Fraction by Ciro Santilli 35 Updated +Created
Fourier transform by Ciro Santilli 35 Updated +Created
Continuous version of the Fourier series.
Of course, every function defined on a finite line segment (i.e. a compact space).
Therefore, the Fourier transform can be seen as a generalization of the Fourier series that can also decompose functions defined on the entire real line.
As a more concrete example, just like the Fourier series is how you solve the heat equation on a line segment with Dirichlet boundary conditions as shown at: Section "Solving partial differential equations with the Fourier series", the Fourier transform is what you need to solve the problem when the domain is the entire real line.
Complex conjugate by Ciro Santilli 35 Updated +Created
Asset bundler by Ciro Santilli 35 Updated +Created
In order to make websites efficient and portable, a lot of transpilation is needed.
Commutative ring by Ciro Santilli 35 Updated +Created
Two ways to see it:
Four Great Classic Novels by Ciro Santilli 35 Updated +Created
In Chinese lit. just "Four Great Masterpieces".
Code drop by Ciro Santilli 35 Updated +Created
Open source development model in which developers develop in private, and only release code to the public during releases.
Notable example project: Android Open Source Project.
This development model basically makes reporting bugs and sending patches a waste of time, because many of them will already have been solved, which is why this development model is evil.
Four-gradient by Ciro Santilli 35 Updated +Created
A 4D gradient with some small special relativity specifics added in (the light of speed and sign change for the time).
Four Beauties by Ciro Santilli 35 Updated +Created
Figure 1.
A modern rendition of the four beauties
. Source. TODO we need a decent older one with CC BY-SA, and illustrating their attributes! Wikimedia failed me.
Cloud chamber by Ciro Santilli 35 Updated +Created
English (language) by Ciro Santilli 35 Updated +Created
Protein folding problem by Ciro Santilli 35 Updated +Created
Formal proof is useless by Ciro Santilli 35 Updated +Created
The only cases where formal proof of theorems seem to have had actual mathematical value is for theorems that require checking a very large number of case, so much so that no human can be fully certain that no mistakes were made. Some examples:
Formal language by Ciro Santilli 35 Updated +Created
for loop by Ciro Santilli 35 Updated +Created
The for loop is a subcase of the while loop.
One theoretical motivation for its existence is that it has the fundamental property that we are immediately certain it will terminate, unlike while loops with arbitrary conditions.
Primitive recursive functions are the complexity class that divides those two.
Food without photosynthesis by Ciro Santilli 35 Updated +Created
This is the future of course, fusion power to generate electricity, and then converting electricity into food somehow.
Hopefully without going through photosynthesis, which feels complicated and wasteful.

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