Solving quadratic equations using continued fractions is a method linked to the approximation of the solutions of these equations through the use of continued fractions. Quadratic equations typically take the form: \[ ax^2 + bx + c = 0 \] where \(a\), \(b\), and \(c\) are coefficients, and \(x\) is the variable we want to solve for.
A relation \( R \) on a set is called a transitive relation if, for all elements \( a, b, c \) in that set, whenever \( a \) is related to \( b \) (denoted \( aRb \)) and \( b \) is related to \( c \) (denoted \( bRc \)), then \( a \) must also be related to \( c \) (denoted \( aRc \)).
List of tropes by Ciro Santilli 37 Updated +Created
Most of them use titles from TV Tropes.
Little-o notation by Ciro Santilli 37 Updated +Created
Stronger version of the big O notation, basically means that ratio goes to zero. In big O notation, the ratio does not need to go to zero.
So in informal terms, big O notation means , and little-o notation means .
E.g.:
  • K does not tend to zero
Validation data set by Ciro Santilli 37 Updated +Created
LLVM IR hello world by Ciro Santilli 37 Updated +Created
Example: llvm/hello.ll adapted from: llvm.org/docs/LangRef.html#module-structure but without double newline.
To execute it as mentioned at github.com/dfellis/llvm-hello-world we can either use their crazy assembly interpreter, tested on Ubuntu 22.10:
sudo apt install llvm-runtime
lli hello.ll
This seems to use puts from the C standard library.
Or we can Lower it to assembly of the local machine:
sudo apt install llvm
llc hello.ll
which produces:
hello.s
and then we can assemble link and run with gcc:
gcc -o hello.out hello.s -no-pie
./hello.out
or with clang:
clang -o hello.out hello.s -no-pie
./hello.out
hello.s uses the GNU GAS format, which clang is highly compatible with, so both should work in general.
LMMS by Ciro Santilli 37 Updated +Created
Very easy to use and pretty powerful MIDI creator!!!
One of the rare audio applications actually works with PulseAudio on Ubuntu 20.04 out-of-the-box, so you don't have to turn off every other audio application!!!
Has lot's of plugins built-in just working out of the box, e.g. ZynAddSubFX out-of-the-box without doing a gazillion complex setup connections.
Most plugins are just simple toys however, ZynAddSubFX is the only super powerful one. The others are more LMMS integrate however, and seem to use a more dedicated LMMS GUI style.
If you open vmpk, you can then right click on a piano track, and go MIDI, Input and it just shows up there, and it does produce sound as shown at: www.youtube.com/watch?v=NpeP2th08ak
TODO: what about recording the input MIDI? Yes, there is a record button on the piano roll!
Local group by Ciro Santilli 37 Updated +Created
The basically composed of only the Andromeda Galaxy and the Milky Way. Every other galaxy is a satellite of those two.
Logarithm of a matrix by Ciro Santilli 37 Updated +Created
Logic synthesis by Ciro Santilli 37 Updated +Created
The output of this step is another Verilog file, but one that exclusively uses interlinked cell library components.
London by Ciro Santilli 37 Updated +Created
Video 1.
Yung Professional Move to London by Sans Beanstalk
. Source.
The sad thing is that the same author also has another accurate video criticizing British suburbia, so there's no escape basically in the UK: www.youtube.com/watch?v=oIJuZbXLZeY.
Video 2.
Werk by Sans Beanstalk
. Source.
Training (ML) by Ciro Santilli 37 Updated +Created
Looking Glass Universe by Ciro Santilli 37 Updated +Created
Cute simple paper-cut stop motion animations videos by Mithuna Yoganathan, a PhD in theoretical physics at the University of Cambridge: www.damtp.cam.ac.uk/person/my332.
This has the seeds of direct good intuition, but often stops a bit too short. Worth a look though, there is value in them for beginners.
Loop-mediated isothermal amplification by Ciro Santilli 37 Updated +Created
Like PCR, but does not require thermal cycling. Thus the "isothermal" in the name: iso means same, so "same temperature".
Not needing the thermo cycling means that the equipment needed is much smaller and cheaper it seems.
Video 1.
Loop Mediated Isothermal Amplification (LAMP) Tutorial by New England Biolabs (2015)
Source. Explains the basic LAMP concept well.
Lorentz invariant by Ciro Santilli 37 Updated +Created
Lorentz transform consequence: everyone sees the same speed of light by Ciro Santilli 37 Updated +Created
OK, so let's verify the main desired consequence of the Lorentz transformation: that everyone observes the same speed of light.
Observers will measure the speed of light by calculating how long it takes the light going towards cross a rod of length laid in the x axis at position .
Each observer will observe two events:
  • : the light touches the left side of the rod
  • : the light touches the right side of the rod
Supposing that the standing observer measures the speed of light as and that light hits the left side of the rod at time , then he observes the coordinates:
Now, if we transform for the moving observer:
and so the moving observer measures the speed of light as:
Los Alamos National Laboratory by Ciro Santilli 37 Updated +Created
Video 1.
Historic Manhattan Project Sites at Los Alamos by Los Alamos National Lab
. Source.
Historian Alan B. Carr:
Lossless compression by Ciro Santilli 37 Updated +Created

Pinned article: ourbigbook/introduction-to-the-ourbigbook-project

Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
We have two killer features:
  1. topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculus
    Articles of different users are sorted by upvote within each article page. This feature is a bit like:
    • a Wikipedia where each user can have their own version of each article
    • a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
    This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
    Figure 1.
    Screenshot of the "Derivative" topic page
    . View it live at: ourbigbook.com/go/topic/derivative
  2. local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:
    This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
    Figure 5. . You can also edit articles on the Web editor without installing anything locally.
    Video 3.
    Edit locally and publish demo
    . Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension.
  3. https://raw.githubusercontent.com/ourbigbook/ourbigbook-media/master/feature/x/hilbert-space-arrow.png
  4. Infinitely deep tables of contents:
    Figure 6.
    Dynamic article tree with infinitely deep table of contents
    .
    Descendant pages can also show up as toplevel e.g.: ourbigbook.com/cirosantilli/chordate-subclade
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact