The Lost Art of Logarithms

https://www.lostartoflogarithms.com/ – Fantástica iniciativa con una cantidad ingente de información sobre los logaritmos

A work in progress, but I'm keeping an eye on this.

"An online book-in-progress by Charles Petzold wherein is explored the utility, history, and ubiquity of that marvelous invention, logarithms including what the hell they are; with some demonstrations of their primary historical application in plane and spherical trigonometry."

https://www.lostartoflogarithms.com/

The Lost Art of Logarithms

https://www.lostartoflogarithms.com/

Euler–Mascheroni constant!

In fact, the last one is:
$${\displaystyle {\int }_1^{+\mathrm{\infty }}\mathrm{d}x(\frac{1}{\lfloor x\rfloor }-\frac{1}{x})=\gamma \approx 0.5772156649}$$

Equivalently,
$${\displaystyle \underset{n\to \mathrm{\infty }}{lim}(\sum _{k=1}^n\frac{1}{k}-\ln n)=\gamma =0.5772156649\dots }$$
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Unsolved problem in mathematics:
Is Euler–Mascheroni constant irrational? If so, is it transcendental?

#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.

https://knowledgezone.co.in/news

An excellent general result.

If $\mathrm{\Re }(s)>1$,
$${\displaystyle {\int }_0^{\mathrm{\infty }}\frac{\ln x}{x^s+1}\mathrm{d}x=\frac{{\pi }^2}{4s^2}[{\sec }^2\left(\frac{\pi }{2s}\right)-{\csc }^2\left(\frac{\pi }{2s}\right)]}$$

Special cases:
$${\displaystyle {\int }_0^{\mathrm{\infty }}\frac{\ln x}{x^2+1}\mathrm{d}x=0}$$
$${\displaystyle {\int }_0^{\mathrm{\infty }}\frac{\ln x}{x^3+1}\mathrm{d}x=-\frac{2{\pi }^2}{27}}$$
$${\displaystyle {\int }_0^{\mathrm{\infty }}\frac{\ln x}{x^4+1}\mathrm{d}x=-\frac{{\pi }^2}{8\sqrt{2}}}$$
$${\displaystyle {\int }_0^{\mathrm{\infty }}\frac{\ln x}{x^5+1}\mathrm{d}x=-\frac{4{\pi }^2}{25}\left(\frac{2+\sqrt{5}}{5+\sqrt{5}}\right)=-\frac{(5+3\sqrt{5}){\pi }^2}{125}}$$

“How Does A Computer/Calculator Compute Logarithms?”, Zach Artrand (https://zachartrand.github.io/SoME-3-Living/).

Via HN: https://news.ycombinator.com/item?id=40749670 (which provides important addenda)

Joost Bürgi and Logarithms - Logarithms are a common idea today, even though we don’t use them as often as we u... - https://hackaday.com/2024/02/27/joost-burgi-and-logarithms/ #retrocomputing #logarithms #sliderule

I had a lot of fun putting this new auction activity together: Evaluating Logarithms Auction.

https://mathequalslove.net/evaluating-logarithms-auction-activity/

#Logarithms explained #BobRoss style

https://www.youtube.com/watch?v=up21mvokyQ4&ab_channel=Tibees

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

Count Leading Zeros for Efficient Logarithms - [Ihsan Kehribar] points out a clever trick you can use to quickly and efficiently ... - https://hackaday.com/2023/02/07/count-leading-zeros-for-efficient-logarithms/ #softwaredevelopment #digitalaudiohacks #countleadingzeros #algorithms #logarithms #dsp