Topics (122k) Articles (123k) Users (292) Discussions (237) Comments (383) Files (715) New article
A field can be seen as an Abelian group that has two group operations defined on it: addition and multiplication.
And then, besides each of the two operations obeying the group axioms individually, and they are compatible between themselves according to the distributive property.
Examples:
It is just mind blowing that Christians, Muslims and Jews can have so many conflicts considering that their religions are basically the same. Uncanny valley comes to mind. See also remarks at: cirosantilli.com/china-dictatorship/zhong-gong
The transfiguration of Jesus is a notable example where Jesus/the Church tries to divert older religions into him. And then Muhammad does the same during isra and Mi'raj, and meets up with Jesus, John the Baptist and Abraham. The Kaaba was also clearly an earlier place of worship of local religions before Muhammad. But of course, Abraham was one of the builders of the Kaaba, so all good.
Ciro Santilli does not believe in free will of course because he is an agnostic and he believes that brains are controlled by the laws of physics, see also: physics and the illusion of life.
The 3D regular convex polyhedrons are super famous, have the name: Platonic solid, and have been known since antiquity. In particular, there are only 5 of them.
The counts per dimension are:
The cool thing is that the 3 that exist in 5+ dimensions are all of one of the three families:Then, the 2 3D missing ones have 4D analogues and the sixth one in 4D does not have a 3D analogue: the 24-cell. Yes, this is the kind of irregular stuff Ciro Santilli lives for.
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!
Intro to OurBigBook
. Source. We have two killer features:
- 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-calculusArticles 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/derivativeVideo 2. OurBigBook Web topics demo. Source. - 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.
- 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
Figure 2. You can publish local OurBigBook lightweight markup files to either OurBigBook.com or as a static website.
Figure 3. Visual Studio Code extension installation.
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. 
- Infinitely deep tables of contents:
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