Ciro Santilli @cirosantilli  40

Can be calculated efficiently with the Extended Euclidean algorithm.

The beauty of this algorithm is that because exponentiation grows really fast, there is no hope that we can ever learn all the digits of an exponential, as there is simply not enough time or memory for that. Therefore, a natural sub-question is if we can know some part of that number, and knowing the smallest digits is the most natural version of that question.

Microscope by Antonie van Leeuwenhoek used to first observe microorganisms.

All of them need a vacuum because you can't shoot elecrons through air, as mentioned at Video "50,000,000x Magnification by AlphaPhoenix (2022)".

One of its main applications is to determine the 3D structure of proteins.

Sometimes you are not able to crystallize the proteins however, and the method cannot be used.

Crystallizing is not simple because:

Cryogenic electron microscopy can sometimes determine the structures of proteins that failed crystallization.

To break the meta means to find a new strategy that offers a significant advantage over the existing meta.

For the specific of video game glitch breaks see: Section "Meta breaking glitch".

Due to Ciro Santilli's self perceived creative personality, Ciro Santilli is very attracted to meta breaks.

It is true that one image is worth a thousand words, but unfortunately it is also true that one image takes up at least as much bytes as a thousand words!

Having one single page to rule them all is of course the ideal setup for a website, as you can Ctrl + F one ToC and quickly find what you want.

And, with Linux Kernel Module Cheat Ciro noticed that it is very hard to write so much intelligent prose that becomes larger than reasonable to load on a single webpage.

He then started using this technique for everything he writes, including this page and Chinese government.

However, if there are too many images on the page, the loading of the last images would take forever in case users want to view the last sections.

There are two solutions to that:

Ciro is still deciding between those two. The traditional approach works for sure but loses the one page to rule them all benefits.

The innovative approach will work for interactive viewing, but archive.org will fail to load the images for example, and there may be other unforseen consequences.

Wikimedia Commons is awesome and automatically converts and serves smaller versions of images, so always choose the smallest images size needed by the output document. Readers can then find the higher resolution versions by following the page source.

This also comes to mind: motherfuckingwebsite.com

zettelkasten.de/posts/overview/ from zettelkasten:

Since images are large, they bring the following challenges:

To solve those problems, the following alternatives appear to be stable enough and should be used decreasing preference:

The following alternatives seem impossible because Ciro could not find if they expose direct links to the images:

The following do have direct links:

For videos, YouTube does not allow download, even of Creative Commons videos so uploading only there is not acceptable as it prevents reuse:

Amazing graphs and formulas.

Python graphics engine open sourced at: github.com/3b1b/manim "Animation engine for explanatory math videos". But for some reason there is a community fork: github.com/ManimCommunity/manim/ "This repository is maintained by the Manim Community, and is not associated with Grant Sanderson or 3Blue1Brown in any way (though we are definitely indebted to him for providing his work to the world). If you want to study how Grant makes his videos, head over to his repository (3b1b/manim). This is a more frequently updated repository than that one, and is recommended if you want to use Manim for your own projects." what a mess.

He got so old from 2012 to 2021 :-)

This dude did well. If only he had written a hyperlinked wiki rather than making videos! It would allow people to jump in at any point and just click back. It would be Godlike.

mathdoctorbob.org/About.html says:

Website: www.theoremoftheday.org/

It is not a practical fighting style. But it is an awesome game/exercise.

"Dojo" is the japanese version of the word that unfortunately came to dominate in the West, the original is of course Chinese Dao4 chang3 (道場) which means:

This is the part of the formalization of mathematics that deals only with the propositions.

In some systems, e.g. including Metamath, modus ponens alone tends to be enough, everything else can be defined based on it.