PSL(2,7) by Ciro Santilli 35 Updated +Created
The second smallest non-Abelian finite simple group after the alternating group of degree 5.
Representation of the Lorentz group by Ciro Santilli 35 Updated +Created
One of the representations of the Lorentz group that show up in the Representation theory of the Lorentz group.
Following the definition of the indefinite orthogonal group, we want to show that only the metric signature matters.
First we can observe that the exact matrices are different. For example, taking the standard matrix of :
and:
both have the same metric signature. However, we notice that a rotation of 90 degrees, which preserves the first form, does not preserve the second one! E.g. consider the vector , then . But after a rotation of 90 degrees, it becomes , and now ! Therefore, we have to search for an isomorphism between the two sets of matrices.
For example, consider the orthogonal group, which can be defined as shown at the orthogonal group is the group of all matrices that preserve the dot product can be defined as:
Annie Dookhan by Ciro Santilli 35 Updated +Created
One is reminded of Nick Leeson.
Number theory by Ciro Santilli 35 Updated +Created
Modulo operation by Ciro Santilli 35 Updated +Created
Mishima: A Life in Four Chapters by Ciro Santilli 35 Updated +Created
Ciro can relate strongly to the level of passion depicted in this film: Section "Don't be a pussy". It almost feels like a business film in that a sense, where the startup is the authors career and passions.
Film about genius by Ciro Santilli 35 Updated +Created
Least common multiple by Ciro Santilli 35 Updated +Created
Floating-point number by Ciro Santilli 35 Updated +Created
Sine and cossine by Ciro Santilli 35 Updated +Created
Series (mathematics) by Ciro Santilli 35 Updated +Created
Train by Ciro Santilli 35 Updated +Created
Video 1.
The failure of the California's high-speed by Vox (2022)
Source.
Basically:
  • too much local power
  • republican/democrat partition means federal projects start in one government, get killed on next
One is reminded of the Superconducting Super Collider on the federal level issues.
youtu.be/rcjr4jbGuJg?t=457 though mentions that the Palmdale detour was mainly to avoid some hills.
Self-driving car company by Ciro Santilli 35 Updated +Created
Self-driving car by Ciro Santilli 35 Updated +Created
Partial differential equation solver by Ciro Santilli 35 Updated +Created
Bicycle tire sizes by Ciro Santilli 35 Updated +Created
Yes, Sheldon he has separate American and British English versions of pages!!!
For example, Kross bicycle (2017) had a Schwalbe tyre with markings:
42-622 (28 x 1.60, 700x40C)
When inflated, the tires were about 3.5cm wide as measured with a ruler.
And the Mavic A319 rim had markings:
622x19C
In this:
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!
Video 1.
Intro to OurBigBook
. Source.
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
    Video 2.
    OurBigBook Web topics demo
    . Source.
  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:
    • to OurBigBook.com to get awesome multi-user features like topics and likes
    • as HTML files to a static website, which you can host yourself for free on many external providers like GitHub Pages, and remain in full control
    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.
    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