity #mindfulness #poetry
caterpillarInfinity dragon...XD
https://www.thingiverse.com/thing:5152665
