Lagrange's identity is a mathematical formula that relates the sums of squares of two sets of variables. It is often stated in the context of inner product spaces or in terms of quadratic forms.
Pendon Museum by Ciro Santilli 40 Updated 2025-07-16
Video 2.
The History of Pendon Museum by World of Railways (2012)
Source. The founder was Australian. His family was wealthy, and he liked cycled around the Vale.
The Nexon Computer Museum is a museum located in Seongnam, South Korea, dedicated to the history and culture of computers and gaming. Opened in 2018, it is a part of Nexon, a well-known video game company, and aims to preserve and showcase the evolution of computer technology and gaming from the 20th century to the present day.
Oxford by Ciro Santilli 40 Updated 2025-07-16
The city clearly exists because it is in the confluence of the river Thames and the River Cherwell. In such confluences, terrain tends to be flat, and fords are also common, with crossings wide and shallow, and so it was an important crossing place.
Notably, the River Cherwell is a natural link between London and the North towards Coventry, and then Birmingham, as it, and then the Thames in which it goes into, puncture through both the Chilterns, then North Essex Downs and the Cotswolds hills. The M40.
Brexit by Ciro Santilli 40 Updated 2025-07-16
There are valid reasons to be pro-Brexit, given the uselessness of the European Union.
The problem was how the campaign was conducted, in a purely nationalistic, populist and fake news manner, and largely supported by business leaders who immediately after still wanted to hire cheap foreign labour, use tax havens and move headquarters to other countries, e.g.:
Cirocoin by Ciro Santilli 40 Updated 2025-07-16
Good pious Cirists earn Cirocoins.
Cirocoins are the most valuable form of currency that exists at any point.
Cirocoins can only be issued by Ciro Santilli.
Cirocoins are strictly nominal, and cannot be traded by recipients with anyone but Ciro, i.e. they are extremely illiquid.
Cirocoins can be removed from recipients at any point if they commit non-Cirist acts.
It is not possible to give a precise number to how many Cirocoins anyone owns. This is decided on a transaction by transaction basis. Ciro can therefore only inform you if your Cirocoin balance increased or decreased, but any attached number has no value, and thus are equivalent to expressions of type "you gained/lost a Cirocoin".
The following inferior currencies come to mind:
The Poincaré–Bendixson theorem is a fundamental result in the field of dynamical systems, particularly concerning the behavior of continuous dynamical systems in two dimensions. It addresses the long-term behavior of trajectories in a planar (2-dimensional) system described by a set of ordinary differential equations.
In simple terms, if you believe in the Schrödinger equation and its modern probabilistic interpretation as described in the Schrödinger picture, then at first it seem that there is no strict causality to the outcome of experiments.
People have then tried to recover that by assuming that there is some inner sate beyond the Schrödinger equation, but these ideas are refuted by Bell test experiments, unless we give up the principle of locality, which feels more important, especially in special relativity, where faster-than-light implies time travel, which breaks causality even more dramatically.
The de Broglie-Bohm theory is a deterministic but non-local formulation of quantum mechanics.

Pinned article: 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 2.
    You can publish local OurBigBook lightweight markup files to either https://OurBigBook.com or as a static website
    .
    Figure 3.
    Visual Studio Code extension installation
    .
    Figure 4.
    Visual Studio Code extension tree navigation
    .
    Figure 5.
    Web editor
    . 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.
    Video 4.
    OurBigBook Visual Studio Code extension editing and navigation demo
    . Source.
  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