New articles - OurBigBook.com

2020-11: kitchen extractor left lamp burnt again. Did I forget to report a right side burn earlier, or is there something wrong with the left one? Also can't find the second bulb that was likely bought last time, so likely the right one burnt and the other bulb was used for it. Buying www.amazon.co.uk/dp/B00LOBUDSS "4 x Eveready 20 W 12 V G4 Dimmable Halogen Capsule Light Bulbs Pack of 4" for 3.66 pounds. Worked, felt a bit more yellow than the previous one. Packet documents 2000 hours, 2800K color, 8000+ switches.

2020-08: kitchen right back had been out for a while, bought: www.amazon.co.uk/dp/B00LN0RPA4 LE GU10 LED Bulbs, Warm White 2700K, 50W Halogen Lamp Equivalent, 4W 350lm, 120° Wide Beam Angle, Recessed or Track Light Bulb, Pack of 5 (Energy Class A++), 5 for 10 pounds.

2019-11: front right kitchen lamp burnt, Sylvania GU10 50W. 50W was likely some useless "incandescent equivalent" measure. Replaced: GE LED 5W 345 lumens 2700K Warm 15k hours, which looks exactly the same.

2019-05: kitchen extractor left lamp burnt. Was: DURA G4 12V20W: www.amazon.co.uk/Halogen-Light-Bulbs-Lamps-5watt/dp/B003IVP12A Replaced: Sainsbury's halogen G4 20W12V.

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k-transitive group by

Ciro Santilli 37 Updated 2025-07-16

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TODO why do we care about this?

Note that if a group is k-transitive, then it is also k-1-transitive.

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Nazi Germany by

Ciro Santilli 37 Updated 2025-07-16

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History of the Netherlands by

Ciro Santilli 37 Updated 2025-07-16

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Point at infinity by

Ciro Santilli 37 Updated 2025-07-16

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Mathieu group

M_{12}

Ciro Santilli 37 Updated 2025-07-16

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Hypercube by

Ciro Santilli 37 Updated 2025-07-16

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square, cube. 4D case known as tesseract.

Convex hull of all

{- 1, 1}^{D}

(Cartesian product power) D-tuples, e.g. in 3D:

( 1,  1,  1)
( 1,  1, -1)
( 1, -1,  1)
( 1, -1, -1)
(-1,  1,  1)
(-1,  1, -1)
(-1, -1,  1)
(-1, -1, -1)

From this we see that there are

2^{D}

vertices.

Two vertices are linked iff they differ by a single number. So each vertex has D neighbors.

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Archaea are more cosely related to the eukaryotes than bacteria by

Ciro Santilli 37 Updated 2025-07-16

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 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!

Video 1.

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-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.
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 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 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.
Internal cross file references done right:
Infinitely deep tables of contents:
Figure 6.
Dynamic article tree with infinitely deep table of contents
.
Live URL: ourbigbook.com/cirosantilli/chordate
Descendant pages can also show up as toplevel e.g.: ourbigbook.com/cirosantilli/chordate-subclade