#logarithms — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #logarithms, aggregated by home.social.
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📸🤯 "This picture broke my brain!" said no one ever after watching a #3B1B video on #logarithms. Because, really, who doesn't crave a deep dive into the thrilling world of image transformations? 🤓🎉 Meanwhile, #Google LLC is busy ensuring that your brain remains blissfully unbroken by updating #YouTube terms and policies that you've definitely read. 📜👍
https://www.youtube.com/watch?v=ldxFjLJ3rVY #imageTransformations #updates #brainBuzz #HackerNews #ngated -
#OnThisDay #SpaceShuttle #Columbia disintegrated during reentry into the Earth's atmosphere (2003) resulting in the deaths of all seven crew members.
Birth Anniversary of Emilio Segrè (1905) - #NobelPrize winner and group leader for the #Manhattan Project. He discovered the elements #Technetium and #Astatine.
Birth Anniversary of John Napier (1550) - best known as the discoverer of #Logarithms.
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The #irony is palpable: a piece on #logarithms that's as accessible as a locked vault in Fort Knox, courtesy of #ModSecurity 😂🔒. This riveting read on mathematical history has been replaced by the stark beauty of a 406 error page—truly a triumph of modern web design! 🚫📉
https://www.lostartoflogarithms.com/ #webdesign #406error #mathhistory #HackerNews #ngated -
Euler–Mascheroni constant! :euler:
In fact, the last one is:
\[\large\displaystyle\int_1^{+\infty}\mathrm dx\ \left(\frac{1}{\lfloor x\rfloor}-\frac1x\right)=\gamma\approx0.5772156649\]Equivalently,
\[\large\displaystyle\lim_{n\to\infty}\left(\sum_{k=1}^n \frac1{k}-\ln n\right)=\gamma=0.5772156649\ldots\]
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Unsolved problem in mathematics:
Is Euler–Mascheroni constant irrational? If so, is it transcendental?#Euler #Mascheroni #EulerMascheroni #Constant #gamma #EulerConstant #EulersConstant #EulerMascheroniConstant #Irrational #Irrationality #Transcendental #Transcendence #Unsolved #UnsolvedProblem #Maths #Mathematics #Indeterminate #IndeterminateForm #IndeterminateForms #Inf #Infinity #HarmonicNumber #HarmonicNumbers #HarmonicSeries #Logarithm #Log #Logarithms #NaturalLogarithm #Integral #ImproperIntegral
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Euler–Mascheroni constant! :euler:
In fact, the last one is:
\[\large\displaystyle\int_1^{+\infty}\mathrm dx\ \left(\frac{1}{\lfloor x\rfloor}-\frac1x\right)=\gamma\approx0.5772156649\]Equivalently,
\[\large\displaystyle\lim_{n\to\infty}\left(\sum_{k=1}^n \frac1{k}-\ln n\right)=\gamma=0.5772156649\ldots\]
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Unsolved problem in mathematics:
Is Euler–Mascheroni constant irrational? If so, is it transcendental?#Euler #Mascheroni #EulerMascheroni #Constant #gamma #EulerConstant #EulersConstant #EulerMascheroniConstant #Irrational #Irrationality #Transcendental #Transcendence #Unsolved #UnsolvedProblem #Maths #Mathematics #Indeterminate #IndeterminateForm #IndeterminateForms #Inf #Infinity #HarmonicNumber #HarmonicNumbers #HarmonicSeries #Logarithm #Log #Logarithms #NaturalLogarithm #Integral #ImproperIntegral
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#OnThisDay #SpaceShuttle #Columbia disintegrated during reentry into the Earth's atmosphere (2003) resulting in the deaths of all seven crew members.
Birth Anniversary of Emilio Segrè (1905) - #NobelPrize winner and group leader for the #Manhattan Project. He discovered the elements #Technetium and #Astatine.
Birth Anniversary of John Napier (1550) - best known as the discoverer of #Logarithms.
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An excellent general result.
If \(\Re(s)>1\),
\[\displaystyle\int_0^\infty\frac{\ln x}{x^s+1}~\mathrm dx=\frac{\pi^2}{4s^2}\left[\sec^2\left(\frac{\pi}{2s}\right)-\csc^2\left(\frac{\pi}{2s}\right)\right]\]Special cases:
\[\displaystyle\int_0^\infty\frac{\ln x}{x^2+1}~\mathrm dx=0\]
\[\displaystyle\int_0^\infty\frac{\ln x}{x^3+1}~\mathrm dx=-\frac{2\pi^2}{27}\]
\[\displaystyle\int_0^\infty\frac{\ln x}{x^4+1}~\mathrm dx=-\frac{\pi^2}{8\sqrt2}\]
\[\displaystyle\int_0^\infty\frac{\ln x}{x^5+1}~\mathrm dx=-\frac{4\pi^2}{25}\left(\frac{2+\sqrt5}{5+\sqrt5}\right)=-\frac{(5+3\sqrt5)\pi^2}{125}\]#Integral #Integrals #GeneralResult #GeneralResults #Result #Results #Logarithms #Logarithm #Integration #DefiniteIntegral #Calculus #IntegralCalculus
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#OnThisDay #SpaceShuttle #Columbia disintegrated during reentry into the Earth's atmosphere (2003) resulting in the deaths of all seven crew members.
Birth Anniversary of Emilio Segrè (1905) - #NobelPrize winner and group leader for the #Manhattan Project. He discovered the elements #Technetium and #Astatine.
Birth Anniversary of John Napier (1550) - best known as the discoverer of #Logarithms.
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#Gravitational waves from giant #BlackHole collision reveal long-sought ‘ringing’ : Nature
Don’t Fall for Big Oil’s #CarbonCapture #Deceptions : Sci Am
The True Nature of #Logarithms : Medium
Check our latest #KnowledgeLinks
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Here are a few #horsetail plants, seen on my walk #today (yesterday, actually).
Plus a wandering "woolly bear" (#TigerMoth) #caterpillar.
Horsetails are 150 million-year-old living fossils that were eaten by - yes! - Jurassic #dinosaurs.
Also, their unique node spacing inspired #JohnNapier in 1614 to invent #logarithms.
Admittedly, some rude US jurisdictions (wtf Oregon...?) classify them as noxious weeds.
But imho this is an amazing plant with a wonderful résumé 💚
